This document summarizes a study on magnetohydrodynamic (MHD) boundary layer flow over a moving vertical plate in a porous medium. The study analyzes the effects of suction and viscous dissipation on heat and mass transfer. The governing equations are reduced to a nonlinear boundary value problem using similarity transformations and solved numerically. Results show that fluid velocity decreases with increasing magnetic parameter and increases with increasing thermal or solutal Grashof numbers, representing the effects of buoyancy forces.
This document summarizes a study that examines heat and mass transfer over a vertical plate in a porous medium with Soret and Dufour effects, a convective surface boundary condition, chemical reaction, and magnetic field. The governing equations for the fluid flow, heat transfer, and mass transfer are presented. Similarity solutions are used to transform the governing partial differential equations into ordinary differential equations, which are then solved numerically. The results are presented graphically to show the influence of various parameters on velocity, temperature, concentration, skin friction, Nusselt number, and Sherwood number.
Homotopy Analysis to Soret and Dufour Effects on Heat and Mass Transfer of a ...iosrjce
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.
Effects of Variable Viscosity and Thermal Conductivity on MHD Free Convection...IRJET Journal
This document summarizes a numerical study that examines the effects of temperature dependent viscosity and thermal conductivity on the steady, laminar boundary layer flow of a dusty fluid near a vertically stretching sheet. The study considers magnetohydrodynamic (MHD) free convection flow with heat generation. The governing nonlinear partial differential equations are reduced to ordinary differential equations using similarity transformations and then solved numerically using a shooting method. Results for velocity, temperature, species concentration, and skin friction, Nusselt, and Sherwood numbers are obtained and analyzed for various physical parameters, providing insights into heat and mass transfer with practical applications in industries like material processing and manufacturing.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
Thermal Effects in Stokes’ Second Problem for Unsteady Second Grade Fluid Flo...IOSR Journals
In this paper, we investigated the effects of magnetic field and thermal in Stokes’ 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.
International Journal of Mathematics and Statistics Invention (IJMSI)inventionjournals
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.
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.
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity
This document summarizes a study that examines heat and mass transfer over a vertical plate in a porous medium with Soret and Dufour effects, a convective surface boundary condition, chemical reaction, and magnetic field. The governing equations for the fluid flow, heat transfer, and mass transfer are presented. Similarity solutions are used to transform the governing partial differential equations into ordinary differential equations, which are then solved numerically. The results are presented graphically to show the influence of various parameters on velocity, temperature, concentration, skin friction, Nusselt number, and Sherwood number.
Homotopy Analysis to Soret and Dufour Effects on Heat and Mass Transfer of a ...iosrjce
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.
Effects of Variable Viscosity and Thermal Conductivity on MHD Free Convection...IRJET Journal
This document summarizes a numerical study that examines the effects of temperature dependent viscosity and thermal conductivity on the steady, laminar boundary layer flow of a dusty fluid near a vertically stretching sheet. The study considers magnetohydrodynamic (MHD) free convection flow with heat generation. The governing nonlinear partial differential equations are reduced to ordinary differential equations using similarity transformations and then solved numerically using a shooting method. Results for velocity, temperature, species concentration, and skin friction, Nusselt, and Sherwood numbers are obtained and analyzed for various physical parameters, providing insights into heat and mass transfer with practical applications in industries like material processing and manufacturing.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
Thermal Effects in Stokes’ Second Problem for Unsteady Second Grade Fluid Flo...IOSR Journals
In this paper, we investigated the effects of magnetic field and thermal in Stokes’ 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.
International Journal of Mathematics and Statistics Invention (IJMSI)inventionjournals
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.
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.
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity
MHD Free Convection and Mass Transfer Flow past a Vertical Flat PlateIJMER
1) This document discusses a study of magnetohydrodynamic (MHD) free convection and mass transfer flow past a vertical flat plate. The study considers the effects of heat source, thermal diffusion, large suction, and a uniform magnetic field applied normal to the flow.
2) Governing equations for momentum, energy, and concentration are introduced and solved using perturbation techniques. Expressions are obtained for velocity, temperature, concentration, skin friction, and rates of heat and mass transfer.
3) Results are discussed through graphs and tables to observe the effects of various parameters like magnetic field, heat source, suction, and thermal diffusion on flow, temperature, concentration, and transport properties.
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.
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.
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
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.
This document summarizes a study that investigates the effect of thermophoresis on unsteady free convective heat and mass transfer in a viscoelastic fluid past a semi-infinite vertical plate. The study uses the Walters-B fluid model to simulate rheological fluids. The dimensionless governing equations are solved using an implicit finite difference scheme. Results show that increasing the thermophoretic parameter decreases velocity and concentration but increases temperature within the boundary layer. Thermophoresis is found to significantly increase the surface mass flux.
Thermal Instability of Chemically Reacting Maxwell Fluid in a Horizontal Poro...IJERA Editor
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.
International Journal of Computational Engineering Research(IJCER) is an intentional online Journal in English monthly publishing journal. This Journal publish original research work that contributes significantly to further the scientific knowledge in engineering and Technology
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
The papers for publication in The International Journal of Engineering& Science are selected through rigorous peer reviews to ensure originality, timeliness, relevance, and readability.
Heat and Mass Transfer Hydromagnetic Radiative Casson Fluid Flow over an Expo...inventionjournals
The present paper examines the hydromagnetic two-dimensional boundary layer flow of a nonNewtonian fluid accompanied by heat and mass transfer towards an exponentially stretching sheet in the presence of chemical reaction and thermal radiation. Casson model is used to characterize non-Newtonian fluid behavior. Using the similarity transformations, the governing partial differential equations are transformed into self-similar ordinary differential equations is solved by using Matlab bvp4c package. The effects of pertinent parameters are presented in both graphical and tabular form.
