This document discusses the effect of mass and partial slip on boundary layer flow of a nanofluid over a porous plate embedded in a porous medium. The governing equations for momentum, energy, and nanoparticle concentration are presented. Similarity transformations are applied to reduce the governing partial differential equations to a system of ordinary differential equations. The equations are then solved numerically using the fourth-order Runge-Kutta method. Results for shear stress, temperature distribution, nanoparticle volume fraction, skin friction coefficient, Nusselt number, and Sherwood number are obtained to illustrate the effects of various parameters including mass slip, partial slip, permeability, thermophoresis, and Brownian motion.
1) The document describes a study of the flow of electrically conducting, chemically reacting and radiating viscoelastic fluid through a porous medium in a vertical porous channel with constant suction.
2) Governing equations for the flow velocity, temperature and concentration profiles are derived based on assumptions like uniform magnetic field, Boussinesq approximation, and negligible induced magnetic field.
3) Closed form solutions for the governing equations are obtained subject to boundary conditions of no slip at the channel walls and oscillating temperature and concentration profiles.
Effects Of Higher Order Chemical Reactions and Slip Boundary Conditions on Na...IJERA Editor
Β
We investigate the effects of higher order chemical reactions on coupled heat and mass transfer from a permeable stretching sheet in nanofluid flow with slip boundary conditions. Nanofluids play an important role in emerging nanotechnology and biotechnology industries where they find application in heat transfer processes. We study the effects of the order of the chemical reaction and chemical reaction parameter. The highly nonlinear and coupled governing differential equations were solved numerically. The solution depends on Brownian motion number, thermophoresis number, thermal convective parameter, mass convective parameter and double diffusive buoyancy parameter. The effects of various engineering parameters are investigated.
This document summarizes a research article that investigates the steady, two-dimensional Falkner-Skan boundary layer flow over a stationary wedge with momentum and thermal slip boundary conditions. The flow considers a temperature-dependent thermal conductivity in the presence of a porous medium and viscous dissipation. Governing partial differential equations are non-dimensionalized and transformed into ordinary differential equations using similarity transformations. The equations are highly nonlinear and cannot be solved analytically, so a numerical solver is used. Numerical results are presented for the skin friction coefficient, local Nusselt number, velocity and temperature profiles for varying parameters like the Falkner-Skan parameter and Eckert number.
Effects Of Heat Source And Thermal Diffusion On An Unsteady Free Convection F...IOSR Journals
Β
This document presents a mathematical analysis of unsteady free convection flow along a porous vertical plate with constant heat and mass flux in a rotating system. The analysis considers the effects of heat source and thermal diffusion. Perturbation technique is used to obtain expressions for velocity, temperature, concentration profiles, skin friction, and Nusselt number. Key findings include that increasing Schmidt number decreases skin friction, increasing Grashoff number increases skin friction, and increasing Prandtl number decreases Nusselt number. Graphs and tables are used to discuss the effects of various parameters on flow variables.
Effect of Rotation on a Layer of Micro-Polar Ferromagnetic Dusty Fluid Heated...IJERA Editor
Β
This paper deals with the theoretical investigation of effect of rotation on micro-polar ferromagnetic dusty fluid
layer heated from below in a porous medium. Linear stability analysis and normal mode analysis methods are
used to find an exact solution for a flat micro-polar ferromagnetic fluid layer contained between two free
boundaries . In case of stationary convection, the effect of various parameters like medium permeability
parameter, non-buoyancy magnetization parameter, micro-polar coupling parameter, spin-diffusion parameter,
micro-polar heat conduction parameter, dust particles parameter and rotation parameter has been analyzed and
results are depicted graphically. In the absence of dust particles, rotation, micro-viscous effect and micro-inertia,
the sufficient condition is obtained for non-oscillatory modes
Prediction of just suspended speed for mixed slurries atfabiola_9
Β
This document describes two new models for predicting the just suspended speed (Njs) for mixtures of solids in stirred tanks: the power model and the momentum model. The power model predicts the mixture Njs based on the sum of the power required to suspend each individual solid phase. The momentum model predicts the mixture Njs based on the sum of the momentum required to suspend each individual solid phase. Both models were developed because the current design heuristic, which assumes the mixture Njs is the maximum Njs of the individual phases, does not adequately capture the effects of particle interactions in mixtures. The models were tested using experimental data for mixtures of various solids up to 27% solids loading in a stirred tank.
Thermal instability of incompressible non newtonian viscoelastic fluid with...eSAT Publishing House
Β
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
1) The document describes a study of the flow of electrically conducting, chemically reacting and radiating viscoelastic fluid through a porous medium in a vertical porous channel with constant suction.
2) Governing equations for the flow velocity, temperature and concentration profiles are derived based on assumptions like uniform magnetic field, Boussinesq approximation, and negligible induced magnetic field.
3) Closed form solutions for the governing equations are obtained subject to boundary conditions of no slip at the channel walls and oscillating temperature and concentration profiles.
Effects Of Higher Order Chemical Reactions and Slip Boundary Conditions on Na...IJERA Editor
Β
We investigate the effects of higher order chemical reactions on coupled heat and mass transfer from a permeable stretching sheet in nanofluid flow with slip boundary conditions. Nanofluids play an important role in emerging nanotechnology and biotechnology industries where they find application in heat transfer processes. We study the effects of the order of the chemical reaction and chemical reaction parameter. The highly nonlinear and coupled governing differential equations were solved numerically. The solution depends on Brownian motion number, thermophoresis number, thermal convective parameter, mass convective parameter and double diffusive buoyancy parameter. The effects of various engineering parameters are investigated.
This document summarizes a research article that investigates the steady, two-dimensional Falkner-Skan boundary layer flow over a stationary wedge with momentum and thermal slip boundary conditions. The flow considers a temperature-dependent thermal conductivity in the presence of a porous medium and viscous dissipation. Governing partial differential equations are non-dimensionalized and transformed into ordinary differential equations using similarity transformations. The equations are highly nonlinear and cannot be solved analytically, so a numerical solver is used. Numerical results are presented for the skin friction coefficient, local Nusselt number, velocity and temperature profiles for varying parameters like the Falkner-Skan parameter and Eckert number.
Effects Of Heat Source And Thermal Diffusion On An Unsteady Free Convection F...IOSR Journals
Β
This document presents a mathematical analysis of unsteady free convection flow along a porous vertical plate with constant heat and mass flux in a rotating system. The analysis considers the effects of heat source and thermal diffusion. Perturbation technique is used to obtain expressions for velocity, temperature, concentration profiles, skin friction, and Nusselt number. Key findings include that increasing Schmidt number decreases skin friction, increasing Grashoff number increases skin friction, and increasing Prandtl number decreases Nusselt number. Graphs and tables are used to discuss the effects of various parameters on flow variables.
Effect of Rotation on a Layer of Micro-Polar Ferromagnetic Dusty Fluid Heated...IJERA Editor
Β
This paper deals with the theoretical investigation of effect of rotation on micro-polar ferromagnetic dusty fluid
layer heated from below in a porous medium. Linear stability analysis and normal mode analysis methods are
used to find an exact solution for a flat micro-polar ferromagnetic fluid layer contained between two free
boundaries . In case of stationary convection, the effect of various parameters like medium permeability
parameter, non-buoyancy magnetization parameter, micro-polar coupling parameter, spin-diffusion parameter,
micro-polar heat conduction parameter, dust particles parameter and rotation parameter has been analyzed and
results are depicted graphically. In the absence of dust particles, rotation, micro-viscous effect and micro-inertia,
the sufficient condition is obtained for non-oscillatory modes
Prediction of just suspended speed for mixed slurries atfabiola_9
Β
This document describes two new models for predicting the just suspended speed (Njs) for mixtures of solids in stirred tanks: the power model and the momentum model. The power model predicts the mixture Njs based on the sum of the power required to suspend each individual solid phase. The momentum model predicts the mixture Njs based on the sum of the momentum required to suspend each individual solid phase. Both models were developed because the current design heuristic, which assumes the mixture Njs is the maximum Njs of the individual phases, does not adequately capture the effects of particle interactions in mixtures. The models were tested using experimental data for mixtures of various solids up to 27% solids loading in a stirred tank.
Thermal instability of incompressible non newtonian viscoelastic fluid with...eSAT Publishing House
Β
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Physical Characterization of a Method for Production of High Stability Suspen...Editor IJCATR
Β
Suspensions/Dispersions are encountered in a wide range of
applications, e.g., liquid abrasive cleaners, ceramics, medicines,
inks, paintsβ¦.etc. In most cases it is necessary to keep the
suspension stable for the product lifetime. A new modified
differential sedimentation measuring system is suggested and used
to identify physical parameters affecting the sedimentation in
suspensions. The technique is discussed in details. It is found that
particle sizes as well as viscosity of continuous phase are the most
important factors governing the stability of a suspension. Empirical
relations are extracted to quantitatively describe the weight effect of
each factor. The modified measuring system shows good accuracy
enough to detect fluctuations in concentration of suspended
particles due to their Brownian diffusion, as well as the particles
concentrations in the stable suspension. This study confirmed the
fact that particles diameters measured by Zetasizer are much
greater than those measured by the transmission electron
microscope. This study presents a proposal for new technique for
particle size separation based on the differential sedimentation in
viscose fluids. This new method is a differential viscosity column.
The proposed size separation technique may help to separate
engineered nano-particles with higher resolution
The present study analyzes the steady boundary layer slip flow of magneto-nanofluid due to an exponentially permeable stretching sheet with heat generation/absorption. In this paper, the effects of Brownian motion and thermophoresis on heat transfer and nanoparticle volume friction are considered. Using shooting technique along with fourth-order Runge-Kutta method the transformed equations are solved. The study reveals that the governing parameters, namely, the magnetic parameter, wall mass suction parameter, Prandtl number, the Lewis number, slip parameter, heat generation/absorption parameter, Brownian motion parameter, and thermophoresis parameter, have major effects on the flow field, the heat transfer, and the nanoparticle volume fraction as well as skin friction, local Nusselt number and local Sherwood number has been discussed in detail.
Numerical Model of Microwave Heating in a Saturated Non-Uniform Porosity Medi...drboon
Β
The microwave heating of a porous medium with a non-uniform porosity is numerically investigated, based on the proposed numerical model. A variation of porosity of the medium is considered. The generalized non-Darcian model developed takes into account of the presence of a solid drag and the inertial effect. The transient Maxwellβs equations are solved by using the finite difference time domain (FDTD) method to describe the electromagnetic field in the wave guide and medium. The temperature profile and velocity field within a medium are determined by the solution of the momentum, energy and Maxwellβs equations. The coupled non-linear set of these equations are solved using the SIMPLE algorithm. In this work, a detailed parametric study is conducted for a heat transport inside a rectangular enclosure filled with saturated porous medium of constant or variable porosity. The numerical results agree well with the experimental data. Variations in porosity significantly affect the microwave heating process as well as convective flow pattern.
