This document summarizes a study that analyzes magnetohydrodynamic (MHD) flow of Newtonian and non-Newtonian nanofluids passing over a magnetic sphere. Nanofluids containing alumina or copper nanoparticles in water or oil bases were examined. Governing equations for continuity, momentum, and energy were derived and non-dimensionalized. The equations were transformed into similarity equations using a stream function and solved numerically. Results showed that increasing the magnetic parameter decreases velocity and temperature. Newtonian nanofluid velocity and temperature were higher than non-Newtonian. Copper-water nanofluid also had higher values than alumina-water.
Effect of Mass Transfer and Hall Current on Unsteady MHD Flow with Thermal Di...IJERA Editor
The paper investigated the effect of mass transfer and Hall current on unsteady MHD flow with Thermal Diffusivity of a viscoelastic fluid in a porous medium. The resultant equations have been solved analytically. The velocity, temperature and concentration distributions are derived, and their profiles for various physical parameters are shown through graphs. The coefficient of Skin friction, Nusselt number and Sherwood number at the plate are derived and their numerical values for various physical parameters are presented through tables. The influence of various parameters such as the thermal Grashof number, mass Grashof number, Schmidt number, Prandtl number, viscoelasticity parameter, Hartmann number, Hall parameter, and the frequency of oscillation on the flow field are discussed. It is seen that, the velocity increases with the increase in Gc, Gr, m and K, and it decreases with increase in Sc,M, n and Pr, temperature decreases with increase in Pr and n, Also, the concentration decreases with the increase in Sc and n.
Non-Darcy Convective Heat and Mass Transfer Flow in a Vertical Channel with C...IJERA Editor
In this paper, We made an attempt to study thermo-diffusion and dissipation effect on non-Darcy convective
heat and Mass transfer flow of a viscous fluid through a porous medium in a vertical channel with Radiation and
heat sources. The governing equations of flow, heat and mass transfer are solved by using regular perturbation
method with δ, the porosity parameter as a perturbation parameter. The velocity, temperature, concentration,
shear stress and rate of Heat and Mass transfer are evaluated numerically for different variations of parameter.
Effect of Magnetic Field on Peristaltic Flow of Williamson Fluid in a Symmetr...IOSRJM
This paper deals with the influence of magnetic field on peristaltic flow of an incompressible Williamson fluid in a symmetric channel with heat and mass transfer. Convective conditions of heat and mass transfer are employed. Viscous dissipation and Joule heating are taken into consideration.Channel walls have compliant properties. Analysis has been carried out through long wavelength and low Reynolds number approach. Resulting problems are solved for small Weissenberg number. Impacts of variables reflecting the salient features of wall properties, concentration and heat transfer coefficient are pointed out. Trapping phenomenon is also analyzed.
Abstract— A scientific investigation is created to examine the nonlinear unfaltering blended convection limit
layer stream and warmth exchange of an incompressible digression hyperbolicnon-Newtonian liquid from a
non-isothermal wedge in the nearness of attractive field. The changed preservation conditions are understood
numerically subject to physically fitting limit conditions utilizing a second-arrange precise verifiable limited
distinction Keller Box method. The numerical code is accepted with past studies. The impact of various rising
non-dimensional parameters, to be specific Weissenberg number (We), power law record (n), blended
convection parameter, weight angle parameter (m), Prandtl number (Pr), Biot number, attractive parameter
(M)and dimensionless extraneous direction on speed and temperature development in the limit layer
administration are inspected in subtle element. Moreover, the impacts of these parameters on surface warmth
exchange rate and nearby skin erosion are additionally examined. Approval with prior Newtonian studies is
introduced and amazing relationship accomplished. It is found that speed is lessened with expanding We,
while, temperature is increased. Expanding n improves speed yet diminishes temperature, a comparable
pattern was seen. An expanding M is found to decline speed however temperature increments.
Keywords— Magnetic parameter, Mixed Convection parameter, Non-Newtonian digression hyperbolic liquid,
power law index, Weissenberg number, Weight inclination parameter.
Effect of Mass Transfer and Hall Current on Unsteady MHD Flow with Thermal Di...IJERA Editor
The paper investigated the effect of mass transfer and Hall current on unsteady MHD flow with Thermal Diffusivity of a viscoelastic fluid in a porous medium. The resultant equations have been solved analytically. The velocity, temperature and concentration distributions are derived, and their profiles for various physical parameters are shown through graphs. The coefficient of Skin friction, Nusselt number and Sherwood number at the plate are derived and their numerical values for various physical parameters are presented through tables. The influence of various parameters such as the thermal Grashof number, mass Grashof number, Schmidt number, Prandtl number, viscoelasticity parameter, Hartmann number, Hall parameter, and the frequency of oscillation on the flow field are discussed. It is seen that, the velocity increases with the increase in Gc, Gr, m and K, and it decreases with increase in Sc,M, n and Pr, temperature decreases with increase in Pr and n, Also, the concentration decreases with the increase in Sc and n.
Non-Darcy Convective Heat and Mass Transfer Flow in a Vertical Channel with C...IJERA Editor
In this paper, We made an attempt to study thermo-diffusion and dissipation effect on non-Darcy convective
heat and Mass transfer flow of a viscous fluid through a porous medium in a vertical channel with Radiation and
heat sources. The governing equations of flow, heat and mass transfer are solved by using regular perturbation
method with δ, the porosity parameter as a perturbation parameter. The velocity, temperature, concentration,
shear stress and rate of Heat and Mass transfer are evaluated numerically for different variations of parameter.