Study on Steady Flow over a Rotating Disk in Porous Medium with Heat Transferiosrjce
The steady flow of an incompressible viscous fluid above an infinite rotating disk in a porous
medium is studied with heat transfer. Numerical solutions of the nonlinear governing equations which govern
the hydrodynamics and energy transfer are obtained and solved using Crank Nicolson method. The effect of
the porosity of the medium on the velocity and temperature distributions is considered
MHD CASSON FLUID FLOW AND HEAT TRANSFER WITH PST AND PHF HEATING CONDITIONS D...IAEME Publication
In the present paper two-dimensional flow of non-Newtonian MHD flow of Casson fluid heat transfer with PST & PHF is considered. Using Nevier Stoke’s Equations of Motion the momentum and energy equations of Casson fluid are derived. These governing equations of motion and temperature are non-linear partial differential equations which are tedious to solve as they are, hence these partial differential equations are converted into Ordinary differential equations using suitable similarity transformations. These ODE’s are then solved numerically by the efficient Runge Kutta Fehlberg method. Effects of various governing parameters on the flow and heat transfer profiles are analyzed. Further the numerical Values of Wall temperature and Wall temperature Profiles are calculated and discussed in detail through graphs in both the cases of PST and PHF.
MHD Mixed Convection Flow from a Vertical Plate Embedded in a Saturated Porou...IJERA Editor
We analysed in this paper the problem of MHD mixed convection flow from a vertical plate embedded in a saturated porous medium in the presence of melting, thermal dispersion, radiation and heat absorption or generation effects for aiding and opposing external flows. Similarity solution for the governing equations is obtained for the flow equations in steady state. The equations are numerically solved by Runge-Kutta fourth order method coupled with shooting technique. The effect of melting and heat absorption or generation under different parametric conditions on velocity, temperature and heat transfer was analyzed for both aiding and opposing flows
Numerical solution of boussinesq equation arising in one dimensional infiltra...eSAT Journals
Abstract Infiltration is a gradual flow or movement of groundwater into and through the pores of an unsaturated porous medium (soil). The fluid infiltered in porous medium (unsaturated soil), its velocity decreases as soil becomes saturated, and such phenomena is called infiltration. The present model deals with the filtration of an incompressible fluid (typically, water) through a porous stratum, the main problem in groundwater infiltration. The present model was developed first by Boussinesq in 1903 and is related to original motivation of Darcy. The mathematical formulation of the infiltration phenomenon leads to a non-linear Boussinesq equation. In the present paper, a numerical solution of Boussinesq equation has been obtained by using finite difference method. The numerical results for a specific set of initial and boundary conditions are obtained for determining the height of the free surface or water mound. The moment infiltrated water enters in unsaturated soil; the infiltered water will start developing a curve between saturated porous medium and unsaturated porous medium, which is called water table or water mound. Crank-Nicolson finite difference scheme has been applied to obtain the required results for various values of time. The obtained numerical results resemble well with the physical phenomena. When water is infiltered through the vertical permeable wall in unsaturated porous medium the height of the free surface steadily and uniformly decreases due to the saturation of infiltered water as time increases. Forward finite difference scheme is conditionally stable. In the present paper, the graphical representation shows that Crank-Nicolson finite difference scheme is unconditionally stable. Numerical solution of the governing equation and graphical presentation has been obtained by using MATLAB coding. Key words: Infiltration, porous media, Darcy’s law, Crank-Nicolson finite difference scheme
Radiation and Soret Effect on Visco-Elastic MHD Oscillatory Horizontal Channe...IJERA Editor
An analysis of radiation and soret effect on visco-elastic mhd oscillatory flow with heat and mass transfer
through a porous medium bounded by two infinite horizontal parallel porous plates in presence of chemical
reaction and a heat source has been presented when one plate is kept at rest while the other is oscillating in its
own plane. The fluid is considered to be non-Newtonian characterized by Walters liquid (Model B′). The
temperature of the stationary plate is assumed to be constant whereas the temperature of the other plate varies
periodically with time about a steady mean. The equations governing the fluid flow, heat and mass transfer have
been solved analytically. The expressions for velocity, temperature, species concentration, non-dimensional
skin-friction at the plates, the coefficient of rate of heat transfer from the plates to the fluid in terms of Nusselt
number in non-dimensional form, the coefficient of rate of mass transfer from the plates to the fluid in terms of
Sharewood number in non-dimensional form are obtained and illustrated graphically to observe the visco-elastic
effects in combination of other flow parameters involved in the solution. It is noticed that the momentum,
thermal and concentration fields are significantly affected by the visco-elastic parameter.
Soret Effect And Effect Of Radiation On Transient Mhd Free Convective Flow Ov...inventionjournals
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 . the effects of governing parameters on the flow variables are discussed graphically.
The document analyzes the performance and emissions of diesel blended with palm kernel oil and an additive. Palm kernel oil was blended with diesel in ratios from 10% to 30% by volume. The blends and pure diesel were tested in a single cylinder diesel engine. Key findings include:
1) The 25% palm kernel oil and 75% diesel blend (B25) showed a 19% reduction in smoke emissions and a 13.3% reduction in hydrocarbon emissions compared to pure diesel.
2) Adding an additive to the B25 blend further reduced smoke by 23.8% and hydrocarbons by 16% compared to pure diesel.
3) The B25 blend and B25 blend with additive showed reductions in carbon
This document discusses a modified coding technique to reduce peak-to-average power ratio (PAPR) in orthogonal frequency division multiplexing (OFDM) systems. It begins by introducing the PAPR problem in OFDM and existing solutions using Golay complementary sequences (GCS). It then presents definitions and theorems regarding recursive Golay complementary codes (RGCC) that can provide codewords with low PAPR. The paper proposes generating a 16-QAM OFDM signal from QPSK Golay complementary pairs using RGCC to achieve both higher coding rate and lower PAPR compared to existing techniques.
This document summarizes an input device and software interface that allows people with severe tetraplegia and anarthria to interact with computers. The input device uses either skin electrical signals processed with neural networks or a proximity sensor activated by minimal movement. The software interface can be adapted to any input device and gives access to standard PC software through a mono-command system navigated by the input signals. The system aims to provide affordable computer access to severely impaired users.
This document summarizes a study on the effects of radiation on magnetohydrodynamic (MHD) free convection flow of a viscous fluid past an exponentially accelerated vertical plate. The governing equations are solved numerically using an implicit finite difference Crank-Nicolson method. It is found that the fluid velocity decreases with increasing magnetic field or radiation parameter. Fluid temperature also decreases with stronger radiation. Shear stress and heat transfer at the plate increase and decrease, respectively, with higher radiation or magnetic parameters.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
MHD Free Convection and Mass Transfer Flow past a Vertical Flat PlateIJMER
1) This document discusses a study of magnetohydrodynamic (MHD) free convection and mass transfer flow past a vertical flat plate. The study considers the effects of heat source, thermal diffusion, large suction, and a uniform magnetic field applied normal to the flow.