The role of strain rate in the dynamic response of materialsAI Publications
Β
We start with the response of ductile materials. To understand the response of these materials to fast dynamic loadings, we introduce two approaches to dynamic viscoplasticity. These are the flowstress approach and the overstress approach, and strain rate has different roles with these two approaches. At very high loading rates the flowstress approach implies very high strength, which is hard to explain by microscale considerations, while the overstress approach does not.We then demonstrate the advantage of using the overstress approach by applying the two approaches to the elastic precursor decay problem. Next use the overstress approach to treat the following problems: 1) the 4th power law response in steady flow of ductile materials; 2) high rate stress upturn (HRSU) of ductile materials; and 3) HRSU of brittle materials. With these examples we demonstrate the advantage of using the overstress approach over the flowstress approach. It follows that HRSU means High (strain) Rate Stress Upturn and not High Rate Strength Upturn, as would follow from using the flowstress approach.
Interrelationships between Characteristic Lengths of Local Scour Holedrboon
Β
This paper presents the results of an experimental study on local scour of noncohesive sediments downstream of a horizontal rigid apron. The experiments were carried out in a rectangular flume with 9m length, 0.5m width and 0.6m height which includes an alluvial test reach of 1.65m length and 0.2m depth at the end of the apron. Two types of uniform sediment with median diameters of 0.73mm and 1.85mm were used in the experiments. Time variations of the maximum scour depth was measured for some experiments. It was found that the scour hole does not reach the equilibrium state even after 48 hours. However, after the first 12 hours, the rate of extension of the maximum scour depth is found to be less than 0.001 cm/min. Although the scour profile seems to be three dimensional in nature, it was found that there is a geometrical similarity between the scour holes in all of the experiments. Variations of the characteristic lengths of the scour hole such as the maximum scour depth, dsm, the maximum extension of hole, L0, and the dune height, hd, are related to each other. Nondimensional graphs and formulas are suggested to determine the variation of these parameters in different conditions.
Thermal Instability of Chemically Reacting Maxwell Fluid in a Horizontal Poro...IJERA Editor
Β
The effect of chemical reaction on the linear stability of a viscoelastic fluid saturated horizontal densely-packed
porous layer is investigated. The viscoelastic properties are given by Maxwell constitutive relations. The porous
layer is cooled from the upper boundary while an adiabatic thermal boundary condition is imposed at the lower
boundary. Linear stability analysis suggests that there is a competition between the processes of viscous
relaxation and thermal diffusion that causes the first convective instability to be oscillatory rather than stationary.
The effect of Deborah number, Darcy-Prandtl number, normalized porosity, and the Frank-Kamenetskii number
on the stability of the system is investigated. Using a weighted residual method we calculate numerically the
convective thresholds for both stationary and oscillatory instability. The effects of viscoelasticity and chemical
reaction on the instability are emphasized. Some existing results are reproduced as the particular cases of the
present study.
Dufour and Soret Effects on Convective Heat and Mass Transfer in Non-Darcy Do...IJERA Editor
Β
This paper deals with the MHD convention non-Darcy flow with heat and mass transfer along the vertical surface in a fluid stratified non porous media in the presence of temperature gradients (Soret effects) and concentration gradients (Dufour effects). The differential equations of the governing flow are expand a in terms of perturbation functions as a result we get set of ordinary differential equations of zero,first and second order so the set of equations are solved by using the implicit finite difference scheme. A parametric study of the physical parameters involve in the problem is conducted and a representative set of numerical results are illustrated graphically
This document presents a simple phenomenological approach to modeling nanoindentation creep using conventional spring and dashpot elements. It describes how creep, which is the time-dependent increase in depth under a held load, can be modeled for a variety of materials using Maxwell and Voigt models. Equations are presented that relate the depth increase over time to the elastic modulus and viscosity of the material being tested. A method is described for fitting experimental nanoindentation data, including holding periods, to these equations to determine material properties while accounting for creep. The approach aims to provide an accessible way to analyze creep in nanoindentation that can be incorporated into computer programs.
International Journal of Mathematics and Statistics Invention (IJMSI)inventionjournals
Β
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
The document describes experiments conducted to determine the relative density of glucose and ethylene glycol using a pycnometer, and the dynamic and kinematic viscosity of glycerin using a falling sphere viscometer. The specific gravity of glucose and ethylene glycol were calculated from measurements of the pycnometer weight with and without the samples. Data from the viscometer test including steel ball mass, elapsed time, and diameter were used to calculate the dynamic and kinematic viscosity of glycerin. A graph of observed velocity versus the ratio of steel ball diameter to viscometer diameter showed consistency in the viscometer data.
Chemical reaction and radiation effect on mhd flow past an exponentially acce...Alexander Decker
Β
This document describes a mathematical analysis of MHD fluid flow past an exponentially accelerated vertical plate embedded in a porous medium. The analysis considers the effects of variable temperature, mass diffusion, radiation, and a heat source on the flow characteristics. The governing equations for this problem are derived and non-dimensionalized. The non-dimensional equations are then solved using the Laplace transform technique. The effects of various physical parameters like the magnetic field, radiation, heat generation, and chemical reaction on the velocity, temperature, and concentration profiles are determined.
This document provides an abstract for a research article on magnetohydrodynamic mixed convection micro polar flow through a porous medium driven by a porous stretching sheet. The following key points are discussed:
- Governing partial differential equations are derived and numerically solved using finite element analysis to study the effects of various parameters on velocity, micro rotation, and temperature profiles.
- Parameters investigated include the Hartmann number, Darcy parameter, surface conditions, and their impact on the fluid flow is explored.
- The study aims to provide insights applicable to processes involving polymer sheet stretching and controlled cooling/heating of strips or filaments during manufacturing.
EFFECT OF SLIP PARAMETER OF A BOUNDARY-LAYER FLOW FOR NANOFLUID OVER A VERTIC...IAEME Publication
Β
In this paper we analyze the effect of momentum slip, thermal slip and solutal slip on stagnation point flow of MHD nanofluid towards stretching sheet .The governing partial differential equation of flow, heat and mass transfer on considered flow are converted into the ordinary differential equations by means of similarity trans formations .The resulting equations are solved by the Runge-Kutta fourth order method with efficient shooting technique. Effects of various governing parameters on flow, heat and mass transfer are studied through the plots. The various numerical tables which are calculated and tabulated. A comparison of our present results with a previous study has been done and we found that an excellent agreement is there with the earlier results and of ours.
The steady laminar two dimensional stagnation point flow of an incompressible electrically conducting magneto-micropolar fluid over a permeable stretching surface with heat source/sink and viscous dissipation in the presence of mass transfer and chemical reaction has been studied. Using the similarity transformations, the governing equations have been transformed into a system of ordinary differential equations. These differential equations are highly nonlinear which cannot be solved analytically. Therefore, forth order Runge-Kutta method along with shooting technique has been used for solving it. Numerical results are obtained for the skin-friction coefficient, the local Nusselt number and Sherwood number as well as the velocity, temperature and concentration profiles for different values of the governing parameters, namely, velocity ratio parameter, boundary parameter, material parameter, magnetic parameter, Prandtl number, Eckert number, heat source/sink parameter, Schmidt number and chemical reaction parameter.
This document discusses research on heat source/sink effects on magnetohydrodynamic mixed convection boundary layer flow over a vertical permeable plate embedded in a porous medium saturated with a nanofluid. Numerical solutions are obtained for the governing similarity equations using a shooting method. Results show that imposition of suction increases velocity profiles and delays boundary layer separation, while injection decreases velocity profiles. Dual solutions exist for opposing flow with different nanoparticles, with upper branch solutions being physically stable. Suction also delays flow separation compared to impermeable or injection cases.
This document summarizes a research paper that examines the steady magnetohydrodynamic mass transfer flow of a polar fluid through a porous medium bounded by an infinite vertical porous plate. The paper presents the governing equations for the fluid flow, angular momentum, energy, and concentration considering effects such as magnetic field, thermal diffusion, and radiation. Exact solutions for the velocity, angular velocity, temperature, and concentration fields are obtained. The skin friction and heat transfer rate are also derived. Graphs illustrate the effects of various parameters on the flow behavior and transport properties.
MHD Chemically Reacting and Radiating Nanofluid Flow over a Vertical Cone Emb...IJLT EMAS
Β
In this study, we examine the combined effects of
thermal radiation, chemical reaction on MHD hydromagnetic
boundary layer flow over a vertical cone filled with nanofluid
saturated porous medium under variable properties. The
governing flow, heat and mass transfer equations are
transformed into ordinary differential equations using similarity
variables and are solved numerically by a Galerkin Finite
element method. Numerical results are obtained for
dimensionless velocity, temperature, nanoparticle volume
fraction, as well as the skin friction, local Nusselt and Sherwood
number for the different values of the pertinent parameters
entered into the problem. The effects of various controlling
parameters on these quantities are investigated. Pertinent
results are presented graphically and discussed quantitatively.
The present results are compared with existing results and found
to be good agreement. It is found that the temperature of the
fluid remarkably enhances with the rising values of Brownian
motion parameter (Nb).
International Journal of Computational Engineering Research(IJCER)ijceronline
Β
The document summarizes a study on the effect of thermal radiation on boundary layer flow of a second-grade fluid over a stretching sheet through a porous medium, where the fluid's viscosity and thermal conductivity are temperature dependent. The governing equations are non-dimensionalized using similarity transformations and then solved numerically. Results show the effects of various parameters like radiation, viscosity, thermal conductivity, and porosity on the fluid's velocity and temperature profiles, as well as the skin friction coefficient and Nusselt number.
Studies of transition metal ion - 5- Sulphosalicylic acid doped PolyanilinesIOSR Journals
Β
This document summarizes a study on transition metal ion-5-sulphosalicylic acid complexes used as dopants for polyaniline. Polyaniline was doped with various transition metal carbonates both with and without 5-sulphosalicylic acid. The doped polyanilines were characterized through various tests. Conductivity was found to increase with increasing acid concentration in the doping solution. Magnetic susceptibility measurements showed paramagnetic behavior for transition metal-doped polyanilines and diamagnetic behavior for polyaniline doped with only 5-sulphosalicylic acid. The polymers were found to be amorphous by XRD. SEM showed small
This document presents a fuzzy logic controller for load frequency control of a two-area interconnected power system. It begins with background on load frequency control and conventional controllers. It then describes modeling a two-area system and developing a fuzzy logic controller with membership functions and rules. Simulation results in MATLAB/Simulink show that the fuzzy controller provides better performance than a PID controller in terms of settling time, overshoot, undershoot and steady state error. The fuzzy controller reduces deviations in frequency and tie-line power for different load disturbances with fast response and minimal error.