Effect of Magnetic Field on Peristaltic Flow of Williamson Fluid in a Symmetr...IOSRJM
This paper deals with the influence of magnetic field on peristaltic flow of an incompressible Williamson fluid in a symmetric channel with heat and mass transfer. Convective conditions of heat and mass transfer are employed. Viscous dissipation and Joule heating are taken into consideration.Channel walls have compliant properties. Analysis has been carried out through long wavelength and low Reynolds number approach. Resulting problems are solved for small Weissenberg number. Impacts of variables reflecting the salient features of wall properties, concentration and heat transfer coefficient are pointed out. Trapping phenomenon is also analyzed.
Abstract— A scientific investigation is created to examine the nonlinear unfaltering blended convection limit
layer stream and warmth exchange of an incompressible digression hyperbolicnon-Newtonian liquid from a
non-isothermal wedge in the nearness of attractive field. The changed preservation conditions are understood
numerically subject to physically fitting limit conditions utilizing a second-arrange precise verifiable limited
distinction Keller Box method. The numerical code is accepted with past studies. The impact of various rising
non-dimensional parameters, to be specific Weissenberg number (We), power law record (n), blended
convection parameter, weight angle parameter (m), Prandtl number (Pr), Biot number, attractive parameter
(M)and dimensionless extraneous direction on speed and temperature development in the limit layer
administration are inspected in subtle element. Moreover, the impacts of these parameters on surface warmth
exchange rate and nearby skin erosion are additionally examined. Approval with prior Newtonian studies is
introduced and amazing relationship accomplished. It is found that speed is lessened with expanding We,
while, temperature is increased. Expanding n improves speed yet diminishes temperature, a comparable
pattern was seen. An expanding M is found to decline speed however temperature increments.
Keywords— Magnetic parameter, Mixed Convection parameter, Non-Newtonian digression hyperbolic liquid,
power law index, Weissenberg number, Weight inclination parameter.
International Journal of Mathematics and Statistics Invention (IJMSI)inventionjournals
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.
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.
Slow steady motion of a thermo viscous fluid between two parallel plates with...eSAT Journals
Abstract
In this paper, the slow steady motion of a second order thermo-viscous fluid between two parallel plates is examined. The closed form
solutions of the velocity and temperature distributions are obtained when thermo-stress coefficient is far less compared to strain
thermal conductivity coefficient and coefficient of cross viscosity for the following two cases: (i) when the upper plate is in relative
motion and (ii) when the upper plate is thermally insulated. The heat transfer coefficient on the upper plate , The mean Bulk
temperature and the transverse force perpendicular to the flow direction are also calculated. It is observed that forces are generated
in transverse directions which are special feature of these types of fluids. The effect of various flow parameters on the flow field have
been discussed with the help of graphical illustrations.
Keywords: Thermo-viscous fluids, Strain thermal conductivity coefficient and Thermo stress Coefficient.
Non-Linear Water Wave Equation Time Series Formulated Using Velocity Equation...IJERA Editor
This article developed a model of time series wave where during the formulation velocity equations as the result of Laplace theory was done. As the result of this method, the continuity equation was substituted to momentum equation, or in other words momentum equation produces a velocity controlled by continuity equation, since Laplace equation comes from continuity equation. Using this method, the concept of calculation velocity at the momentum equation was also developed where calculation velocity is equal to average velocity of the depth of the Airy long wave equation
Integration of Finite Element Method with Runge – Kuta Solution AlgorithmIJERA Editor
Runge – Kuta (RK) method is reasonably simple and robust for numerical solution of differential equations but it requires an intelligent adaptive step-size routine; to achieve this, there is need to develop a good logical computer code. This study develops a finite element code in Java using Runge-Kuta method as a solution algorithm to predict dynamic time response of structural beam under impulse load. The solution obtained using direct integration and the present work is comparable.
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.
Exact Solutions of the Klein-Gordon Equation for the Q-Deformed Morse Potenti...ijrap
In this work, we solve the Klein-Gordon (KG) equation for the general deformed Morse potential with
equal scalar and vector potentials by using the Nikiforov-Uvarov (NU) method, which is based on the
solutions of general second-order linear differential equation with special functions. The energy
eigenvalues and corresponding normalized eigenfunctions are obtained. It is found that the eigenfunctions
can be expressed by the Laguerre polynomials. Our solutions have a good agreement with earlier study.
The peer-reviewed International Journal of Engineering Inventions (IJEI) is started with a mission to encourage contribution to research in Science and Technology. Encourage and motivate researchers in challenging areas of Sciences and Technology.
Influence of MHD on Unsteady Helical Flows of Generalized Oldoyd-B Fluid betw...IJERA Editor
Considering a fractional derivative model for unsteady magetohydrodynamic (MHD)helical flows of an
Oldoyd-B fluid in concentric cylinders and circular cylinder are studied by using finite Hankel and Laplace
transforms .The solution of velocity fields and the shear stresses of unsteady magetohydrodynamic
(MHD)helical flows of an Oldoyd-B fluid in an annular pipe are obtained under series form in terms of
Mittag –leffler function,satisfy all imposed initial and boundary condition , Finally the influence of model
parameters on the velocity and shear stress are analyzed by graphical illustrations.