2) Governing equations for momentum, energy, and concentration are introduced and solved using perturbation techniques. Expressions are obtained for velocity, temperature, concentration, skin friction, and rates of heat and mass transfer.
3) Results are discussed through graphs and tables to observe the effects of various parameters like magnetic field, heat source, suction, and thermal diffusion on flow, temperature, concentration, and transport properties.
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.
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.
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
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.
This document summarizes a study that investigates the effect of thermophoresis on unsteady free convective heat and mass transfer in a viscoelastic fluid past a semi-infinite vertical plate. The study uses the Walters-B fluid model to simulate rheological fluids. The dimensionless governing equations are solved using an implicit finite difference scheme. Results show that increasing the thermophoretic parameter decreases velocity and concentration but increases temperature within the boundary layer. Thermophoresis is found to significantly increase the surface mass flux.
Thermal Instability of Chemically Reacting Maxwell Fluid in a Horizontal Poro...IJERA Editor
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.
International Journal of Computational Engineering Research(IJCER) is an intentional online Journal in English monthly publishing journal. This Journal publish original research work that contributes significantly to further the scientific knowledge in engineering and Technology
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
The papers for publication in The International Journal of Engineering& Science are selected through rigorous peer reviews to ensure originality, timeliness, relevance, and readability.
Heat and Mass Transfer Hydromagnetic Radiative Casson Fluid Flow over an Expo...inventionjournals
The present paper examines the hydromagnetic two-dimensional boundary layer flow of a nonNewtonian fluid accompanied by heat and mass transfer towards an exponentially stretching sheet in the presence of chemical reaction and thermal radiation. Casson model is used to characterize non-Newtonian fluid behavior. Using the similarity transformations, the governing partial differential equations are transformed into self-similar ordinary differential equations is solved by using Matlab bvp4c package. The effects of pertinent parameters are presented in both graphical and tabular form.
Study on Steady Flow over a Rotating Disk in Porous Medium with Heat Transferiosrjce
The steady flow of an incompressible viscous fluid above an infinite rotating disk in a porous
medium is studied with heat transfer. Numerical solutions of the nonlinear governing equations which govern
the hydrodynamics and energy transfer are obtained and solved using Crank Nicolson method. The effect of
the porosity of the medium on the velocity and temperature distributions is considered
MHD CASSON FLUID FLOW AND HEAT TRANSFER WITH PST AND PHF HEATING CONDITIONS D...IAEME Publication
In the present paper two-dimensional flow of non-Newtonian MHD flow of Casson fluid heat transfer with PST & PHF is considered. Using Nevier Stoke’s Equations of Motion the momentum and energy equations of Casson fluid are derived. These governing equations of motion and temperature are non-linear partial differential equations which are tedious to solve as they are, hence these partial differential equations are converted into Ordinary differential equations using suitable similarity transformations. These ODE’s are then solved numerically by the efficient Runge Kutta Fehlberg method. Effects of various governing parameters on the flow and heat transfer profiles are analyzed. Further the numerical Values of Wall temperature and Wall temperature Profiles are calculated and discussed in detail through graphs in both the cases of PST and PHF.
MHD Mixed Convection Flow from a Vertical Plate Embedded in a Saturated Porou...IJERA Editor
We analysed in this paper the problem of MHD mixed convection flow from a vertical plate embedded in a saturated porous medium in the presence of melting, thermal dispersion, radiation and heat absorption or generation effects for aiding and opposing external flows. Similarity solution for the governing equations is obtained for the flow equations in steady state. The equations are numerically solved by Runge-Kutta fourth order method coupled with shooting technique. The effect of melting and heat absorption or generation under different parametric conditions on velocity, temperature and heat transfer was analyzed for both aiding and opposing flows
Numerical solution of boussinesq equation arising in one dimensional infiltra...eSAT Journals
Abstract Infiltration is a gradual flow or movement of groundwater into and through the pores of an unsaturated porous medium (soil). The fluid infiltered in porous medium (unsaturated soil), its velocity decreases as soil becomes saturated, and such phenomena is called infiltration. The present model deals with the filtration of an incompressible fluid (typically, water) through a porous stratum, the main problem in groundwater infiltration. The present model was developed first by Boussinesq in 1903 and is related to original motivation of Darcy. The mathematical formulation of the infiltration phenomenon leads to a non-linear Boussinesq equation. In the present paper, a numerical solution of Boussinesq equation has been obtained by using finite difference method. The numerical results for a specific set of initial and boundary conditions are obtained for determining the height of the free surface or water mound. The moment infiltrated water enters in unsaturated soil; the infiltered water will start developing a curve between saturated porous medium and unsaturated porous medium, which is called water table or water mound. Crank-Nicolson finite difference scheme has been applied to obtain the required results for various values of time. The obtained numerical results resemble well with the physical phenomena. When water is infiltered through the vertical permeable wall in unsaturated porous medium the height of the free surface steadily and uniformly decreases due to the saturation of infiltered water as time increases. Forward finite difference scheme is conditionally stable. In the present paper, the graphical representation shows that Crank-Nicolson finite difference scheme is unconditionally stable. Numerical solution of the governing equation and graphical presentation has been obtained by using MATLAB coding. Key words: Infiltration, porous media, Darcy’s law, Crank-Nicolson finite difference scheme
Radiation and Soret Effect on Visco-Elastic MHD Oscillatory Horizontal Channe...IJERA Editor
An analysis of radiation and soret effect on visco-elastic mhd oscillatory flow with heat and mass transfer
through a porous medium bounded by two infinite horizontal parallel porous plates in presence of chemical
reaction and a heat source has been presented when one plate is kept at rest while the other is oscillating in its
own plane. The fluid is considered to be non-Newtonian characterized by Walters liquid (Model B′). The
temperature of the stationary plate is assumed to be constant whereas the temperature of the other plate varies
periodically with time about a steady mean. The equations governing the fluid flow, heat and mass transfer have
been solved analytically. The expressions for velocity, temperature, species concentration, non-dimensional
skin-friction at the plates, the coefficient of rate of heat transfer from the plates to the fluid in terms of Nusselt
number in non-dimensional form, the coefficient of rate of mass transfer from the plates to the fluid in terms of
Sharewood number in non-dimensional form are obtained and illustrated graphically to observe the visco-elastic
effects in combination of other flow parameters involved in the solution. It is noticed that the momentum,
thermal and concentration fields are significantly affected by the visco-elastic parameter.