This document describes a numerical model developed to simulate tsunami propagation and inundation in the coastal region of Bangladesh. Six potential tsunami scenarios were identified based on earthquake sources in the Bay of Bengal. Initial surface level maps were generated for each scenario using a geological model. The tsunami model was developed using the MIKE21 modeling system with nested grids down to 600m resolution covering the coastal region. The model was calibrated with the 2004 Sumatra tsunami and then simulated each scenario to generate maximum inundation maps. An inundation risk map was then produced combining the results, showing high risk areas like Sundarbans, Nijhum Dwip, and Cox's Bazaar coast.
Physical Characterization of a Method for Production of High Stability Suspen...Editor IJCATR
Β
Suspensions/Dispersions are encountered in a wide range of
applications, e.g., liquid abrasive cleaners, ceramics, medicines,
inks, paintsβ¦.etc. In most cases it is necessary to keep the
suspension stable for the product lifetime. A new modified
differential sedimentation measuring system is suggested and used
to identify physical parameters affecting the sedimentation in
suspensions. The technique is discussed in details. It is found that
particle sizes as well as viscosity of continuous phase are the most
important factors governing the stability of a suspension. Empirical
relations are extracted to quantitatively describe the weight effect of
each factor. The modified measuring system shows good accuracy
enough to detect fluctuations in concentration of suspended
particles due to their Brownian diffusion, as well as the particles
concentrations in the stable suspension. This study confirmed the
fact that particles diameters measured by Zetasizer are much
greater than those measured by the transmission electron
microscope. This study presents a proposal for new technique for
particle size separation based on the differential sedimentation in
viscose fluids. This new method is a differential viscosity column.
The proposed size separation technique may help to separate
engineered nano-particles with higher resolution
The present study analyzes the steady boundary layer slip flow of magneto-nanofluid due to an exponentially permeable stretching sheet with heat generation/absorption. In this paper, the effects of Brownian motion and thermophoresis on heat transfer and nanoparticle volume friction are considered. Using shooting technique along with fourth-order Runge-Kutta method the transformed equations are solved. The study reveals that the governing parameters, namely, the magnetic parameter, wall mass suction parameter, Prandtl number, the Lewis number, slip parameter, heat generation/absorption parameter, Brownian motion parameter, and thermophoresis parameter, have major effects on the flow field, the heat transfer, and the nanoparticle volume fraction as well as skin friction, local Nusselt number and local Sherwood number has been discussed in detail.
Numerical Model of Microwave Heating in a Saturated Non-Uniform Porosity Medi...drboon
Β
The microwave heating of a porous medium with a non-uniform porosity is numerically investigated, based on the proposed numerical model. A variation of porosity of the medium is considered. The generalized non-Darcian model developed takes into account of the presence of a solid drag and the inertial effect. The transient Maxwellβs equations are solved by using the finite difference time domain (FDTD) method to describe the electromagnetic field in the wave guide and medium. The temperature profile and velocity field within a medium are determined by the solution of the momentum, energy and Maxwellβs equations. The coupled non-linear set of these equations are solved using the SIMPLE algorithm. In this work, a detailed parametric study is conducted for a heat transport inside a rectangular enclosure filled with saturated porous medium of constant or variable porosity. The numerical results agree well with the experimental data. Variations in porosity significantly affect the microwave heating process as well as convective flow pattern.
The role of strain rate in the dynamic response of materialsAI Publications
Β
We start with the response of ductile materials. To understand the response of these materials to fast dynamic loadings, we introduce two approaches to dynamic viscoplasticity. These are the flowstress approach and the overstress approach, and strain rate has different roles with these two approaches. At very high loading rates the flowstress approach implies very high strength, which is hard to explain by microscale considerations, while the overstress approach does not.We then demonstrate the advantage of using the overstress approach by applying the two approaches to the elastic precursor decay problem. Next use the overstress approach to treat the following problems: 1) the 4th power law response in steady flow of ductile materials; 2) high rate stress upturn (HRSU) of ductile materials; and 3) HRSU of brittle materials. With these examples we demonstrate the advantage of using the overstress approach over the flowstress approach. It follows that HRSU means High (strain) Rate Stress Upturn and not High Rate Strength Upturn, as would follow from using the flowstress approach.
Interrelationships between Characteristic Lengths of Local Scour Holedrboon
Β
This paper presents the results of an experimental study on local scour of noncohesive sediments downstream of a horizontal rigid apron. The experiments were carried out in a rectangular flume with 9m length, 0.5m width and 0.6m height which includes an alluvial test reach of 1.65m length and 0.2m depth at the end of the apron. Two types of uniform sediment with median diameters of 0.73mm and 1.85mm were used in the experiments. Time variations of the maximum scour depth was measured for some experiments. It was found that the scour hole does not reach the equilibrium state even after 48 hours. However, after the first 12 hours, the rate of extension of the maximum scour depth is found to be less than 0.001 cm/min. Although the scour profile seems to be three dimensional in nature, it was found that there is a geometrical similarity between the scour holes in all of the experiments. Variations of the characteristic lengths of the scour hole such as the maximum scour depth, dsm, the maximum extension of hole, L0, and the dune height, hd, are related to each other. Nondimensional graphs and formulas are suggested to determine the variation of these parameters in different conditions.
Thermal Instability of Chemically Reacting Maxwell Fluid in a Horizontal Poro...IJERA Editor
Β
The effect of chemical reaction on the linear stability of a viscoelastic fluid saturated horizontal densely-packed
porous layer is investigated. The viscoelastic properties are given by Maxwell constitutive relations. The porous
layer is cooled from the upper boundary while an adiabatic thermal boundary condition is imposed at the lower
boundary. Linear stability analysis suggests that there is a competition between the processes of viscous
relaxation and thermal diffusion that causes the first convective instability to be oscillatory rather than stationary.
The effect of Deborah number, Darcy-Prandtl number, normalized porosity, and the Frank-Kamenetskii number
on the stability of the system is investigated. Using a weighted residual method we calculate numerically the
convective thresholds for both stationary and oscillatory instability. The effects of viscoelasticity and chemical
reaction on the instability are emphasized. Some existing results are reproduced as the particular cases of the
present study.
Dufour and Soret Effects on Convective Heat and Mass Transfer in Non-Darcy Do...IJERA Editor
Β
This paper deals with the MHD convention non-Darcy flow with heat and mass transfer along the vertical surface in a fluid stratified non porous media in the presence of temperature gradients (Soret effects) and concentration gradients (Dufour effects). The differential equations of the governing flow are expand a in terms of perturbation functions as a result we get set of ordinary differential equations of zero,first and second order so the set of equations are solved by using the implicit finite difference scheme. A parametric study of the physical parameters involve in the problem is conducted and a representative set of numerical results are illustrated graphically
This document presents a simple phenomenological approach to modeling nanoindentation creep using conventional spring and dashpot elements. It describes how creep, which is the time-dependent increase in depth under a held load, can be modeled for a variety of materials using Maxwell and Voigt models. Equations are presented that relate the depth increase over time to the elastic modulus and viscosity of the material being tested. A method is described for fitting experimental nanoindentation data, including holding periods, to these equations to determine material properties while accounting for creep. The approach aims to provide an accessible way to analyze creep in nanoindentation that can be incorporated into computer programs.
International Journal of Mathematics and Statistics Invention (IJMSI)inventionjournals
Β
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
The document describes experiments conducted to determine the relative density of glucose and ethylene glycol using a pycnometer, and the dynamic and kinematic viscosity of glycerin using a falling sphere viscometer. The specific gravity of glucose and ethylene glycol were calculated from measurements of the pycnometer weight with and without the samples. Data from the viscometer test including steel ball mass, elapsed time, and diameter were used to calculate the dynamic and kinematic viscosity of glycerin. A graph of observed velocity versus the ratio of steel ball diameter to viscometer diameter showed consistency in the viscometer data.
Chemical reaction and radiation effect on mhd flow past an exponentially acce...Alexander Decker
Β
This document describes a mathematical analysis of MHD fluid flow past an exponentially accelerated vertical plate embedded in a porous medium. The analysis considers the effects of variable temperature, mass diffusion, radiation, and a heat source on the flow characteristics. The governing equations for this problem are derived and non-dimensionalized. The non-dimensional equations are then solved using the Laplace transform technique. The effects of various physical parameters like the magnetic field, radiation, heat generation, and chemical reaction on the velocity, temperature, and concentration profiles are determined.
This document provides an abstract for a research article on magnetohydrodynamic mixed convection micro polar flow through a porous medium driven by a porous stretching sheet. The following key points are discussed:
- Governing partial differential equations are derived and numerically solved using finite element analysis to study the effects of various parameters on velocity, micro rotation, and temperature profiles.
- Parameters investigated include the Hartmann number, Darcy parameter, surface conditions, and their impact on the fluid flow is explored.
- The study aims to provide insights applicable to processes involving polymer sheet stretching and controlled cooling/heating of strips or filaments during manufacturing.
EFFECT OF SLIP PARAMETER OF A BOUNDARY-LAYER FLOW FOR NANOFLUID OVER A VERTIC...IAEME Publication
Β
In this paper we analyze the effect of momentum slip, thermal slip and solutal slip on stagnation point flow of MHD nanofluid towards stretching sheet .The governing partial differential equation of flow, heat and mass transfer on considered flow are converted into the ordinary differential equations by means of similarity trans formations .The resulting equations are solved by the Runge-Kutta fourth order method with efficient shooting technique. Effects of various governing parameters on flow, heat and mass transfer are studied through the plots. The various numerical tables which are calculated and tabulated. A comparison of our present results with a previous study has been done and we found that an excellent agreement is there with the earlier results and of ours.
The steady laminar two dimensional stagnation point flow of an incompressible electrically conducting magneto-micropolar fluid over a permeable stretching surface with heat source/sink and viscous dissipation in the presence of mass transfer and chemical reaction has been studied. Using the similarity transformations, the governing equations have been transformed into a system of ordinary differential equations. These differential equations are highly nonlinear which cannot be solved analytically. Therefore, forth order Runge-Kutta method along with shooting technique has been used for solving it. Numerical results are obtained for the skin-friction coefficient, the local Nusselt number and Sherwood number as well as the velocity, temperature and concentration profiles for different values of the governing parameters, namely, velocity ratio parameter, boundary parameter, material parameter, magnetic parameter, Prandtl number, Eckert number, heat source/sink parameter, Schmidt number and chemical reaction parameter.
This document discusses research on heat source/sink effects on magnetohydrodynamic mixed convection boundary layer flow over a vertical permeable plate embedded in a porous medium saturated with a nanofluid. Numerical solutions are obtained for the governing similarity equations using a shooting method. Results show that imposition of suction increases velocity profiles and delays boundary layer separation, while injection decreases velocity profiles. Dual solutions exist for opposing flow with different nanoparticles, with upper branch solutions being physically stable. Suction also delays flow separation compared to impermeable or injection cases.