Analytical Solution Of Schrödinger Equation With Mie–Type Potential Using Fac...ijrap
we have obtained the analytical solution of Schrödinger wave equation with Mie – type potential
using factorization method. We have also obtained energy eigenvalues of our potential and the
corresponding wave function using an ansatz and then compare the result to standard Laguerre’s
differential equation. Under special cases our potential model reduces two well known potentials such as
Coulomb and the Kratzer Feus potentials.
Two-dimension curvature of a wire: A simple model using shear modulus conceptSparisoma Viridi
Observation of wire bending can give information about shear modulus of the system, A model based on definition of shear modulus is constructed and tested for arbitrary parameters and also for nanowire.
NEW SCENARIO FOR TRANSITION TO SLOW 3-D TURBULENCE PART I.SLOW 1-D TURBULENCE...ijrap
Analyticalnon-perturbative study of thethree-dimensional nonlinear stochastic partialdifferential equation
with additive thermal noise, analogous to thatproposed by V.N.Nikolaevskii [1]-[5] to describelongitudinal
seismic waves, ispresented. Theequation has a threshold of short-waveinstability and symmetry, providing
longwavedynamics.New mechanism of quantum chaos generating in nonlineardynamical systemswith
infinite number of degrees of freedom is proposed. The hypothesis is said,that physical turbulence could be
identifiedwith quantum chaos of considered type. It is shown that the additive thermal noise destabilizes
dramatically the ground state of theNikolaevskii system thus causing it to make a direct transition from a
spatially uniform to a turbulent state.
Weighted Analogue of Inverse Maxwell Distribution with ApplicationsPremier Publishers
In the present study, we established a new statistical model named as weighted inverse Maxwell distribution (WIMD). Its several statistical properties including moments, moment generating function, characteristics function, order statistics, shanon entropy has been discussed. The expression for reliability, mode, harmonic mean, hazard rate function has been derived. In addition, it also contains some special cases that are well known. Moreover, the behavior of probability density function (p.d.f) has been shown through graphs by choosing different values of parameters. Finally, the performance of the proposed model is explained through two data sets. By which we conclude that the established distribution provides better fit.
Effects of Hall and thermal on MHD Stokes’ second problem for unsteady second...IJERA Editor
In this paper, we investigated the combined effects of Hall and thermal on MHD Stokes’ second problem for
unsteady second grade fluid flow through 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 in detail with the aid of graphs.
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.
Unsteady MHD Flow Past A Semi-Infinite Vertical Plate With Heat Source/ Sink:...IJERA Editor
In the present paper a numerical attempt is made to study the combined effects of heat source and sink on unsteady laminar boundary layer flow of a viscous, incompressible, electrically conducting fluid along a semiinfinite vertical plate. A magnetic field of uniform strength is applied normal to the flow. The governing boundary layer equations are solved numerically, using Crank-Nicolson method. Graphical results of velocity and temperature fields, tabular values of Skin-friction and Nusselt are presented and discussed at various parametric conditions. From this study, it is found that the velocity and temperature of the fluid increase in the presence of heat source but they decrease in the presence of heat absorption parameter.
International Journal of Mathematics and Statistics Invention (IJMSI)inventionjournals
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.
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.
Slow steady motion of a thermo viscous fluid between two parallel plates with...eSAT Journals
Abstract
In this paper, the slow steady motion of a second order thermo-viscous fluid between two parallel plates is examined. The closed form
solutions of the velocity and temperature distributions are obtained when thermo-stress coefficient is far less compared to strain
thermal conductivity coefficient and coefficient of cross viscosity for the following two cases: (i) when the upper plate is in relative
motion and (ii) when the upper plate is thermally insulated. The heat transfer coefficient on the upper plate , The mean Bulk
temperature and the transverse force perpendicular to the flow direction are also calculated. It is observed that forces are generated
in transverse directions which are special feature of these types of fluids. The effect of various flow parameters on the flow field have
been discussed with the help of graphical illustrations.
Keywords: Thermo-viscous fluids, Strain thermal conductivity coefficient and Thermo stress Coefficient.
Non-Linear Water Wave Equation Time Series Formulated Using Velocity Equation...IJERA Editor
This article developed a model of time series wave where during the formulation velocity equations as the result of Laplace theory was done. As the result of this method, the continuity equation was substituted to momentum equation, or in other words momentum equation produces a velocity controlled by continuity equation, since Laplace equation comes from continuity equation. Using this method, the concept of calculation velocity at the momentum equation was also developed where calculation velocity is equal to average velocity of the depth of the Airy long wave equation
Integration of Finite Element Method with Runge – Kuta Solution AlgorithmIJERA Editor
Runge – Kuta (RK) method is reasonably simple and robust for numerical solution of differential equations but it requires an intelligent adaptive step-size routine; to achieve this, there is need to develop a good logical computer code. This study develops a finite element code in Java using Runge-Kuta method as a solution algorithm to predict dynamic time response of structural beam under impulse load. The solution obtained using direct integration and the present work is comparable.
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.
Exact Solutions of the Klein-Gordon Equation for the Q-Deformed Morse Potenti...ijrap
In this work, we solve the Klein-Gordon (KG) equation for the general deformed Morse potential with
equal scalar and vector potentials by using the Nikiforov-Uvarov (NU) method, which is based on the
solutions of general second-order linear differential equation with special functions. The energy
eigenvalues and corresponding normalized eigenfunctions are obtained. It is found that the eigenfunctions
can be expressed by the Laguerre polynomials. Our solutions have a good agreement with earlier study.