Soret Effect And Effect Of Radiation On Transient Mhd Free Convective Flow Ov...inventionjournals
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 . the effects of governing parameters on the flow variables are discussed graphically.
The document analyzes the performance and emissions of diesel blended with palm kernel oil and an additive. Palm kernel oil was blended with diesel in ratios from 10% to 30% by volume. The blends and pure diesel were tested in a single cylinder diesel engine. Key findings include:
1) The 25% palm kernel oil and 75% diesel blend (B25) showed a 19% reduction in smoke emissions and a 13.3% reduction in hydrocarbon emissions compared to pure diesel.
2) Adding an additive to the B25 blend further reduced smoke by 23.8% and hydrocarbons by 16% compared to pure diesel.
3) The B25 blend and B25 blend with additive showed reductions in carbon
This document discusses a modified coding technique to reduce peak-to-average power ratio (PAPR) in orthogonal frequency division multiplexing (OFDM) systems. It begins by introducing the PAPR problem in OFDM and existing solutions using Golay complementary sequences (GCS). It then presents definitions and theorems regarding recursive Golay complementary codes (RGCC) that can provide codewords with low PAPR. The paper proposes generating a 16-QAM OFDM signal from QPSK Golay complementary pairs using RGCC to achieve both higher coding rate and lower PAPR compared to existing techniques.
This document summarizes an input device and software interface that allows people with severe tetraplegia and anarthria to interact with computers. The input device uses either skin electrical signals processed with neural networks or a proximity sensor activated by minimal movement. The software interface can be adapted to any input device and gives access to standard PC software through a mono-command system navigated by the input signals. The system aims to provide affordable computer access to severely impaired users.
This document summarizes a study on the effects of radiation on magnetohydrodynamic (MHD) free convection flow of a viscous fluid past an exponentially accelerated vertical plate. The governing equations are solved numerically using an implicit finite difference Crank-Nicolson method. It is found that the fluid velocity decreases with increasing magnetic field or radiation parameter. Fluid temperature also decreases with stronger radiation. Shear stress and heat transfer at the plate increase and decrease, respectively, with higher radiation or magnetic parameters.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
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The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercise causes chemical changes in the brain that may help alleviate symptoms of mental illness and boost overall mental well-being.
This business plan outlines a company called Amikom Yogyakarta located in Yogyakarta, Indonesia. The business plan is dated May 16, 2013 and mentions Amikom Yogyakarta seven times, suggesting it is presenting a strategy and vision for this particular company located in Yogyakarta, Indonesia.
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International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
This document presents an analysis of free convective flow and heat transfer of a viscous incompressible fluid over a linearly moving vertical porous plate with suction and viscous dissipation. The fluid viscosity is assumed to vary linearly with temperature. Governing boundary layer equations are non-dimensionalized using similarity transformations and reduced to a boundary value problem. The problem is solved numerically using a shooting method along with the 4th order Runge-Kutta method. Results for dimensionless velocity and temperature distributions are presented for various parameter values, and skin friction and Nusselt numbers are reported in tables.
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.
Effects of Variable Fluid Properties and MHD on Mixed Convection Heat Transfe...IOSR Journals
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 – Forchheimer – 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 – Kutta and Newton – 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
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.
The International Journal of Engineering and Science (The IJES)theijes
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
Soret Effect And Effect Of Radiation On Transient Mhd Free Convective Flow Ov...inventionjournals
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 . the effects of governing parameters on the flow variables are discussed graphically.
International Journal of Computational Engineering Research(IJCER)ijceronline
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.
International Journal of Computational Engineering Research(IJCER)ijceronline
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
Analytical solution for Transient MHD flow through a Darcian porous regime in...inventionjournals
International Journal of Engineering and Science Invention (IJESI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJESI publishes research articles and reviews within the whole field Engineering Science and Technology, 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.
Radiation and Mass Transfer Effects on MHD Natural Convection Flow over an In...IJMER
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.
Heat Transfer on Steady MHD rotating flow through porous medium in a parallel...IJERA Editor
We discussed the combined effects of radiative heat transfer and a transverse magnetic field on steady rotating flow of an electrically conducting optically thin fluid through a porous medium in a parallel plate channel and non-uniform temperatures at the walls. The analytical solutions are obtained from coupled nonlinear partial differential equations for the problem. The computational results are discussed quantitatively with the aid of the dimensionless parameters entering in the solution.
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
International Journal of Computational Engineering Research(IJCER) is an intentional online Journal in English monthly publishing journal. This Journal publish original research work that contributes significantly to further the scientific knowledge in engineering and Technology
Thermal radiation effects on mhd free convection flow of a micropolar fluid p...Alexander Decker
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) 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.
This document presents a study of melting with thermal dispersion on non-Darcy MHD mixed convective flow from a vertical plate embedded in a saturated porous medium. The governing equations for steady non-Darcy flow accounting for thermal dispersion, melting, inertia, and magnetic effects are derived. Similarity solutions are obtained and numerically solved using a shooting method. Results show that the velocity decreases with increasing magnetic parameter in aiding flow and increases in opposing flow. The Nusselt number decreases with increasing melting parameter but increases with thermal dispersion parameter.
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.
Radiation Effects on MHD Free Convective Rotating Flow with Hall EffectsIJERA Editor
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.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
1. M.Prasanna Lakshmi, N. Bhaskar Reddy, T.Poornima / International Journal of Engineering
Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue 5, September- October 2012, pp.149-159
MHD Boundary Layer Flow of Heat and Mass Transfer over a
Moving Vertical Plate in a Porous Medium with Suction and
Viscous Dissipation
M.Prasanna Lakshmi, N. Bhaskar Reddy and T.Poornima
Department of Mathematics, Sri Venkateswara University, Tirupati-517502.