This document summarizes a research paper that examines the steady magnetohydrodynamic mass transfer flow of a polar fluid through a porous medium bounded by an infinite vertical porous plate. The paper presents the governing equations for the fluid flow, angular momentum, energy, and concentration considering effects such as magnetic field, thermal diffusion, and radiation. Exact solutions for the velocity, angular velocity, temperature, and concentration fields are obtained. The skin friction and heat transfer rate are also derived. Graphs illustrate the effects of various parameters on the flow behavior and transport properties.
MHD Chemically Reacting and Radiating Nanofluid Flow over a Vertical Cone Emb...IJLT EMAS
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In this study, we examine the combined effects of
thermal radiation, chemical reaction on MHD hydromagnetic
boundary layer flow over a vertical cone filled with nanofluid
saturated porous medium under variable properties. The
governing flow, heat and mass transfer equations are
transformed into ordinary differential equations using similarity
variables and are solved numerically by a Galerkin Finite
element method. Numerical results are obtained for
dimensionless velocity, temperature, nanoparticle volume
fraction, as well as the skin friction, local Nusselt and Sherwood
number for the different values of the pertinent parameters
entered into the problem. The effects of various controlling
parameters on these quantities are investigated. Pertinent
results are presented graphically and discussed quantitatively.
The present results are compared with existing results and found
to be good agreement. It is found that the temperature of the
fluid remarkably enhances with the rising values of Brownian
motion parameter (Nb).
International Journal of Computational Engineering Research(IJCER)ijceronline
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The document summarizes a study on the effect of thermal radiation on boundary layer flow of a second-grade fluid over a stretching sheet through a porous medium, where the fluid's viscosity and thermal conductivity are temperature dependent. The governing equations are non-dimensionalized using similarity transformations and then solved numerically. Results show the effects of various parameters like radiation, viscosity, thermal conductivity, and porosity on the fluid's velocity and temperature profiles, as well as the skin friction coefficient and Nusselt number.
Studies of transition metal ion - 5- Sulphosalicylic acid doped PolyanilinesIOSR Journals
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This document summarizes a study on transition metal ion-5-sulphosalicylic acid complexes used as dopants for polyaniline. Polyaniline was doped with various transition metal carbonates both with and without 5-sulphosalicylic acid. The doped polyanilines were characterized through various tests. Conductivity was found to increase with increasing acid concentration in the doping solution. Magnetic susceptibility measurements showed paramagnetic behavior for transition metal-doped polyanilines and diamagnetic behavior for polyaniline doped with only 5-sulphosalicylic acid. The polymers were found to be amorphous by XRD. SEM showed small
This document presents a fuzzy logic controller for load frequency control of a two-area interconnected power system. It begins with background on load frequency control and conventional controllers. It then describes modeling a two-area system and developing a fuzzy logic controller with membership functions and rules. Simulation results in MATLAB/Simulink show that the fuzzy controller provides better performance than a PID controller in terms of settling time, overshoot, undershoot and steady state error. The fuzzy controller reduces deviations in frequency and tie-line power for different load disturbances with fast response and minimal error.
This document describes a numerical model developed to simulate tsunami propagation and inundation in the coastal region of Bangladesh. Six potential tsunami scenarios were identified based on earthquake sources in the Bay of Bengal. Initial surface level maps were generated for each scenario using a geological model. The tsunami model was developed using the MIKE21 modeling system with nested grids down to 600m resolution covering the coastal region. The model was calibrated with the 2004 Sumatra tsunami and then simulated each scenario to generate maximum inundation maps. An inundation risk map was then produced combining the results, showing high risk areas like Sundarbans, Nijhum Dwip, and Cox's Bazaar coast.
This document describes the design and development of a manually operated reaper. The reaper was designed to help small-scale farmers harvest grains more efficiently at a low cost. Several modifications were made to address issues identified during testing of an earlier prototype. These included adding an extra cutting blade to address clogging, adjusting the position of the crop divider, and adding a flat belt conveyor mechanism to reduce harvesting losses. The document provides detailed specifications of the reaper components and descriptions of testing conducted to evaluate the performance of the modified design.
This document describes the design and implementation of an electricity supply switching control system using a programmable logic controller (PLC). The system intelligently switches between mains power, solar power, and a diesel generator to supply uninterrupted power to loads. The PLC is programmed using ladder logic to monitor input signals and control output devices like contactors based on the power source availability. A truth table defines the logic conditions and a flowchart shows the algorithm. The PLC switches on solar power initially if mains power fails, then starts the diesel generator and switches to it after 3 seconds. If mains power returns, it takes priority over solar or diesel to power the loads.
This document proposes a methodology for forensic investigation of criminal activity on multitenant cloud web hosting platforms. It presents challenges of investigating crimes in such an environment due to lack of access to physical servers and scattered data across multiple virtual machines and data centers. The proposed architecture uses a MAC Address Derivation Algorithm (MADA) to trace the physical network location of criminals by identifying their IP and MAC addresses from DHCP and firewall logs. When illegal access is detected, the process generates an investigation report by applying MADA to obtain location details based on the user ID of the unauthorized access. This helps law enforcement agencies further investigate cybercrimes on multitenant cloud systems.
This document discusses the design and analysis of a digital down converter (DDC) for WiMAX applications using MATLAB. It contains the following key points:
1. It describes the functional blocks and design of a DDC, including a mixer, numerically controlled oscillator (NCO), and FIR filter chain.
2. It discusses WiMAX standards and requirements for DDC design in WiMAX systems.
3. It presents the windowing technique for designing FIR filters and compares different window functions to determine the best filter specifications.
Development of Shape Based Leaf CategorizationIOSR Journals
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The document describes a methodology for shape-based leaf categorization using image processing and computer vision techniques. The approach involves binarizing leaf images, detecting corners using Harris corner detection, determining the convex hull by joining corner points, and characterizing shapes by calculating internal angles of the convex hull. The internal angles of the input leaf image are compared to those of images in a database to retrieve the most similar leaf images based on matching angle arrays. Key steps include corner detection, convex hull formation, angle calculation, and angle array comparison for classification and retrieval of leaf images by shape.
The document reviews various text categorization methods and proposes a new supervised term weighting method using normalized term frequency and relevant frequency (ntf.rf). It begins by discussing existing text categorization methods and their limitations. Specifically, existing methods often require labeled training data, cleaned datasets, and work best on linearly separable data. The document then proposes the new ntf.rf method to address these limitations by incorporating preprocessing and leveraging both normalized term frequency and relevant frequency to assign term weights. Finally, the document outlines how ntf.rf could improve text categorization by providing a more effective term weighting approach.
The Effects of Rauwolfia Vomitoria Extract on the Liver Enzymes of Carbon Tet...IOSR Journals
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This study investigated the effects of Rauwolfia vomitoria extract on liver enzymes in rats with carbon
tetrachloride-induced hepatotoxicity. Rats were divided into four groups: a control, Rauwolfia vomitoria extract,
carbon tetrachloride, and carbon tetrachloride with Rauwolfia vomitoria extract. Liver enzymes and weights
were measured after treatment. Carbon tetrachloride significantly increased liver enzymes and weight compared
to controls, while Rauwolfia vomitoria prevented these increases, indicating it has a protective effect against
carbon tetrachloride-induced liver damage.
This document analyzes and surveys trust in cloud computing environments. It discusses the need for trust between cloud service users and providers. Several trust issues are identified, including access by insiders, nesting of services, degree of exposure, and risk. Various existing trust models are examined, including those based on service level agreements, virtual environments, and propositional logic terms. User behavior-based trust models are focused on, as it is important to evaluate the trustworthiness of both users and providers. The models are found to be lacking in transparency and parameters for calculating trust values. Overall, the document aims to address trust issues and analyze existing trust models for cloud services.
Cash Flow Valuation Mode Lin Discrete TimeIOSR Journals
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This document summarizes key concepts related to cash flow valuation in discrete time using discounted cash flow analysis. It introduces probability spaces, stochastic processes, martingales, and defines cash flow, discounting, and discount rate processes. The value of a cash flow is modeled as the expected discounted sum of future cash flows. Discounting links future cash flows to their present value using a discount factor that accounts for the time value of money and risk. The discount rate captures the cost of capital and risk of non-payment implied by the discount process.
This document summarizes a proposed passive image forensic method to detect resampling forgery in digital images. Resampling is a common operation used in image forgeries to resize or rotate image regions. The proposed method detects periodic correlations introduced during resampling. It uses a k-nearest neighbors algorithm and support vector machine classifier to identify periodicity maps of resampled images. Experimental results on test images show the method achieves high recall and precision rates when detecting resampled regions, outperforming conventional techniques. The method provides a way to detect image manipulations involving resampling without requiring pre-embedded signatures in images.
This document provides a comparative perspective on the postgraduate historical research formats of Sudan and Nigeria. Some key differences discussed include:
- In Sudan, original certificates must be authenticated for admission, while this is not required in Nigeria.
- In Nigeria, abstracts cannot be more than one or in another language, while in Sudan abstracts must be provided in both English and Arabic.
- Sudan requires explicitly stating research results and recommendations in the text, while this is not mandatory in Nigeria where historians are not expected to speculate or pass judgment.
- Overall, the document finds some similarities in research stages and requirements but also noteworthy differences in the admission processes and abstract/language requirements between the two countries.
This summarizes an academic paper that proposes an automatic ontology creation method for classifying research papers. It uses text mining techniques like classification and clustering algorithms. It first builds a research ontology by extracting keywords and patterns from previous papers. It then uses a decision tree algorithm to classify new papers into disciplines defined in the ontology. The classified papers are then clustered based on similarities to group them. The method was tested on a dataset of 100 papers and achieved average precision of 85.7% for term-based and 89.3% for pattern-based keyword extraction.
This document proposes a cloud-based system to remotely monitor vital health statistics using Internet of Things (IoT). The system would allow children living abroad to monitor parents' health statistics. IoT devices like thermometers and blood pressure monitors would send readings to a smartphone app. The app would send anonymized data like user ID, device ID, and readings to a cloud database. Authorized users could access the aggregate data on a web portal. The system would also send reminders to users and monitors to ensure regular health checks. The goal is to help people remotely monitor loved ones' health with consistency and reliability despite long distances.
This study examined the correlation between central corneal thickness (CCT) and results from Frequency Doubling Technology Perimetry (FDT) in 180 patients aged 40 or older with high intraocular pressure (IOP) but normal optic discs. The average CCT across both eyes was 531 microns. Abnormal FDT results were found in 18 subjects, who had thinner average CCT of 519 microns, compared to 532 microns in 162 subjects with normal FDT results. The study concludes that among patients with high IOP but normal discs, thicker corneas are associated with a lower risk of early glaucomatous damage detected by FDT, compared to patients with thinner corneas.