The peer-reviewed International Journal of Engineering Inventions (IJEI) is started with a mission to encourage contribution to research in Science and Technology. Encourage and motivate researchers in challenging areas of Sciences and Technology.
Influence of MHD on Unsteady Helical Flows of Generalized Oldoyd-B Fluid betw...IJERA Editor
Considering a fractional derivative model for unsteady magetohydrodynamic (MHD)helical flows of an
Oldoyd-B fluid in concentric cylinders and circular cylinder are studied by using finite Hankel and Laplace
transforms .The solution of velocity fields and the shear stresses of unsteady magetohydrodynamic
(MHD)helical flows of an Oldoyd-B fluid in an annular pipe are obtained under series form in terms of
Mittag –leffler function,satisfy all imposed initial and boundary condition , Finally the influence of model
parameters on the velocity and shear stress are analyzed by graphical illustrations.
Analytical Solution Of Schrödinger Equation With Mie–Type Potential Using Fac...ijrap
we have obtained the analytical solution of Schrödinger wave equation with Mie – type potential
using factorization method. We have also obtained energy eigenvalues of our potential and the
corresponding wave function using an ansatz and then compare the result to standard Laguerre’s
differential equation. Under special cases our potential model reduces two well known potentials such as
Coulomb and the Kratzer Feus potentials.
Two-dimension curvature of a wire: A simple model using shear modulus conceptSparisoma Viridi
Observation of wire bending can give information about shear modulus of the system, A model based on definition of shear modulus is constructed and tested for arbitrary parameters and also for nanowire.
NEW SCENARIO FOR TRANSITION TO SLOW 3-D TURBULENCE PART I.SLOW 1-D TURBULENCE...ijrap
Analyticalnon-perturbative study of thethree-dimensional nonlinear stochastic partialdifferential equation
with additive thermal noise, analogous to thatproposed by V.N.Nikolaevskii [1]-[5] to describelongitudinal
seismic waves, ispresented. Theequation has a threshold of short-waveinstability and symmetry, providing
longwavedynamics.New mechanism of quantum chaos generating in nonlineardynamical systemswith
infinite number of degrees of freedom is proposed. The hypothesis is said,that physical turbulence could be
identifiedwith quantum chaos of considered type. It is shown that the additive thermal noise destabilizes
dramatically the ground state of theNikolaevskii system thus causing it to make a direct transition from a
spatially uniform to a turbulent state.
Weighted Analogue of Inverse Maxwell Distribution with ApplicationsPremier Publishers
In the present study, we established a new statistical model named as weighted inverse Maxwell distribution (WIMD). Its several statistical properties including moments, moment generating function, characteristics function, order statistics, shanon entropy has been discussed. The expression for reliability, mode, harmonic mean, hazard rate function has been derived. In addition, it also contains some special cases that are well known. Moreover, the behavior of probability density function (p.d.f) has been shown through graphs by choosing different values of parameters. Finally, the performance of the proposed model is explained through two data sets. By which we conclude that the established distribution provides better fit.
Effects of Hall and thermal on MHD Stokes’ second problem for unsteady second...IJERA Editor
In this paper, we investigated the combined effects of Hall and thermal on MHD Stokes’ second problem for
unsteady second grade fluid flow through 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 in detail with the aid of graphs.
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.
Unsteady MHD Flow Past A Semi-Infinite Vertical Plate With Heat Source/ Sink:...IJERA Editor
In the present paper a numerical attempt is made to study the combined effects of heat source and sink on unsteady laminar boundary layer flow of a viscous, incompressible, electrically conducting fluid along a semiinfinite vertical plate. A magnetic field of uniform strength is applied normal to the flow. The governing boundary layer equations are solved numerically, using Crank-Nicolson method. Graphical results of velocity and temperature fields, tabular values of Skin-friction and Nusselt are presented and discussed at various parametric conditions. From this study, it is found that the velocity and temperature of the fluid increase in the presence of heat source but they decrease in the presence of heat absorption parameter.
International Journal of Engineering and Science Invention (IJESI)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.
Effect of an Inclined Magnetic Field on Peristaltic Flow of Williamson Fluid ...QUESTJOURNAL
ABSTRACT: This paper deals with the influence ofinclined magnetic field on peristaltic flow of an incompressible Williamson fluid in an inclined channel with heat and mass transfer. Viscous dissipation and Joule heating are taken into consideration.Channel walls have compliant properties. Analysis has been carried out through long wavelength and low Reynolds number approach. Resulting problems are solved for small Weissenberg number. Impacts of variables reflecting the salient features of wall properties, concentration and heat transfer coefficient are pointed out. Trapping phenomenon is also analyzed.