ABSTRACT
The present paper analyzes the MHD An excellent summary of applications is given by
effects on the steady free convective boundary Huges and Young [5]. Raptis [6] studied
layer flow of a viscous incompressible fluid over a mathematically the case of time varying two
linearly moving porous vertical semi-infinite plate dimensional natural convective flow of an
with suction and viscous dissipation. The incompressible, electrically conducting fluid along an
governing boundary layer equations are reduced infinite vertical porous plate embedded in a porous
to a two-point boundary value problem using medium. Helmy [7] analyzed MHD unsteady free
similarity transformations. The resultant problem convection flow past a vertical porous plate
is solved numerically using the Runge - Kutta embedded in a porous medium. Elabashbeshy [8]
fourth order method along with shooting studied heat and mass transfer along a vertical plate
technique. The effects of various governing in the presence of magnetic field. Chamkha and
parameters on the fluid velocity, temperature, Khaled [9] investigated the problem of coupled heat
concentration, skin-friction coefficient, Nusselt and mass transfer by magnetohydrodynamic free
number and Sherwood number are shown in convection from an inclined plate in the presence of
figures and tables and discussed in detail. internal heat generation or absorption.
Transport of momentum and thermal energy
Keywords- Heat and Mass Transfer, MHD, in fluid-saturated porous media with low porosities is
Moving vertical plate Porous media, Viscous commonly described by Darcy’s model for
Dissipation conservation of momentum and by the energy
equation based on the velocity field found from this
1. INTRODUCTION model (Kaviany [10]). In contrast to rocks, soil, sand
Combined heat and mass transfer (or and other media that do fall in this category, certain
double-diffusion) in fluid-saturated porous media porous materials, such as foam metals and fibrous
finds applications in a variety of engineering media, usually have high porosity. Vajravelu [11]
processes such as heat exchanger devices, petroleum examined the steady flow and heat transfer in a
reservoirs, chemical catalytic reactors and processes, porous medium with high porosity. Hong et al. [12],
geothermal and geophysical engineering, moisture Chen and Lin [13] and Jaisawal and Soundalgekar
migration in a fibrous insulation and nuclear waste [14] studied the natural convection in a porous
disposal and others. Double diffusive flow is driven medium with high porosity. Ibrahim et al [15]
by buoyancy due to temperature and concentration analytically derived the heat and mass transfer of a
gradients. Bejan and Khair [1] investigated the free chemical convective process assuming an
convection boundary layer flow in a porous medium exponentially decreasing suction velocity at the
owing to combined heat and mass transfer. Lai and surface of a porous plate and a two terms harmonic
Kulacki [2] used the series expansion method to function for the rest of the variables. Ali [16]
investigate coupled heat and mass transfer in natural discussed the effect of suction or injection on the free
convection from a sphere in a porous medium. The convection boundary layers induced by a heated
suction and blowing effects on free convection vertical plate embedded in a saturated porous
coupled heat and mass transfer over a vertical plate in medium with an exponential decaying heat
a saturated porous medium were studied by Raptis et generation.
al. [3] and Lai and Kulacki [4], respectively. Viscous mechanical dissipation effects are
Magnetohydrodynamic flows have important in geophysical flows and also in certain
applications in meteorology, solar physics, cosmic industrial operations and are usually characterized by
fluid dynamics, astrophysics, geophysics and in the the Eckert number. Mahajan and Gebhart [17]
motion of earth’s core. In addition from the reported the influence of viscous heating dissipation
technological point of view, MHD free convection effects in natural convective flows, showing that the
flows have significant applications in the field of heat transfer rates are reduced by an increase in the
stellar and planetary magnetospheres, aeronautical dissipation parameter. Gebhart and Mollendorf [18]
plasma flows, chemical engineering and electronics. considered the effects of viscous dissipation for
149 | P a g e
2. M.Prasanna Lakshmi, N. Bhaskar Reddy, T.Poornima / International Journal of Engineering
Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue 5, September- October 2012, pp.149-159
external natural convection flow over a surface. 2
Soundalgekar [19] analyzed viscous dissipative heat u u 2 u B0
u v u g T (T T ) g c (C C ) u
on the two-dimensional unsteady free convective x y y 2 K'
flow past an infinite vertical porous plate when the
temperature oscillates in time and there is constant
suction at the plate. Israel Cookey et al. [20] (2)
investigated the influence of viscous dissipation and 2
T T T 2
u
radiation on unsteady MHD free convection flow past v (3)
c p y
u
an infinite heated vertical plate in a porous medium x y y 2
with time dependent suction. Ramachandra Prasad C C C
2
and Bhaskar Reddy [21] presented radiation and mass u v Dm (4)
x y y 2
transfer effects on an unsteady MHD free convection
The boundary conditions for the velocity,
flow past a heated vertical plate with viscous
temperature and concentration fields are
dissipation.
In this chapter an attempt is made to study u B x , V , T Tw T a x , C C w C b x at y = 0
the MHD effects on the steady free convective
boundary layer flow of a viscous incompressible fluid u 0,T T , C C as y (5)
over a linearly started porous vertical semi-infinite where B is a constant, “a” and “b” denotes the
plate with suction and viscous dissipation. The basic stratification rate of the gradient of ambient
equations governing the flow field are partial temperature and concentration profiles, u, v, T and C
differential equations and these have been reduced to are the fluid x-component of velocity, y-component
a set of ordinary differential equations by applying of velocity, temperature and concentration
suitable similarity transformations. The resultant respectively, ν is the fluid kinematics viscosity, -
equations are coupled and non-linear, and hence are
the density, - the electric conductivity of the fluid,
solved numerically using the fourth order Runge -
Kutta method along with shooting technique. The T and c - the coefficients of thermal and
effects of various governing parameters on the concentration expansions respectively, k - the
velocity, temperature, concentration are presented thermal conductivity, C - the free stream
graphically and discussed quantitatively. The local
skin-friction coefficient and the heat and mass concentration, B0 - the magnetic induction, Dm - the
transfer rates are illustrated for representative values mass diffusivity and g is the gravitational
of the major parameters. acceleration, K ' - the permeability of the porous
To the best of authors’ knowledge, MHD medium and - the thermal diffusivity.
effects on a free convective flow over a moving To transform equations (2) - (4) into a set of
vertical plate with a viscous dissipation have not been ordinary differential equations, the following
reported. This motivated us to carry out the present similarity transformations and dimensionless
work. variables are introduced.