1) The document studies the impact of emulsified water-diesel mixtures on engine performance and emissions. Diesel was emulsified with 3%, 5%, and 7% water by volume.
2) Test results showed that adding water to diesel emulsions improved brake thermal efficiency and reduced brake specific fuel consumption compared to pure diesel. Emissions of nitrogen oxides and particulate matter also decreased with the addition of up to 5% water.
3) The presence of water in the emulsions lowers combustion temperatures, reducing nitrogen oxide emissions. It also increases the expansion work and reduces compression work in the engine, improving efficiency.
Video Encryption and Decryption with Authentication using Artificial Neural N...IOSR Journals
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Abstract :Multimedia data security is becoming important with the continuous increase of digital
communications on internet. With the rapid development of various multimedia technologies, more and more
multimedia data are generated and transmitted in the medical, commercial, and military fields, which may
include some sensitive information which should not be accessed by or can only be partially exposed to the
general users. . The encryption algorithms developed to secure text data are not suitable for multimedia
application because of the large data size and real time constraint. Therefore, there is a great demand for
secured data storage and transmission techniques. Information security has traditionally been ensured with
data encryption and authentication techniques. The secrecy of communication is maintained by secret key
exchange. In effect the strength of the algorithm depends solely on the length of the key. The presented work
aims at secure video transmission using randomness in encryption algorithm, thereby creating more confusion
to obtain the original data. The security of the original cipher has been enhanced by addition of impurities to
misguide the cryptanalyst. Since the encryption process is one way function, the artificial neural networks are
best suited for this purpose as they possess features like high security, no distortion and its ability to perform for
non linear input-output characteristics, In the presented work the need for key exchange is also eliminated,
which is otherwise a perquisite for most of the algorithms used today. The proposed work finds its application in
medical imaging systems, military image database communication and confidential video conferencing, and
similar such application. The results are obtained through the use of MATLAB 7.14.0
Keywords: Artificial Neural networks, Back propagation algorithm, video encryption and decryption, cipher
and decipher
Wireless Sensor Network: an emerging entrant in HealthcareIOSR Journals
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This document discusses the potential for wireless sensor networks in healthcare applications. It describes how wireless sensor networks can be used to monitor patients remotely by collecting physiological data from sensor devices. Some challenges to the adoption of this technology in healthcare include ensuring privacy and security of medical data transmitted over wireless networks. The document also provides examples of how wireless body area networks and wearable sensor devices can help monitor aspects of health and enable at-home health monitoring.
Homotopy Analysis to Soret and Dufour Effects on Heat and Mass Transfer of a ...iosrjce
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The objective of this paper is to study the Soret and Dufour effects on the free convection boundary
layer flow of an incompressible, viscous and chemically reacting fluid over a vertical plate in the presence of
viscous dissipation. The governing partial differential equations are converted to a set of ordinary differential
equations using suitable similarity transformations. The resulting equations are solved analytically using
homotopy analysis method (HAM). The convergence of obtained analytical solutions is explicitly discussed. The
effects of various parameters on dimensionless velocity, temperature and concentration profiles are discussed
with the help of graphs. The numerical values of skin friction, Nusselt number and Sherwood number for
different parameters are presented in tabular form. Our results are compared with the previously published
results and are found to be in good agreement.
Radiation and magneticfield effects on unsteady naturalAlexander Decker
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This document discusses research on the effects of thermal radiation and magnetic fields on unsteady natural convective flow of nanofluids past an infinite vertical plate with a heat source. The following key points are discussed:
- Governing equations for the unsteady, two-dimensional flow are derived taking into account radiation, magnetic fields, and thermophysical properties of nanofluids.
- The equations are solved numerically using Laplace transform techniques. Parameters like radiation, magnetic field, heat source, and nanoparticle volume fraction are examined.
- It is found that increasing the magnetic field decreases fluid velocity, while radiation, heat source, and nanoparticle volume fraction more strongly influence velocity and temperature profiles. Nanoparticle shape
Radiation and magneticfield effects on unsteady naturalAlexander Decker
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This document discusses research on the effects of thermal radiation and magnetic fields on unsteady natural convective flow of nanofluids past an infinite vertical plate with a heat source. The following key points are discussed:
- Governing equations for the unsteady, two-dimensional flow are derived taking into account radiation, magnetic fields, and thermophysical properties of nanofluids.
- The equations are solved numerically using Laplace transform techniques. Parameters like radiation, magnetic field, heat source, and nanoparticle volume fraction are examined.
- It is found that increasing the magnetic field decreases fluid velocity, while radiation, heat source, and nanoparticle volume fraction have a greater influence on fluid velocity and temperature profiles. Nan
This document presents a numerical solution for unsteady heat and mass transfer flow past an infinite vertical plate with variable thermal conductivity, taking into account Dufour number and heat source effects. The governing equations are non-linear and coupled, and were solved numerically using an implicit finite difference scheme. Various parameters, including Dufour number and heat source, were found to influence the velocity, temperature, and concentration profiles. Skin friction, Nusselt number, and Sherwood number were also calculated.
Magnetohydrodynamic mixed convection flow and boundary layer control of a nan...IAEME Publication
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This research work is focused on the numerical solution of steady MHD mixed convection boundary layer flow of a nanofluid over a semi-infinite flat plate with heat generation/absorption and viscous dissipation effects in the presence of suction and injection. Gyarmatiβs variational principle developed on the thermodynamic theory of irreversible processes is employed to solve the problem
numerically. The governing boundary layer equations are approximated as simple polynomial functions, and the functional of the variational principle is constructed.
This document presents a study on the finite difference solutions of magnetohydrodynamic free convective flow with constant suction and variable thermal conductivity in a Darcy-Forchheimer porous medium. The governing equations for the flow are non-dimensionalized and solved using the Crank-Nicolson finite difference method. Steady-state analytical solutions are also obtained using perturbation methods to check the accuracy of the numerical solutions. The velocity, temperature, and concentration profiles are illustrated and skin friction, Nusselt number, and Sherwood number are tabulated and discussed for different parameters like variable thermal conductivity and Darcy-Forchheimer number. It is found that velocity and temperature increase with variable thermal conductivity while concentration decreases
Effect of Radiation on Mixed Convection Flow of a Non-Newtonian Nan fluid ove...IJMER
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International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
Thermal radiation effects on mhd free convection flow of a micropolar fluid p...Alexander Decker
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This document summarizes a study on thermal radiation effects on magnetohydrodynamic (MHD) free convection flow of a micropolar fluid past a stretching surface embedded in a non-Darcian porous medium. The governing equations for momentum, angular momentum, and energy are solved numerically. Key findings include:
1) The micropolar fluid model helps reduce drag forces and acts as a cooling agent compared to classical fluids.
2) Parameters like the Darcy number, radiation, magnetic field, and porous medium properties influence the velocity, microrotation, temperature, skin friction, and heat transfer.
3) Increased microrotation constant and coupling constant reduce skin friction but increase heat transfer.
International Journal of Mathematics and Statistics Invention (IJMSI)inventionjournals
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This document presents a study of unsteady magnetopolar free convection flow through a porous medium with radiation and variable suction. The governing equations for this problem are derived and solved using a series expansion method. Results are presented graphically showing the effects of various parameters like permeability, magnetic field, thermal Grashof number, and slip on velocity, angular velocity, temperature, concentration, skin friction, and heat transfer rate for the fluids air and water. Key findings include that decreasing thermal Grashof number decreases skin friction in air but increases it in water, and decreasing the temperature jump parameter increases the heat transfer rate.
HYDROMAGNETIC MIXED CONVECTION MICRO POLAR FLOW DRIVEN BY A POROUS STRETCHING...IAEME Publication
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We analyze a finite element solution for the magneto hydrodynamics mixed convection micro polar flow through a porous medium driven by a porous stretching sheet with uniform suction. The governing partial differential equations are solved numerically by using finite element technique. The
effect of Hartmann number, Darcy parameter and surface condition on velocity, micro rotation and temperature functions has been study.
Radiation and Mass Transfer Effects on MHD Natural Convection Flow over an In...IJMER
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A numerical solution for the unsteady, natural convective flow of heat and mass transfer along an inclined plate is presented. The dimensionless unsteady, coupled, and non-linear partial differential conservation equations for the boundary layer regime are solved by an efficient, accurate and unconditionally stable finite difference scheme of the Crank-Nicolson type. The velocity, temperature, and concentration fields have been studied for the effect of Magnetic parameter, buoyancy ratio parameter, Prandtl number, radiation parameter and Schmidt number. The local skin-friction, Nusselt number and Sherwood number are also presented and analyzed graphically.
Radiation Effects on MHD Free Convective Rotating Flow with Hall EffectsIJERA Editor
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In this paper, we have studied the unsteady an incompressible MHD rotating free convection flow of Viscoelastic fluid through a porous medium with simultaneous heat and mass transfer near an infinite vertical oscillating porous plate under the influence of uniform transverse magnetic field. The governing equations of the flow field are solved by a regular perturbation method for small elastic parameter. The expressions for the velocity, temperature, concentration have been derived analytically and also its behaviour is computationally discussed with reference to different flow parameters with the help of graphs. The skin friction, the Nusselt number and the Sherwood number are also obtained and their behaviour discussed.
Soret Effect And Effect Of Radiation On Transient Mhd Free Convective Flow Ov...inventionjournals
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The present paper is concerned to analyze the radiation, Magneto hydrodynamic and soret effects on unsteady flow heat and mass transfer characteristics in a viscous, incompressible and electrically conduction fluid over a semi-infinite vertical porous plate through porous media the porous plate is subjected to a transverse variable suction velocity. The transient, non linear and coupled dimensionless governing equations for this investigation are solved analytically using perturbation technique about a small parameter ο₯ . the effects of governing parameters on the flow variables are discussed graphically.
Soret Effect And Effect Of Radiation On Transient Mhd Free Convective Flow Ov...inventionjournals
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The present paper is concerned to analyze the radiation, Magneto hydrodynamic and soret effects on unsteady flow heat and mass transfer characteristics in a viscous, incompressible and electrically conduction fluid over a semi-infinite vertical porous plate through porous media the porous plate is subjected to a transverse variable suction velocity. The transient, non linear and coupled dimensionless governing equations for this investigation are solved analytically using perturbation technique about a small parameter ο₯ . the effects of governing parameters on the flow variables are discussed graphically.
Carbon Nanotubes On Unsteady MHD Non-Darcy Flow Over A Porous Wedge In The Pr...IJERA Editor
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This document summarizes a research paper that investigates the effects of copper nanoparticles and carbon nanotubes on unsteady magnetohydrodynamic (MHD) non-Darcy flow over a porous wedge in the presence of thermal radiation energy. The paper presents the mathematical model and governing equations for the problem. Boundary layer equations are derived to analyze the flow and heat transfer characteristics. The equations are non-dimensionalized using appropriate variables and transformations.