Study of Magnetohydrodynamic Fluid Flows and Their Applicationsijtsrd
In this paper a detailed study is presented on magnetohydrodynamic fluid flows with their basic governing equations. Basic concept of magnetohydrodynamic is discussed in detail. The results of various problems done by researchers are presented and addressed properly. The various applications of magnetohydrodynamic fluid flows have been presented. Dr. Vishal Saxena ""Study of Magnetohydrodynamic Fluid Flows and Their Applications"" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-4 | Issue-2 , February 2020, URL: https://www.ijtsrd.com/papers/ijtsrd29931.pdf
Paper Url : https://www.ijtsrd.com/mathemetics/applied-mathematics/29931/study-of-magnetohydrodynamic-fluid-flows-and-their-applications/dr-vishal-saxena
Similarity Solution of an Unsteady Heat and Mass Transfer Boundary Layer Flow...iosrjce
The unsteady hydromagnetic boundary layer flow of an incompressible and electrically conducting
fluid through a porous medium bounded by a moving surface has been considered. It is assumed that the moving
surface has a velocity profile with respect to time and fluid flow is taken under the influence of a transverse
magnetic field. The similarity solution is used to transform the system of partial differential equations,
describing the problem under consideration, into a boundary value problem of coupled ordinary differential
equations and an efficient numerical technique is implemented to solve the reduced system. The effects of the
parameters such as Magnetic parameter, Prandtl number and Eckert number are discussed graphically on
velocity and temperature distributions
Thermal Energy on Water and Oil placed Squeezed Carreau Nanofluids FlowMOHAMMED FAYYADH
this research work is focused on the numerical study regarding Carreau nanofluids’ squeezed flow via a permeable sensor surface. The nanofluids’ thermal conductivity is considered to be dependent on temperature. A convenient transformation is employed to reorganize governing equations into ordinary differential equations. The Runge–Kutta method and shooting technique are employed to accurately solve the boundary layer momentum as well as heat equations. Graphical and tabular aids are used to evaluate the solutions of applicable parameter with regards to temperature as well as the rate of heat transfer. In this work, a comparison is done from three nanofluids, i.e. copper, oxide aluminum and SWCNTs (nanoparticles) based fluids (water, crude oil and ethylene glycol) to improve heat transfer. It is found that the temperature dimensionless was dropped and dominated with the squeezed flow parameter and nanoparticle volume fraction parameter. That is for all nanomaterials. When compared with water and ethylene glycol, crude oil is cooler and a thinner thermal boundary layer is presented. For the rate of heat transfer (Nusselt number) was higher in: Ethylene glycol- SWCNT with high permeable velocity parameter 0.2, Ethylene glycol- SWCNT with low squeeze flow parameter 0.1 and Ethylene glycol- oxide aluminum with low nanoparticle volume fraction 0.05
The effect of magnetic field on the boundary layer flow over a stretching she...IAEME Publication
The boundary layer flow created due to a linearly stretching sheet in a nanofluid is studied numerically. The boundary value problem consisting of nonlinear partial differential equations are converted into nonlinear ordinary differential equations, using similarity transformation and are solved numerically using Runge-Kutta Fourth order method, with shooting technique. The transport equations include the effects of Brownian motion and thermophoresis.
GDQ SIMULATION FOR FLOW AND HEAT TRANSFER OF A NANOFLUID OVER A NONLINEARLY S...AEIJjournal2
This paper presents the generalized differential quadrature (GDQ) simulation for analysis of a nanofluid
over a nonlinearly stretching sheet. The obtained governing equations of flow and heat transfer are
discretized by GDQ method and then are solved by Newton-Raphson method. The effects of stretching
parameter, Brownian motion number (Nb), Thermophoresis number (Nt) and Lewis number (Le), on the
concentration distribution and temperature distribution are evaluated. The obtained results exhibit that
Similar to MHD Newtonian and non-Newtonian Nano Fluid Flow Passing On A Magnetic Sphere with Mixed Convection Effect (20)
In order to study the WGS on an industrial scale at a low pressure, the modeling andsimulation of a WGS reactor operating at a pressure close to Patm and processing an industrial charge in the presence of a high temperature shift catalyst (Fe2O3/Cr2O3) were performed. The Profiles of the carbon monoxide conversion, temperature and pressure along the reactor were obtained. The effect of several operating parameters (inlet temperature, H2O/CO ratio) on the conversion of carbon monoxide along the reactor has been determined. The estimated catalytic mass to convert 60.5% of the carbon monoxide contained in the inlet is 170.76 t. The pressure drops in the reactor are not negligible and the maximum temperaturereached is without any harmful effect on the catalyst. The choice of an optimal inlet temperature and a high H2O/CO ratio improves the conversion of carbon monoxide.
As we are all aware,therecent discovery of the Higgs boson has revealed a highly massive particle, the value of which lies between 125and 126.5 GeV/c2.. According to the basic concepts of Quantum Mechanics, and in full compliance with the Uncertainty Principle and Yukawa intuitions, we were able to calculate the maximum limit of the Higgs boson‟s field of action. From the calculations show that the Higgs boson presents a range of action really very small, namely 9.8828∙10-16[cm], that is slightly smaller than 10-15[cm]. This value is justified by the considerable mass that the Higgs bosonacquires, in perfect agreement with the Uncertainty Principle.
The dependencies of total pressure, velocity, vorticity, turbulent length, turbulent dissipation, turbulent viscosity, turbulent energy and turbulent time of moving fluid from a straight pipe length of a circular cross section are presented in graphical and mathematical forms. Changing analysis of considered parameters was performed at mass flow rates of 0.45, 1.0 and 1.5 kg/s. A transition boundary of laminar flow of fluid to turbulent flow is at the distance of 2/5 of length from the inlet of the pipe (at accepted total length of the pipe of 1000 mm).