B T T
y , x B f ( ), ( ) ,
2. MATHEMATICAL ANALYSIS Tw T
A steady two-dimensional laminar free
C C , B0 , Gt g T (Tw T ) ,
2
convection flow of a viscous incompressible ( ) M
electrically conducting fluid along a linearly started Cw C B xB 2
porous vertical semi-infinite plate embedded in a g c (Cw C ) , , ,
Gc Pr Sc
porous medium, in the presence of suction and xB 2
Dm
viscous dissipation, is considered. The x-axis is taken
, Ec B2 x2 . (6)
along the plate in the upward direction and the y-axis K
is taken normal to it. The velocity of the fluid far K ' xB c p (Tw T )
away from the plate surface is assumed to be zero for where f ( ) is the dimensionless stream function,
a quiescent state fluid. The variations of surface ( ) - the dimensionless temperature, ( ) - the
temperature and concentration are linear. A uniform
dimensionless concentration, - the similarity
magnetic field is applied in the direction
perpendicular to the plate. The transverse applied variable, M -the Magnetic parameter, Gt -the local
magnetic field and magnetic Reynolds number are thermal Grashof number, Gc -the local solutal
assumed to be very small, so that the induced Grashof number, Pr-the Prandtl number, Sc -the
magnetic field, Hall effects and Joule heating are Schmidt number, K -the permeability parameter and
negligible. Now, under the usual Boussinesq’s Ec -the Eckert number.
approximation, the governing boundary layer The mass concentration equation (1) is satisfied by
equations of the flow field are the Cauchy-Riemann equations
u v (7)
0 (1) u ,v
x y y x
150 | P a g e
3. M.Prasanna Lakshmi, N. Bhaskar Reddy, T.Poornima / International Journal of Engineering
Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue 5, September- October 2012, pp.149-159
where F V is the dimensionless suction be Pr=0.72 which corresponds to air, the value of
B
w
Schmidt number (Sc) are chosen to be
velocity. Sc=0.24,0.62,0.78,2.62, representing diffusing
In view of equations (6) and (7), equations (2) to (4) chemical species of most common interest in air like
transform into H2 , H 2O, NH 3 and Propyl Benzene respectively.
f ff f '( f ' M ) Gt Gc Kf ' 0 Fig. 1 shows the dimensionless velocity
(8) profiles for different values of magnetic parameter M.
It is be seen that, as expected, the velocity decreases
" Pr f ' Pr f ' Ecf ''2 0 (9) with an increase in the magnetic parameter M. The
" Scf ' Scf ' 0 (10) magnetic parameter is found to retard the velocity at
The corresponding boundary conditions are all points of the flow field. It is because that the
application of transverse magnetic field will result in
f ' 1, f Fw , 1, 1 at 0 a resistive type force (Lorentz force) similar to drag
force which tends to resist the fluid flow and thus
f ' 0, 0 as (11) reducing its velocity. Also, the boundary layer
where the prime symbol represents the derivative thickness decreases with an increase in the magnetic
with respect to . parameter. Fig.2 illustrates the effect of the thermal
Grashof number (Gt) on the velocity field. The
Other physical quantities of interest for the
thermal Grashof number signifies the relative effect
problem of this type are the local skin-friction
of the thermal buoyancy force to the viscous
coefficient, the local Nusselt number and Sherwood
hydrodynamic force. The flow is accelerated due to
number which are, respectively, proportional
the enhancement in buoyancy force corresponding to
to f ''(0), '(0) and '(0) . an increase in the thermal Grashof number i.e. free
convection effects. It is noticed that the thermal
3. SOLUTION OF THE PROBLEM Grashof number (Gt) influences the velocity within
The set of coupled non-linear governing the boundary layer when compared to far away from
boundary layer equations (8) - (10) together with the the plate. It is seen that as the thermal Grashof
boundary conditions (11) are solved numerically by number (Gt) increases, the velocity increases.
using Runge-Kutta fourth order technique along with The effect of mass (solutal) Grashof number
shooting method. First of all, higher order non-linear (Gc) on the velocity is illustrated in Fig.3. The mass
differential Equations (8)-(10) are converted into (solutal) Grashof number (Gc) defines the ratio of the
simultaneous linear differential equations of first species buoyancy force to the viscous hydrodynamic
order and they are further transformed into initial force. It is noticed that the velocity increases with
value problem by applying the shooting technique increasing values of the solutal Grashof number.
(Jain et al. [22]). The resultant initial value problem Further as the mass Grashof number (Gc) increases,
is solved by employing Runge-Kutta fourth order the velocity field near the boundary layer increases.
technique. The step size =0.05 is used to obtain It is noticed that, for higher values of mass Grashof
number (Gc), the profiles are found to be more
the numerical solution with five decimal place
parabolic. Fig.4 illustrates the effect of the Schmidt
accuracy as the criterion of convergence. From the
number (Sc) on the velocity. The Schmidt number
process of numerical computation, the skin-friction
(Sc) embodies the ratio of the momentum diffusivity
coefficient, the Nusselt number and the Sherwood
to the mass (species) diffusivity. It physically relates
number, which are respectively proportional to
the relative thickness of the hydrodynamic boundary
f ''(0), (0) and (0) , are also sorted out and layer and mass-transfer (concentration) boundary
their numerical values are presented in a tabular layer. It is observed that as the Schmidt number (Sc)
form. increases, the velocity decreases. Fig.5 illustrates the
effect of permeability parameter (K) on the velocity.
4. RESULTS AND DISCUSSION It is noticed that as the permeability parameter
In order to get a physical insight of the increases, the velocity decreases. As seen in the
problem, a representative set of numerical results are earlier cases, far away from the plate, the effect is not
shown graphically in Figs.1-20, to illustrate the that much significant.
influence of physical parameters viz., the suction The effect of the magnetic parameter M on
parameter Fw, magnetic parameter M , permeability the temperature is illustrated in Fig.7. It is observed
parameter K, buoyancy parameters (Gt, Gc), Eckert that as the magnetic parameter M increases, the
number Ec and Schmidt number Sc on the temperature increases. From Figs. 8 and 9, it is
velocity f ' ,temperature and concentration observed that the thermal boundary layer thickness
. Numerical results for the skin-friction,
increases with an increase in thermal or Solutal
Grashof number (Gt or Gc). Fig. 10 illustrates the
Nusselt number and Sherwood number are reported effect of suction parameter (Fw) on the temperature.
in the Tables 1 and 2. The Prandtl number is taken to It is noticed that as the suction parameter increases an
151 | P a g e
4. M.Prasanna Lakshmi, N. Bhaskar Reddy, T.Poornima / International Journal of Engineering
Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue 5, September- October 2012, pp.149-159
increasing trend in the temperature field is noticed.