This document summarizes a study on mixed convective heat and mass transfer flow of a visco-elastic fluid over a stretching sheet. The study considers the effects of chemical reaction, temperature gradient dependent heat sink, and magnetic field. The governing equations for momentum, energy and diffusion are presented and non-linear similarity transformations are applied to reduce the equations to an ordinary differential equation system. The system is solved numerically using a Runge-Kutta method with shooting techniques to determine skin friction coefficient, Nusselt number, and Sherwood number.
MHD convection flow of viscous incompressible fluid over a stretched vertical...IJERA Editor
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The effect of thermal radiation, viscous dissipation and hall current of the MHD convection flow of the viscous incompressible fluid over a stretched vertical flat plate has been discussed by using regular perturbation and homotophy perturbation technique with similarity solutions. The influence of various physical parameters on velocity, cross flow velocity and temperature of fluid has been obtained numerically and through graphs.
Effects of Variable Fluid Properties and MHD on Mixed Convection Heat Transfe...IOSR Journals
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The effects of variable Fluid Properties like variation of permeability, porosity, thermal conductivity and magnetic field on Mixed Convection Heat transfer from Vertical Heated Plate Embedded in a Sparsely Packed Porous Medium have been approached numerically. The boundary layer flow in the porous medium is governed by Lapwood β Forchheimer β Brinkman extended Darcy model and the Lorentz force. The natures of these equations are highly non-linear and coupled each other. The non-linear differential equations are non-dimensionalised using the non-dimensional parameter involving Grashoff number Gr, Prandtl number Pr, Hartmann number M, Eckert number E and so on. Similarity transformations are employed and the resulting ordinary differential equations are solved numerically by using shooting algorithm with Runge β Kutta and Newton β Raphson method to obtain velocity and temperature distributions. Besides, skin friction and Nusselt number are also computed for various physical parameters governing the problem under consideration. It is found that the inertial parameter has a significant influence in decreasing the flow field, whereas its influence is reversed on the rate of heat transfer for all values of permeability considered. The effect of Magnetic field is diminution with velocity of the fluid flow. Further, the obtained results under the two limiting conditions were found to be in good agreement with the existing results
Thermal Effects in Stokesβ Second Problem for Unsteady Second Grade Fluid Flo...IOSR Journals
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In this paper, we investigated the effects of magnetic field and thermal in Stokesβ second problem for unsteady second grade fluid flow through a porous medium. The expressions for the velocity field and the temperature field are obtained analytically. The effects of various pertinent parameters on the velocity field and temperature field are studied through graphs in detail.
This document provides a technical review of secure banking using RSA and AES encryption methodologies. It discusses how RSA and AES are commonly used encryption standards for secure data transmission between ATMs and bank servers. The document first provides background on ATM security measures and risks of attacks. It then reviews related work analyzing encryption techniques. The document proposes using a one-time password in addition to a PIN for ATM authentication. It concludes that implementing encryption standards like RSA and AES can make transactions more secure and build trust in online banking.
This document analyzes the performance of various modulation schemes for achieving energy efficient communication over fading channels in wireless sensor networks. It finds that for long transmission distances, low-order modulations like BPSK are optimal due to their lower SNR requirements. However, as transmission distance decreases, higher-order modulations like 16-QAM and 64-QAM become more optimal since they can transmit more bits per symbol, outweighing their higher SNR needs. Simulations show lifetime extensions up to 550% are possible in short-range networks by using higher-order modulations instead of just BPSK. The optimal modulation depends on transmission distance and balancing the energy used by electronic components versus power amplifiers.
This document provides a review of mobility management techniques in vehicular ad hoc networks (VANETs). It discusses three modes of communication in VANETs: vehicle-to-infrastructure (V2I), vehicle-to-vehicle (V2V), and hybrid vehicle (HV) communication. For each communication mode, different mobility management schemes are required due to their unique characteristics. The document also discusses mobility management challenges in VANETs and outlines some open research issues in improving mobility management for seamless communication in these dynamic networks.
This document provides a review of different techniques for segmenting brain MRI images to detect tumors. It compares the K-means and Fuzzy C-means clustering algorithms. K-means is an exclusive clustering algorithm that groups data points into distinct clusters, while Fuzzy C-means is an overlapping clustering algorithm that allows data points to belong to multiple clusters. The document finds that Fuzzy C-means requires more time for brain tumor detection compared to other methods like hierarchical clustering or K-means. It also reviews related work applying these clustering algorithms to segment brain MRI images.
1) The document simulates and compares the performance of AODV and DSDV routing protocols in a mobile ad hoc network under three conditions: when users are fixed, when users move towards the base station, and when users move away from the base station.
2) The results show that both protocols have higher packet delivery and lower packet loss when users are either fixed or moving towards the base station, since signal strength is better in those scenarios. Performance degrades when users move away from the base station due to weaker signals.
3) AODV generally has better performance than DSDV, with higher throughput and packet delivery rates observed across the different user mobility conditions.
This document describes the design and implementation of 4-bit QPSK and 256-bit QAM modulation techniques using MATLAB. It compares the two techniques based on SNR, BER, and efficiency. The key steps of implementing each technique in MATLAB are outlined, including generating random bits, modulation, adding noise, and measuring BER. Simulation results show scatter plots and eye diagrams of the modulated signals. A table compares the results, showing that 256-bit QAM provides better performance than 4-bit QPSK. The document concludes that QAM modulation is more effective for digital transmission systems.
The document proposes a hybrid technique using Anisotropic Scale Invariant Feature Transform (A-SIFT) and Robust Ensemble Support Vector Machine (RESVM) to accurately identify faces in images. A-SIFT improves upon traditional SIFT by applying anisotropic scaling to extract richer directional keypoints. Keypoints are processed with RESVM and hypothesis testing to increase accuracy above 95% by repeatedly reprocessing images until the threshold is met. The technique was tested on similar and different facial images and achieved better results than SIFT in retrieval time and reduced keypoints.
This document studies the effects of dielectric superstrate thickness on microstrip patch antenna parameters. Three types of probes-fed patch antennas (rectangular, circular, and square) were designed to operate at 2.4 GHz using Arlondiclad 880 substrate. The antennas were tested with and without an Arlondiclad 880 superstrate of varying thicknesses. It was found that adding a superstrate slightly degraded performance by lowering the resonant frequency and increasing return loss and VSWR, while decreasing bandwidth and gain. Specifically, increasing the superstrate thickness or dielectric constant resulted in greater changes to the antenna parameters.
This document describes a wireless environment monitoring system that utilizes soil energy as a sustainable power source for wireless sensors. The system uses a microbial fuel cell to generate electricity from the microbial activity in soil. Two microbial fuel cells were created using different soil types and various additives to produce different current and voltage outputs. An electronic circuit was designed on a printed circuit board with components like a microcontroller and ZigBee transceiver. Sensors for temperature and humidity were connected to the circuit to monitor the environment wirelessly. The system provides a low-cost way to power remote sensors without needing battery replacement and avoids the high costs of wiring a power source.
1) The document proposes a model for a frequency tunable inverted-F antenna that uses ferrite material.
2) The resonant frequency of the antenna can be significantly shifted from 2.41GHz to 3.15GHz, a 31% shift, by increasing the static magnetic field placed on the ferrite material.
3) Altering the permeability of the ferrite allows tuning of the antenna's resonant frequency without changing the physical dimensions, providing flexibility to operate over a wide frequency range.
This document summarizes a research paper that presents a speech enhancement method using stationary wavelet transform. The method first classifies speech into voiced, unvoiced, and silence regions based on short-time energy. It then applies different thresholding techniques to the wavelet coefficients of each region - modified hard thresholding for voiced speech, semi-soft thresholding for unvoiced speech, and setting coefficients to zero for silence. Experimental results using speech from the TIMIT database corrupted with white Gaussian noise at various SNR levels show improved performance over other popular denoising methods.
This document reviews the design of an energy-optimized wireless sensor node that encrypts data for transmission. It discusses how sensing schemes that group nodes into clusters and transmit aggregated data can reduce energy consumption compared to individual node transmissions. The proposed node design calculates the minimum transmission power needed based on received signal strength and uses a periodic sleep/wake cycle to optimize energy when not sensing or transmitting. It aims to encrypt data at both the node and network level to further optimize energy usage for wireless communication.
This document discusses group consumption modes. It analyzes factors that impact group consumption, including external environmental factors like technological developments enabling new forms of online and offline interactions, as well as internal motivational factors at both the group and individual level. The document then proposes that group consumption modes can be divided into four types based on two dimensions: vertical (group relationship intensity) and horizontal (consumption action period). These four types are instrument-oriented, information-oriented, enjoyment-oriented, and relationship-oriented consumption modes. Finally, the document notes that consumption modes are dynamic and can evolve over time.
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1. IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE)
e-ISSN: 2278-1684,p-ISSN: 2320-334X, Volume 13, Issue 4 Ver. II (Jul. - Aug. 2016), PP 42-49
www.iosrjournals.org
DOI: 10.9790/1684-1304024249 www.iosrjournals.org 42 | Page
Effect of Mass and Partial Slip on Boundary Layer Flow of a
Nanofluid over a Porous Plate Embedded In a Porous Medium
Falana Ayodeji1
; Alao Ahmed Abubakar2
; Oladejo Oluyemisi Joy-Felicia3
1, 2
Department of Mechanical Engineering, University of Ibadan, Ibadan, Nigeria
3
Department of Civil Engineering, University of Ibadan, Ibadan, Nigeria
Abstract: This article is concerned with the effect of mass and partial slip on boundary layer flow of a
nanofluid over a porous plate embedded in a porous medium. By taking suitable similarity variables, the
governing partial differential equations are made dimensionless and then reduce to ordinary differential
equations with the associated boundary conditions. The equations are then solved numerically using fourth
order Runge-Kutta method.The results for the shear stress, the temperature distribution, the nanoparticle
volume fraction, the skin friction coefficient,πβ²β²
0 , the reduced Nusselt number, βπβ²(0)and the reduced
Sherwood number,βπβ²
0 are presented graphically illustrating the effects of mass slip, partial slip,
permeability, thermophoresis, Brownian motion, Lewis number and Prandtl number. Our analysis reveals,
among others, that skin friction increases with a decreasing mass slip and that the Nusselt number is a
decreasing function, while the sherwood number is an increasing function of the thermophoretic number ππ‘. A
comparison with previously published literatures on special case of the problem shows excellent agreement.