Building materials used for the walls of simple houses in lower-middle-class areas in Indonesia are currently dominated by brick. This study proposes that soil-paper blocks coated with calcium silicate board may be a suitable alternative, with high embodied energy and density. The research aims to obtain an optimal wall thickness to provide protection against cooling and embodied energy in low income houses, as well as against the temperature conditions in these buildings in highland and lowland areas. Determination of wall thickness is performed by simulation of a 9 m2 building model with thick variables. Cooling calculations involved the use of Archipak software. Temperature measurements were carried out using a data logger on a sample of soil-paper blocks. The results indicate that the optimal wall thickness for protection against cooling and embodied energy is 8 cm. Soil-paper block has a lower density than brick. The use of calcium silicate boards does not affect the internal temperature of a low income house, but they can be used as protection against rainwater and as a substitute for wall plastering.
Adaptive-optimal control involves re-identification of the machining process and the model obtained is used to calculate the optimal process parameters.
Optimal control characterizes the addiction of the technical and economic indicators to process parameters. Characteristic for performance technical indicators is that their dependence to parameter values of process has a limitative, what leads to one of the following conclusions, appropriately or inappropriately, and therefore can serve as restrictions in optimization problem.
Economic indicators have a continuous dependence of process parameters and therefore they are used as objective functions.
Knowledge management (KM) has become an effective way of managing organization‟s intellectual capital or, in other words, organization‟s full experience, skills and knowledge that is relevant for more effective performance in future. The paper proposes a knowledge management to achieve a competitive control of the machining systems. Then an application of Knowledge Management in engineering has been attempted to explain. The model can be used by the manager for the choosing of competitive orders.
Ceftriaxone is one of the third generations of cephalosporin antibiotics and commercially found as a sodium salt. The market demand for it is still high in recent years, including in Indonesia. However, there is no local production manufacture yet. A high yield of ceftriaxone sodium would be an advantage in industrial scale. Ceftriaxone was synthesized by reacting 7–amino–3–[(2,5–dihydro–6–hydroxy–2–methyl–5–oxo–1,2,4–triazin–3–yl) thiomethyl] cephalosporanic acid (7-ACT) with 2-Mercaptobenzothiazolyl (Z)-2-(2-Aminothiazole-4-yl)-2-Methoxyimino Acetate (MAEM) then with sodium salt in basic condition. The product was generated by solventing-out using acetone. The products were analyzed by HPLC quantitatively and the structure was confirmed using FTIR, MS and NMR. In this research, the variation in the mole ratio of reactants against the yield of product was evaluated. The result showed that the variations in mole ratio reactants affect the yield production. The higher ratio of MAEM would be the higher yield is obtained. The results show that the yield was 72,17% at mole ratio 1:2 which has 99,32% purity. This result could be a consideration in industrial production scale in ceftriaxone sodium preparation.
The challenges of river water quality management are so enormous, due to the unpredictive modes of contamination. Monitoring different sources of pollutant load contribution to the river basin is also quite tasking, resulting to laborious and expensive process which sometimes lead to analytical errors. This study deals with the assessment of the physico– chemicaland bacteriological parameters of water samples from River Amba during the period of August 2017 to January 2018 and developing regression models. Water quality Parameters such as Temperature, Turbidity (NTU), Suspended solids (mg/l), Colour, Total solids, Total dissolved solids, Electrical conductivity (μs/cm), pH, Hardness, Chemical Oxygen Demand, Dissolved Oxygen (DO), and Total Coliform were obtained and compared with water quality standards. The results of the water quality analysis of the study in comparison with drinking water quality standard issued byWorld Health Organization(WHO) and National Agency for Food and Drug Administration Control (NAFDAC) revealed that most of the water quality parameters were not adequate to pronounce the water potable. Hence adequate water treatment processes should be employed to make the water fit for consumption and other domestic uses. Statistical analysis was done, in which the systematic correlation and regressionanalysis showed a significant linear relationship between different pairs of water quality parameters. The highest correlation coefficient between different pairs of parameters obtained is (r = 0.999), resulting from the correlation between TS and SS. Multiple regression analysis was also carried out and regression equations were developed. It was observed that the parameters studied had a positive correlation with each other.
Time, in the globalized world, is one of the most important factors about the economy, science and health. Mankind has made various efforts to use time efficiently for many years. In these studies transport came to the fore and it has become indispensable. In the light of today's technological conditions, air transport is developing at an increasing rate. Every day many aircrafts are produced, which have different speeds, weight and volume, for serve to transport. Therefore to make structures for easy and safe transport need a stable soil. Particularly suitable areas for the airport grounds in cities today, not being physically proper that construction of the airport made on soil with low bearing capacity, swelling potential of an expansive soil, settlement of soil etc, areas. In this study, soil problems encountered in the construction of airports will be explained and a summary of studies on the solution of these problems will be presented.