Fig.11 depicts the effect of the Schmidt number (Sc)
on the temperature. It is observed that as the Schmidt 1.0
number (Sc) increases, the temperature increases. Fig.
12 shows the variation of the thermal boundary-layer
with the permeability parameter (K). It is noticed that 0.8 M = 0 .1 ,1 .0 ,2 .0 ,3 .0
the thermal boundary layer thickness increases with
an increase in the permeability parameter. Fig. 13
shows the variation of the thermal boundary-layer 0.6
with the Eckert number (Ec). It is observed that the f '
thermal boundary layer thickness increases with an
increase in the Eckert number (Ec). 0.4
The effect of magnetic parameter M on the
concentration field is illustrated Fig.14. As the
0.2
magnetic parameter M increases, the concentration is
found to be increasing. The effect of buoyancy
parameters (Gt, Gc) on the concentration field is
0.0
illustrated Figs. 15 and 16. It is noticed that the
0 1 2 3 4
concentration boundary layer thickness decreases
with an increase in the thermal or Solutal Grashof
numbers (Gt or Gc). Fig. 17 illustrates the effect of Fig.1: Variation of the velocity f with M
suction parameter (Fw) on the concentration. As the
for Pr=0.72, Sc=0.62, Gt=Gc =2, Fw =0.1,
suction parameter increases, an increasing trend in
K=0.1, Ec=0.1.
the concentration field is noticed. The effect of
Schmidt number (Sc) on the concentration is
illustrated in Fig.18. As expected, as the Schmidt
number (Sc) increases, the concentration decreases. 1 .2
The influence of the permeability parameter (K) on
the concentration field is shown in Fig.19. It is
noticed that the concentration increases 1 .0
monotonically with the increase of the permeability G t = 2 .0 ,4 .0 ,6 .0 ,8 .0
parameter. The influence of the Eckert number Ec on
0 .8
the concentration field is shown in Fig.20. It is
noticed that the concentration decreases f '
monotonically with the increase of the Eckert number 0 .6
Ec.
In order to benchmark our numerical results, the
0 .4
present results for the Skin-friction coefficient,
Nusselt number, Sherwood number in the absence of
both permeability parameter and Eckert number for 0 .2
various values of M, Gt, Gc, Fw and Sc are compared
with those of Ibrahim and Makinde [23] and found
them in excellent agreement as demonstrated in Table 0 .0
0 1 2 3 4
1. From Table 2, it is found that the local skin friction
together with the local heat and mass transfer rates at
the moving plate increases with increasing intensity
of buoyancy forces (Gt or Gc) or the Schmidt number Fig.2: Variation of the velocity f with Gt
(Sc), However, an increase in the magnetic field (M) for Pr=0.72, Sc=0.62, Gc =2, Ec=0.1,
or magnitude of fluid suction (Fw), permeability M=K=0.1.
parameter (K) or Eckert number (Ec) causes a
decrease in both the skin friction and surface heat
transfer rates and an increase in the surface mass
transfer rate.
152 | P a g e
5. M.Prasanna Lakshmi, N. Bhaskar Reddy, T.Poornima / International Journal of Engineering
Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue 5, September- October 2012, pp.149-159
1 .2 1.0
1 .0
G c = 2 .0 ,4 .0 ,6 .0 ,8 .0 0.8
K = 0 .1 ,1 .0 ,2 .0 ,3 .0
0 .8
f' 0.6
0 .6 f '
0.4
0 .4
0 .2
0.2
0 .0 0.0
0 1 2 3 4 0 1 2 3 4
Fig.3: Variation of the velocity f with Gc for Fig .5: Variation of the velocity f with K
Pr=0.72, Sc=0.62, Gt =2, Ec=0.1, Fw =M=K=0.1. for Pr=0.72, Sc=0.62, Gt=Gc =2, Ec=0.1,
Fw =M=0.1.
1.0
1.0
0.8 S c = 0 .2 4 ,0 .6 2 ,0 .7 8 ,2 .6 2
0.8
E c = 0 .1 ,1 .0 ,2 .0 ,3 .0
0.6
0.6
f'
f '
0.4
0.4
0.2
0.2
0.0
0 1 2 3 4 0.0
0 1 2 3 4
Fig.4: Variation of the velocity f with Sc
for Pr=0.72, Gt=Gc =2, Ec=0.1, Fw =M=K=0.1. Fig .6: Variation of the velocity f with Ec
for Pr=0.72, Sc=0.62, Gt=Gc =2,
K = Fw =M=0.1.
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Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue 5, September- October 2012, pp.149-159
1.0 1.0
0.8 0.8
0.6 0.6
M = 0 .1 ,1 .0 ,2 .0 ,3 .0
0.4 0.4
G c = 2 .0 ,4 .0 ,6 .0 ,8 .0
0.2 0.2
0.0 0.0
0 1 2 3 4 0 1 2 3 4
Fig.7: Variation of the temparatue θ with M Fig.9: Variation of the temperature θ with Gc
for Pr=0.72, Sc=0.62, Gt =Gc =2, Ec=0.1, for Pr=0.72, Sc=0.62, Gt =2, Ec =0.1,
Fw =K=0.1. Fw =M=K=0.1.
1.0
1.0
0.8
0.8
0.6
0.6
F w = 0 .1 ,0 .5 ,1 .0 ,2 .0
0.4 0.4
G t = 2 .0 ,4 .0 ,6 .0 ,8 .0
0.2 0.2
0.0 0.0
0 1 2 3 4 0 1 2 3 4
Fig.10: Variation of the temperature θ with Fw
Fig.8: Variation of the temperature θ with Gt for Pr=0.72, Sc=0.62, Gc =Gt =2, Ec=0.1,
for Pr=0.72, Sc=0.62, Gc =2, Ec =0.1, M=K=0.1.
Fw =M=K=0.1.
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Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue 5, September- October 2012, pp.149-159
1.0 1.0
0.8 0.8
0.6 0.6
E c = 0 .1 ,1 .0 ,2 .0 ,3 .0
0.4 0.4
S c = 0 .2 4 ,0 .6 2 ,0 .7 8 ,2 .6 2
0.2 0.2
0.0 0.0
0 1 2 3 4 0 1 2 3 4
Fig.13: Variation of the temperature θ with Ec
Fig.11: Variation of the temperature θ with Sc For Pr=0.72, Sc=0.62, Gt =Gc =2, Fw =M=0.1,
For Pr=0.72, Gt =Gc=2, Ec=0.1, Fw =M=K=0.1. K=0.1.