Keywords:Mass slip; Partial velocity slip; Permeable plate;Thermophoresis; Similarity variable
I. Introduction
The dynamics of fluids in porous media is generally dominated by the porous matrix which pervades
the entire volume. A porous medium or a porous material is a material containing pores (voids). The skeletal
portion of the material is often called the βmatrixβ or βframeβ. Usually, pores are typically filled with a fluid
(liquid or gas). Extremely small voids are called molecular interstices and very large ones are called
caverns.Nanofluids have enormous potentials in enhancing heat transfer performances because of their thermo-
physical properties when compared to their conventional particle fluid suspensions. They have found
applications inadvanced nuclear systems, biological sensors, hybrid power engines, fuel cells etc. Nanoparticles
are made of oxides such as carbides, silica, alumina, copper oxides etc. Ahmad and Pop [1] studied mixed
convection boundary layer flow from a vertical flat plate embedded in a porous medium filled with nanofluids.
Nield and Kuznetsov [2] studied the problem proposed by Cheng and Minkowycz [3] about the natural
convection past a vertical plate in a porous medium saturated by a nanofluid taking into account the Brownian
motion and Thermophoresis.Bhattacharyya [4] investigated the effect of slip on boundary layer flow and mass
transfer with chemical reaction over a permeable flat plate in a porous medium. Buongiorno [5] made a
comprehensive survey of convective transport in nanofluids. He explained the enhanced heat transfer
characteristics of nanofluids and their abnormal increase in thermal conductivities as a result of two main
effects, namely, the Brownian diffusion and the thermophoretic diffusion of the nanoparticles. Buongiorno and
Hu [6] investigated on the nanofluid coolants in advanced nuclear systems. Khan and Pop [7] used the model of
Kuznetsov and Nield [8] to study the fundamental work on the boundary layer flow of nanofluid over a
stretching sheet. Makinde and Aziz [9] extended the work of Khan and Pop [7] for convective boundary
conditions.
Recently, Nur Husna Md. Yusoff et al. [10] studied the combined similarity-numerical solutions of
MHD Boundary layer slip flow of non-Newtonian power-law nanofluids over a radiating moving plate.
Moreover, Ali Pakravan and Yaghoubi [11] studied the combined effect of thermophoresis, Brownian motion
and Dufour effects on natural convection of nanofluids. Lai and Kulacki [12] discussed the coupled heat and
mass transfer by mixed convection from a vertical plate in a saturated porous medium. Hsu and Cheng [13]
studied problems on Darcian and non-Darcian effects on a vertical plate natural convection in porous media.
Kaviany [14] used the Darcy-Brinkman model to study the effects of boundary and inertia forces on forced
convection over a fixed impermeable heated plate embedded in a porous medium. Kumari et al. [15]
investigated the non-Darcian effects on forced convection heat transfer over a flat plate in a highly porous
medium.
It is important to note that Darcyβs classical flow model is a fundamental law relating the pressure
gradient, viscosity and fluid velocity linearly through porous medium. Any deviation from Darcyβs law and
assumptions is termed as non-Darcy flow. Darcyβs law works for creeping fluids of Reynolds number within a
range of 1 to 10 Ishak et al. [16]. Most often, it is assumed that the upper limit of the applicability of Darcyβs
2. Effect of Mass and Partial Slip on Boundary Layer Flow of a Nanofluid over a Porous Plateβ¦.
DOI: 10.9790/1684-1304024249 www.iosrjournals.org 43 | Page
law is between π π of 1 and 2 Bear [17]. The aim of this paper is to investigate mass and partial slip effect on
boundary layer flow of a nanofluid over a porous plate embedded in a porous media.
However, to the best of authorβs knowledge, no attempt has been made to investigate the effect of mass
and partial slip on boundary layer flow of a nanofluid over a porous plate embedded in a porous media. Hence,
the problem is investigated. The governing partial differential equations are transformed to a system of ordinary
differential equations using similarity approach and the resulting equations are then solved numerically using
Runge-Kutta method. An investigation is carried out to illustrate the effect of various governing parameters viz.,
temperature, nanoparticle volume fraction, shear stress, skin friction coefficient, Nusselt and Sherwood number
are discussed in details.
II. Formulation of the Problem
Consider a steady, two-dimensional, boundary layer flow of a nanofluid over a porous plate embedded
in a porous medium. The x-axis is taking along the surface of the porous plate and the y-axis perpendicular to it.
The temperature ππ€ and concentration πΆ π€ on the surface of the plate are kept constant, and assumed to be
greater than the ambient temperature and concentration,πβandπΆβ, respectively. A physical geometry of the
model is given in Fig 1 below. The governing equations of the flow field can be written in dimensional form as:
Fig: 1Geometry of the physical model
βπ’
βπ₯
+
βv
βπ¦
= 0 (1)
π’
βπ’
βπ₯
+ v
βπ’
βπ¦
= π
β2 π’
βπ¦2 β
π
π
π’ β π’β (2)
π’
βπ
βπ₯
+ v
βπ
βπ¦
= πΌ
β2 π
βπ¦2 + π[π· π΅
βπΆ
βπ¦
βπ
βπ¦
+
π· π
πβ
βπ
βπ¦
2
] (3)
π’
βπΆ
βπ₯
+ v
βπΆ
βπ¦
= π· π΅
β2 πΆ
βπ¦2 +
π· π
πβ
β2 π
βπ¦2 (4)
Where u and v are the velocity components in the x and y directions respectively, π’β is the free stream
velocity, π is the viscosity, π is the temperature of the nanofluid, πΆ is the concentration of the nanofluid, ππ€ is
the temperature along the porous plate, πΆ π€ is the concentration along the porous plate, Tβ and Cβ are the
ambient temperature and concentration respectively, π =
π
π
is the kinematic viscosity, π = π 0 π₯ is the Darcy
permeability of the porous medium, DB is the Brownian motion coefficient, DT is the thermophoresis
coefficient, π is the thermal conductivity, (ππ) π is the heat capacitance of the nanoparticles, (ππ) π is the heat
capacitance of the base fluid, πΌ =
π
(ππ ) π
is the thermal diffusivity, π =
(ππ) π
(ππ ) π
is the ratio between the heat
capacitance of the nanoparticles and the heat capacitance of the base fluid.
The boundary conditions for velocity, temperature and concentration components are given by:
π’ = π π€ + L1
βu
βy
, v = 0, π = ππ€ , πΆ = πΆ π€ + D1
βC
βy
ππ‘ π¦ = 0 (5a)
π’ β πβ, π β πβ, πΆ β πΆβ ππ π¦ β β (5b)
Where L1 = πΏβ
(π π π₯ )
1
2, is the velocity slip factor and D1 = π·β
(π π π₯ )
1
2 is the mass slip factor with πΏβ
and π·β
being
initial values of velocity and mass slip having dimension of length and π π π₯ =
πβ π₯
π
, is the local Reynolds
number.
III. Similarity Analysis
The stream function π π₯, π¦ is introduce as
π’ =
βπ
βπ¦
andv = β
βπ
βπ₯
(6)
For the expression in Eq. (6), the continuity equation Eq. (1) is satisfied. Using Eq. (6), the momentum equation
Eq. (2), energy equation Eq. (3) and the concentration of specie equation Eq. (4) takes the following form
3. Effect of Mass and Partial Slip on Boundary Layer Flow of a Nanofluid over a Porous Plateβ¦.
DOI: 10.9790/1684-1304024249 www.iosrjournals.org 44 | Page
βπ
βy
β2
π
βπ₯ βy
β
βπ
βπ₯
β2
π
βπ¦2
= π
β3
π
βπ¦3
β
π
π
βπ
βy
β π’β (7)
βπ
βy
βπ
βπ₯
β
βπ
βπ₯
βπ
βπ¦
= πΌ
β2
π
βπ¦2
+ π[π· π΅
βπΆ
βπ¦
βπ
βπ¦
+
π· π
πβ
βπ
βπ¦
2
] (8)
βπ
βy
βπΆ
βπ₯
β
βπ
βπ₯
βπΆ
βπ¦
= π· π΅
β2
πΆ
βπ¦2
+
π· π
πβ
β2
π
βπ¦2
(9)
The boundary conditions in Eq. (5a) and (5b) for the velocity components reduce to
βπ
βy
= Uw + L1
β2
π
βy2
,
βπ
βx
= o, at y = 0;
βπ
βy
β Uβ as y β β (10)
We now introduce the dimensionless variables for π, π and πΆ below
π x, y = uβΞ½xπ π , π π =
T β Tβ
Tw β Tβ
and π π =
C β Cβ
Cw β Cβ
(11)
Where π is the similarity variable and is defined as π = π¦
π’β
π£π₯
From Eq. (11), we finally obtain the following self-similar equation as:
πβ²β²β²
+
1
2
ππβ²β²
β π πβ²
β 1 = 0 (12)
πβ²β²
ππ
+ πππβ²
πβ²
+ ππ‘(πβ²
)2
+
1
2
ππβ²
= 0 (13)
πβ²β²
+
ππ‘
ππ
πβ²β²
+
πΏπ
2
ππβ²
= 0 (14)
The boundary conditions Eq. (10) and (5) are transformed to the following forms:
π = 0 , πβ²
= 1 + ππβ²β²
, π = 1, π = 1 + ππβ²
at π = 0 (15a)
πβ²
β 1, π β 0, π β 0 asπ β β (15b)
Where p = Lβ π’β
π
, is the velocity slip parameterandq = Dβ π’β
π
is the mass slip parameter.
IV. Numerical Methods
The coupled set of non-linear differential equations (12)-(4) along with the boundary conditions (15a)
and (15b) form a three point BVP and does not form a closed form analytical solution. Therefore, it is solved
numerically using fourth order classical βRunge-Kutta Methodβ. In this method, we first convert the governing
equations together with the boundary condition into first order system.
π¦β²
1
= π¦2, π¦β²
2
= π¦3, π¦β²
3
= β 0.5π¦1 π¦3 β π π¦2 β 1 ,
π¦β²
4
= π¦5, π¦β²
5
= βππ ππ π¦5 π¦7 + ππ‘ π¦5
2
+ 0.5π¦1 π¦5 , and
π¦β²6
= π¦7, π¦β²6
= β 0.5πΏ π π¦1 π¦7 + ππ‘π π¦β²
5
Where π¦1 = π, π¦2 = πβ²
, π¦3 = πβ²β²
, π¦4 = π, π¦5 = πβ²
, π¦6 = π, π¦7 = πβ²
With the boundary conditions
π 0 = 0, πβ² 0 = 1 + pπβ²β²(0), π 0 = 1 and π 0 = 1 + qπβ²(0)
The method employed is the Adaptive Runge-Kutta method (Dormand-prince method) which
is implemented in MATLAB as an m-file in the form of ode. It automatically finds the appropriate step size Ξπ
by comparing the results of a fourth-order and fifth-order method. It requires size function evaluations per Ξπ,
and construct a fourth-fifth order method from these function evaluations.