People in a big city as Antananarivo, capital of Madagascar, have leads to take street foods for their daily nutritional needs. This food habits may be a risk for consumers due to contaminations from street environment and bad practices related to hygiene. This study aimed to examine the quality and safety of street vended foods in Antananarivo, on January 2016 to December 2017.Six hundred and sixty two samples including 126samples of melting salads, 70 beef skewers, 54 chicken skewers, and typical Malagasy foods as : mofoanana (67 samples), mofogasy (64 samples), ramanonaka (64), makasaoka (66), mofoakondro (62) and kobandravina(89);were randomly collected from the streetvendors in Antananarivo marketsto evaluate their bacteriological quality.International Methods (ISO) was adopted for to find the load of Total Aerobic Bacteria andEnterobateriaceae,Escherichia coli and to search pathogen bacteria as Salmonella, Campylobacter jejuni, Escherichia coli O157H7 and Bacillus cereus in these foods.The results revealed that the mean values ofthe Total Aerobic Bacteria count was 0.1x106- 4.8x106cfu/g. Enterobacteriaceaecount range from 0.4x102 to 1.9x102cfu/g. Escherichia coli count range from 0.04x102cfu/g. to 0.19 x102cfu/g.Salmonellawas only present in melting salads, beef skewers and chicken skewers samples. Bacillus cereus count range from 0,1x102 to 1,5x102cfu/g. Campylobacter jejuniwas only present in samples of ramanonaka and kobandravina. Two strains of presumptive Eschercichia coli O157 H7 (βglucuronidase -) were isolated. PCR method was used to confirm the identity of these two isolates. A high contamination above 106 cfu/g food and the presence of potential pathogens bacteria could be hazardous. Systematic inspections and training of food vendors on food hygiene and application of hazard analysis critical control point (HACCP) has been recognised as measures to guarantee improvement of the quality of street foods.
In order to clean up soils contaminated with hydrocarbons, the bioremediation activity of Pseudomonas putida was studied. Pseudomonas putida is a bacterium that can withstand the harshest environmental conditions. It is able to metabolize a wide range of petroleum hydrocarbons which is used as a source of carbon and energy. Given the potential of this microorganism, an experiment wasconducted on this strain.
For the isolation of this microorganism, a sample ofsoil from the Vakinankaratra region in the urban commune of Antsirabe II, Madagascar was microbiologically analysed. The bacterial identification was based on a study of the morphological, physicochemical and sequential analysis of the 16S rDNA gene.
Scored tablets provide dose flexibility, ease of swallowing and cost savings. However, some problems with scored tablets can be confronted like difficulty of breaking, unequally breaking and loss of mass upon breaking. This paper investigates the effect of score lines on the density distribution using continuum modelling. In keeping with previous work in the pharmaceutical field, a modified Drucker Prager Cap model is described briefly and used in the simulations. Coulomb friction is included between powder and tools. The microcrystalline cellulose (MCC) Vivapur® 102 was used to identify the model parameters using experimental tests with instrumented die, shear cell and diametrical crushing. The obtained results indicate that simulations may be useful not only to determine density distributions within tablets, but also may provide indications about performance of score lines.
In a plethora of countries, buildings are adapted to the local climate condition using sustainable architecture techniques and materials, thereby the highest level of climatic comfort is provided. For example, the walls and roofs reflecting sunlight have been used for centuries in the warm regions of the world, while in the cold regions, the maximum use of solar energy has been tended.
The process of modernization has created a high density, thereby demand for fast and affordable constructions in cities has subsequently increased, resulting in reduced attention to environmentally sustainable architecture techniques that, in turn, has led to the financial loss and scarcity of non-renewable energy resources over long periods of time.
Regarding the energy crisis and the necessity of saving non-renewable energy, the reduced need to use heating/cooling systems is assumed to be one of the key goals in advanced building design.
The present study was conducted based on causal research and simulation. Design Builder thermal simulation software was used as the tool to this end. Therefore, a building with/out solar chimney was modeled and analyzed to identify the effect of solar chimney on the amount of energy used for heating.
The control of motor rotation speed by the change of resistor resistance value in armature circuit is called ‘resistor control”. For the regulation of resistance value R0, included in armature winding circuit, we can use various technical solutions. The most used solution is the discrete variation of armature added resistance value by shunting its parts with contactors contacts. Nowadays, the change of resistor resistance in armature circuit can be realized by shunting with a given porosity γ of resistor R0 trough electronic keys. In this paper, we study the design of control system represented on figure 1.
A poultry yield prediction model have then designed using a data mining and machine learning technique called Classification and Regression Tree (CART) algorithm. The developed model has been optimized and pruned using the Reduced Error Pruning (REP) algorithm to improve prediction accuracy. An algorithm to make the prediction model flexible and capable of making predictions irrespective of poultry size or population has been proposed. The model can be used by poultry farmers to predict yield even before a breeding season. The model can also be used to help farmers take decisions to ensure desirable yield at the end of the breeding season.
Today, Web site design is used to make sites useful to users, with accessible functions, resources and information. Therefore, that design involves use of methodologies that allow an adequate structuring of them resources and organization, permitting users to access them quickly, easily and intuitively. This research consisted of a usability study oriented to website structure designers using a methodology based on concepts of ontology design. This study includes a planning to evaluate the design and the structure of website in aspects such as: ease of use, efficient access to information and performance on the tasks focused to total satisfaction of end user. Heuristic tests were used as diagnostic tools to evaluate usability of website design structures; these were supported by a heuristic evaluation guide and in the Sirius methodology[3]. The results obtained from them, allowed us to detect opportunities for improvement and optimization in website design, and in refining the Web interface oriented to end users.
Acceptance of a website is determined by various factors, one of the most important is the organization that allows users to access to functions, resources and information that it contains. This work consisted of a study of comparative usability between a website designed using principles of linguistics and design of ontologies and other using a strategy of a commercial product. A plan was designed and applied to evaluate the following aspects of website: ease of use, efficiency to access its information, efficacy to perform tasks and user satisfaction. Heuristic and user tests were used as diagnostic tools in usability evaluations, and an observation guide was made by an external evaluator as a complement to previous tests. The results clearly shown that is better use the proposed website design methodology. This allows to create site more structured, functional and with greater ease of access to resources that it contain.