1.0 1.0
0.8 0.8
0.6 0.6
M = 0 .1 ,1 .0 ,2 .0 ,3 .0
0.4 K = 0 .1 ,1 .0 ,2 .0 ,3 .0 0.4
0.2 0.2
0.0 0.0
0 1 2 3 4 0 1 2 3 4
Fig.12: Variation of the temperature θ with K Fig.14: Variation of the concentration with M
for Pr=0.72, Sc=0.62, Gt =Gc=2, Ec=0.1, For Pr=0.72, Sc=0.62, Gt =Gc =2, Ec=0.1,
Fw=M=0.1. Fw =K=0.1.
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Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue 5, September- October 2012, pp.149-159
1.0 1.0
0.8 0.8
0.6
0.6
G t = 2 .0 ,4 .0 ,6 .0 ,8 .0
0.4 F w = 0 .1 ,0 .5 ,1 .0 ,2 .0
0.4
0.2
0.2
0.0
0 1 2 3 4 0.0
0 1 2 3 4
Fig.15: Variation of the concentration with Gt
for Pr=0.72, Sc=0.62, M=0.1, Gc =2, Ec=0.1, Fig.17: Variation of the concentration with Fw
Fw =K=0.1.
for Pr=0.72,Sc=0.62,Gt=Gc=2,Ec=0.1, M=K=0.1.
1.0 1.0
0.8 0.8
0.6
0.6
S c = 0 .2 4 ,0 .6 2 ,0 .7 8 ,2 .6 2
0.4
0.4 G c = 2 .0 ,4 .0 ,6 .0 ,8 .0
0.2
0.2
0.0
0.0
0 1 2 3 4 0 1 2 3 4
Fig.18: Variation of the concentration with Sc
Fig.16: Variation of the concentration with Gc for Pr=0.72 Gt=Gc =2, Ec=0.1, Fw =M=K=0.1.
for Pr=0.72, Sc=0.62, Gt=2, Ec=0.1
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9. M.Prasanna Lakshmi, N. Bhaskar Reddy, T.Poornima / International Journal of Engineering
Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue 5, September- October 2012, pp.149-159
1.0 1.0
0.8
0.8
0.6
0.6
K = 0 .1 ,1 .0 ,2 .0 ,3 .0 0.4 E c = 0 .1 ,1 .0 ,2 .0 ,3 .0
0.4
0.2
0.2
0.0
0 1 2 3 4
0.0
0 1 2 3 4
Fig.20: Variation of the concentration with Ec
Fig.19: Variation of the concentration with K
for Pr=0.72, Sc=0.62, Gt =Gc =2, K= Fw =M=0.1.
for Pr=0.72, Sc=0.62, Gt =Gc =2, Ec=0.1,
Fw=M=0.1.
Table 1 Computations showing comparison with Ibrahim and Makinde [23] results for
f ''(0) , '(0) , '(0) at the plate with Gr , Gc , M , Fw , Sc for Pr =0.72, K=0, Ec=0.
Gr Gc M Fw Sc Ibrahim and Makinde [23] Present work
f ''(0) '(0) '(0) f ''(0) '(0) '(0)
0.1 0.1 0.1 0.1 0.62 0.888971 0.7965511 0.7253292 0.897945 0.805082 0.740192
0.5 0.1 0.1 0.1 0.62 0.695974 0.8379008 0.7658018 0.70684 0.841012 0.773803
1.0 0.1 0.1 0.1 0.62 0.475058 0.8752835 0.8020042 0.485886 0.876165 0.806773
0.1 0.5 0.1 0.1 0.62 0.686927 0.8421370 0.7701717 0.699552 0.843609 0.776285
0.1 1.0 0.1 0.1 0.62 0.457723 0.8818619 0.8087332 0.470894 0.880875 0.811303
0.1 0.1 1.0 0.1 0.62 1.264488 0.7089150 0.6400051 1.2696 0.734784 0.675272
0.1 0.1 3.0 0.1 0.62 1.868158 0.5825119 0.5204793 1.87194 0.63906 0.588803
0.1 0.1 0.1 1.0 0.62 0.570663 0.5601256 0.5271504 0.575823 0.566525 0.537923
0.1 0.1 0.1 3.0 0.62 0.275153 0.2955702 0.2902427 0.00301923 0.143197 0.143829
0.1 0.1 0.1 0.1 0.78 0.893454 0.7936791 0.8339779 0.901088 0.803798 0.841183
0.1 0.1 0.1 0.1 2.62 0.912307 0.7847840 1.6504511 0.918401 0.797633 1.64733
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10. M.Prasanna Lakshmi, N. Bhaskar Reddy, T.Poornima / International Journal of Engineering
Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue 5, September- October 2012, pp.149-159
Table 2 Variation of f ''(0) , '(0) , '(0) at [5] Huges W.F. and Young F.J. (1966), The
Electro-Magneto Dynamics of fluids, John
the porous plate with K, Ec for Gr = Gc =2, M =
Wiley and Sons, New York.
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K Ec f ''(0) '(0) '(0) Int. J. Energy Res., Vol.10, pp.97-101.
0.1 0.1 0.94395 0.761108 0.731902 [7] Helmy K.A. (1998), MHD unsteady free
0.5 0.1 1.11587 0.72043 0.701346 convection flow past a vertical porous
1.0 0.1 1.30489 0.676969 0.669635 plate, ZAMM, Vol.78, pp.255-270.
1.5 0.1 1.47298 0.639974 0.64341 [8] Elabashbeshy E.M.A. (1997), Heat and
2.0 0.1 1.62552 0.60796 0.621302 mass transfer along a vertical plate with
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0.1 2.0 0.932094 0.116807 0.735831 [9] Chamkha A.J. and Khaled A.R.A. (2001),
Similarity solutions for hydromagnetic
5. CONCLUSIONS simultaneous heat and mass transfer by
From the present study, we arrive at the natural convection from an inclined plate
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By comparing the present results with absorption, Heat Mass Transfer, Vol.37,
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An increase in the Eckert number causes convection from an isothermal vertical
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