V. Results and Discussion
In other to find out the effect of mass and partial slip on the boundary layer flow of a nanofluid over a
porous plate embedded in a porous medium, numerical computations are carried out. The results obtained are
presented graphically to highlight salient features of the flow, the heat and the nanoparticle volume transfer
characteristics. Table 1 shows the comparison of our results with Mania and Rama [18] and Table 2 shows our
comparison with Khan and Pop [7], Anwar and Khan et al. [19] and Poornima and Bhaskar [20]. A good
agreement is found and this supports the validity of our results for other cases.
Table 1: Comparisons of results for reduced Nusselt number βπβ²(0) and reduced Sherwood number βπβ²(0)
with πΏπ = ππ = 10, π = π = π = 0 andππ = 0.1
ππ‘ Mania and Rama. [18] Present result
βπβ²(0) βπβ²(0) βπβ²(0) βπβ²(0)
0.1 0.952376 2.12939 0.9524 2.1294
0.2 0.365357 2.51522 0.3654 2.5152
0.3 0.135514 2.60881 0.1355 2.6088
0.4 0.049465 2.60384 0.0495 2.6038
0.5 0.017922 2.57310 0.0179 2.5731
4. Effect of Mass and Partial Slip on Boundary Layer Flow of a Nanofluid over a Porous Plateβ¦.
DOI: 10.9790/1684-1304024249 www.iosrjournals.org 45 | Page
From Figure 2 (a, b and g), the outcome of increase in permeability parameter, Lewis number
and velocity slip on the dimensionless temperature is very small, and even with the continuous increase in these
parameters, the decrease in temperature is almost unnoticed. Figure 2(c) shows the effect of mass slip on the
dimensionless temperature in the flow field. The fluid temperature is maximum for π = 0 (no mass slip). The
increment of mass slip causes the temperature to decrease. But this decrease is very small and even upon
continuous increase in mass slip, temperature decrease becomes unnoticed or died out at a certain level. Figure
2(d) interprets the effect of ππ while Figure 2(e) demonstrates the influence of ππ‘. A significant increase in
temperature accompanies a rise in ππ and ππ‘ from 0.1 through 0.2 to 0.5, figures 2(d) and 2(e). With increasing
diffusion in the regime, the boundary
Fig. 2 Variations of dimensionless temperature profiles with π , πΏπ, π, ππ , ππ‘, ππ and π
Layer gets heated which causes the thermal boundary layer thickness to increase. Figure 2(f)
displays the influence of ππ on the dimensionless temperature. Temperature is found to have decrease as
ππ increases. The decrease in temperature is more pronounced for fluids with higher Prandtl number ππ and
5. Effect of Mass and Partial Slip on Boundary Layer Flow of a Nanofluid over a Porous Plateβ¦.
DOI: 10.9790/1684-1304024249 www.iosrjournals.org 46 | Page
hence increasing the rate of heat transfer. Fluids with lower Prandtl number ππ have larger thermal diffusivity.
Figure 3 (a, c and g) depicts the dimensionless Nano particles volume fraction profiles for various values of
permeability parameter π , velocity slip π and Prandtl number ππ respectively. It is observed from these figures
that an increase or decrease in any of the parameters (π , π andππ ) has no effect on the nanoparticles volume
fraction especially at the boundary (wall) i.e. π = 0 and regions far away from the free stream. The
dimensionless nanoparticles volume fraction decreases with an increasing Lewis number πΏπ as seen in Figure
3(b). This can further be explained from the definition of Lewis number, since Lewis number is inversely
proportional to the Brownian motion coefficient having a kinematic viscosity, π i. e. πΏπ =
π
π· π΅
. As a result, fluids
with higher Lewis number will have lower nanoparticles volume fraction.
Figure 3(d) shows the effect of mass slip on the dimensionless nanoparticle volume fraction. As a result
of mass slip on the boundary, the rate of mass transfer from the boundary of the plate to free stream reduces and
the dimensionless solute decreases. From Figure 3(e) and 3(f), we note that the nanoparticle volume fraction
profiles decreases with an increasing ππ and it increases with an increase in ππ‘. Figure 4(a) depicts the
dimensionless shear stress profiles for different values of permeability π , the shear stress for a flat plate (π = 0)
is zero, but decreases at a boundary layer thickness of π = 1 and π = 3 (for plate with permeability of π =
0.3 and π = 0.7 respectively) then increases to a certain level and then decreases. Shear stress becomes zero at
π = 1 (high permeability). The dimensionless shear stress decreases with an increasing Lewis number at a
boundary layer thickness of π = 1 (for fluids withπΏπ = 7) and π = 2 (for fluids withπΏπ = 10 through 15) as
seen in Figure 4(b). At higher Lewis number of πΏπ = 20, shear stress is zero. Figure 4(c). Illustrate the effect of
Prandtl number ππ on the dimensionless shear stress. Shear stress becomes zero for fluids with Prandtl number
of (ππ = 6, 6.5 through 7). Shear stress is < 0 and > 0 for fluids with Prandtl number of 5 and 5.5 respectively.
As a result of the presence of velocity slip (p) on the wall of the plate, shear stress is zero over a boundary layer
thickness of π = 2 and then it increases and decreases towards free stream as seen in Figure 4(d).
6. Effect of Mass and Partial Slip on Boundary Layer Flow of a Nanofluid over a Porous Plateβ¦.
DOI: 10.9790/1684-1304024249 www.iosrjournals.org 47 | Page
Fig. 3 Variations of dimensionless Nano particles volume fraction profiles with π , πΏπ, π, ππ , ππ‘, ππand π
Figure 4(e). Demonstrate the influence of mass slip on the dimensionless shear stress. Shear
stress is < 0 for fluids with no mass slip and for fluids with mass slip of (q=0.2 through 0.5 to 1.2) over a
boundary layer thickness of π = 2, then it increases towards free stream. It is observed from Figure 4(f) that
shear stress is zero for fluids with higher Brownian diffusion of ππ = 0.4 through 0.5, shear stress < 0 over a
boundary layer thickness of π = 2 then it increases towards free stream for fluids with Brownian diffusion of
ππ = 0.1, 0.2 and 0.3. In Figure 4(g), shear stress < 0 for ππ‘ = 1 at π = 2, then increases towards free stream.
As ππ‘ increases from 0.2, through 0.3 to 0.5, shear stress becomes zero over a boundary layer thickness of π = 2
then increases towards free stream. From Figure 5, skin friction at the boundary of the plate i.e. π = 0 increases
with decreasing mass slip, and as free stream is approached with an increasing slip velocity, skin friction
decreases with an increasing mass slip.
Fig. 4 Variations of dimensionless shear stress profiles with π , πΏπ, ππ , π, π, ππ , and ππ‘
πΌπΌ
7. Effect of Mass and Partial Slip on Boundary Layer Flow of a Nanofluid over a Porous Plateβ¦.
DOI: 10.9790/1684-1304024249 www.iosrjournals.org 48 | Page
Fig. 5 Skin friction against p
Table 2: Comparisons of results for reduced Nusselt number βπβ²(0) and reduced Sherwood number βπβ²(0)
with πΏπ = ππ = 10, π = π = π = 0
ππ ππ‘ Khan and Pop [7] Anwar and Khan et al. [19] Poornima and Bhaskar. [20] Present result
βπβ²(0) βπβ²(0) βπβ²(0) βπβ²(0) βπβ²(0) βπβ²(0) βπβ²(0) βπβ²(0)
0.1 0.1 0.9524 2.1294 0.9524 2.1294 0.952376 2.12939 0.9524 2.1294
0.2 0.2 0.3654 2.5152 0.3654 2.5152 0.365357 2.51522 0.3654 2.5152
0.3 0.3 0.1355 2.6088 0.1355 2.6088 0.135514 2.60881 0.1355 2.6088
0.4 0.4 0.0495 2.6038 0.0495 2.6038 0.049465 2.60384 0.0495 2.6038
0.5 0.5 0.0179 2.5731 0.0179 2.5731 0.017922 2.57310 0.0179 2.5731
VI. Concluding Remarks
In summary, this study has numerically analyzed the effect of mass and partial slip on
boundary layer flow of a nanofluid over a porous plate embedded in a porous medium. By using the similarity
transformation approach, the governing partial differential equations are transformed into non-linear ordinary
differential equations and the resulting problem is solved using Runge-Kutta method. The influence of the
governing parameters on the heat and mass transfer has been closely examined. The following conclusions are
drawn from the analysis:
1. Dimensionless temperature decreases slightly with increasing permeability π , Lewis number πΏπ, mass slip π
and velocity slip π. Dimensionless temperature also decreases with an increase in Prandtl number ππ while a
significant increase in ππ and ππ‘ accompanies a rise in temperature.
2. At the boundary(π = 0), an increase or decrease in permeability π , velocity slip π and Prandtl number ππ
do not bring about any increase or decrease in the dimensionless nanoparticles volume fraction i.e. it is not
affected by any of this parameters. The dimensionless nanoparticle volume fraction decreases with
increasing Lewis number πΏπ, mass slip π and Brownian diffusion ππ but increases with an increasing
Thermophoresis ππ‘.
3. Skin friction with an increasing slip velocity π, increases with a decreasing mass slip π.
4. The permeability π , Lewis number πΏπ and velocity slip π have no effect on the heat transfer. An increase in
mass slip π and Prandtl number ππ is accomplish with an increase in heat transfer while an increase in ππ
and ππ‘ causes a decrease.
5. The permeability π , velocity slip π and Prandtl number ππ do not affect the rate of mass transfer. At the
boundary π = 0 , the rate of mass transfer decreases significantly with increasing mass slip π and Lewis
number πΏπ. Mass transfer also decreases with an increasing ππ‘ and increases with an increasing ππ .
Nomenclature
πΆ Nanoparticle volume fraction
πΆ π€ Nanoparticle volume fraction on the plate
πΆβ Nanoparticle volume fraction in the free stream
ππ’ π₯ Nusselt number
π π π₯ Local Reynolds number
π Temperature of the fluid
ππ€ Temperature of the plate
π· Diffusion coefficient
π·1 Mass slip factor
8. Effect of Mass and Partial Slip on Boundary Layer Flow of a Nanofluid over a Porous Plateβ¦.
DOI: 10.9790/1684-1304024249 www.iosrjournals.org 49 | Page
π·π π₯ Local Darcy number
πΏ Reference length
πΏ1 Velocity slip factor
π Permeability parameter
ππ Prandtl number
πΏπ Lewis number
ππ‘ Thermophoresis parameter
ππ Brownian parameter
πβ Free stream velocity
π π€ Wall velocity
π’ Velocity component in x-direction
π£ Velocity component in y-direction
π₯ Distance along the plate
π¦ Distance perpendicular to the plate
Greek Symbols
π Velocity slip parameter
π Similarity variable
π Mass slip parameter
π Coefficient of fluid viscosity
π Kinematic fluid viscosity
π Dimensionless nanoparticle volume fraction
π Fluid density
π Stream function
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