Epoxidized sunflower oil (ESO) has been used to toughen epoxy resin GELR 128 cured with an accelerated aliphatic amine curing agent (Kingcure K-11) at room temperature. There was difference in the properties of the polymer composite materials based on epoxy resin GELR 128 cured by Kingcure K-11 between two processes: one-stage process and two-stage process for mixing ESO with epoxy resin GELR 128 at various content of ESO. The results showed that the two-stage process is considered to be more advantageous than the one-stage process. It can be concluded that the impact strength, critical stress intensity factor Kic and decomposition temperature of the polymer composite materials based on epoxy resin GELR 128 cured by Kingcure K-11 with content of ESO 5 phr in two-stage process was greater ones in one-stage process (impact strength: 35.012 kJ/m2, Kic: 2.72 MPa and decomposition temperature: 385.81 0C respectively).
A Network Intrusion Detection System (NIDS) monitors a network for malicious activities or policy violations [1]. The Kernel-based Virtual Machine (KVM) is a full virtualization solution for Linux on x86 hardware virtualization extensions [2]. We design and implement a back-propagation network intrusion detection system in KVM. Compared to traditional Back Propagation (BP) NIDS, the Particle Swarm Optimization (PSO) algorithm is applied to improve efficiency. The results show an improved system in terms of recall and precision along with missing detection rates.
In this paper, we consider the scaling invariant spaces for fractional Navier-Stokes in the
Lebesgue spaces ( ) p n L R and homogeneous Besov spaces
, ( ) s n
p q B R respectively.
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MHD Newtonian and non-Newtonian Nano Fluid Flow Passing On A Magnetic Sphere with Mixed Convection Effect
1. International Journal of Innovation Engineering and Science Research
www.ijiesr.com
Volume 2 Issue 6 November-December 2018 26|P a g e
ABSTRACT
MHD Newtonian and non-Newtonian Nano Fluid
Flow Passing On A Magnetic Sphere with Mixed
Convection Effect
Basuki Widodo, Yolanda Norasia, Dieky Adzkiya
Department of Mathematics, Faculty of Mathematics, Computing, and Data Sciences
Institut Teknologi Sepuluh Nopember
Indonesia
This paper considers the problem of magneto-hydrodynamics (MHD) Newtonian and non-Newtonian nano fluid
flow passing on a magnetic sphere with mixed convection effect. Nano Fluid is a combination of liquid fluid as a
base fluid with small solid nano particles. Water is chosen as Newtonian base fluid and oil is chosen as non-
Newtonian base fluid. Then, Alumina and Copper are chosen as solid particle in nano fluid. We further construct
governing equation by applying continuity equation, momentum equation, and energy equation to obtain
dimensional governing equations. The dimensional governing equations that have been obtained are converted
into non-dimensional governing equations by substituting non-dimensional variables. The non-dimensional
governing equations are further transformed into similarity equations using stream function and solved
numerically using Euler Implicit Finite Difference method. We further analyse the effect of magnetic parameter
towards velocity and temperature in MHD nano fluid flow. The results show that the increases of magnetic
parameter impacts to the decrease of velocity and temperature. Then, the velocity and temperature of Newtonian
nano fluid are higher than the velocity and temperature of non-Newtonian nano fluid. Also, the velocity and
temperature of copper-water are higher than the velocity and temperature of Alumina-water.
Keywords—Newtonian and non-Newtonian nano fluid; MHD; Sphere; Euler Implicit Finite Difference.
I. INTRODUCTION
Nano fluid is a combination of liquid fluid as a base fluid with small solid nano particles [1]. Nano fluid is
divided into two types, i.e. Newtonian nano fluid and non-Newtonian nano fluid. Newtonian nano fluid is
a base fluid in nano fluid which has a linear relationship between viscosity and shear stress. However,
non-Newtonian nano fluid is the opposite of Newtonian nano fluid. In this paper, water is chosen as
Newtonian base fluid and oil is chosen as non-Newtonian base fluid. Then, Alumina (𝐴𝑙2 𝑂3) and
Copper (𝐶𝑢) are chosen as solid particle in nano fluid. Alumina (𝐴𝑙2 𝑂3) contains metal oxide and
copper (𝐶𝑢) contains metal. These types of fluids are used in industrial area that needs for heating and
cooling based on heat transfer [2].
Because of those, we conduct a research how to analyse MHD nano fluid flow problem using
numerical simulation based on mathematical modelling. Putra et al [3] have illustrated the natural
convection of nano-fluids. Their investigations stated that the thermal conductivity of solid nano
particles can be increased when mixed with base fluid. Wen and Ding [4] have discussed about
experimental investigation into convection heat transfer of nano fluids at the entrance region under
laminar flow conditions. Akbar et al [5] have investigated unsteady MHD nano fluid flow through a
channel with moving porous walls and medium by using Runge Kutta. The results show that the heat
transfer rate increases and mass transfer rate decreases with the increase of Reynolds number. Mahat
et al [6] also have observed mixed convection boundary layer flow past a horizontal circular cylinder in
visco-elastic nano fluid with constant wall temperature and solved numerically by using the Keller-Box
2. Basuki Widodo et al. “International Journal of Innovation Engineering and Science Research”
Volume 2 Issue 6 November-December 2018 27|P a g e
method. The results indicate that the velocity and temperature are increased by increasing the values
of nano particles volume fraction and mixed convection parameter. Juliyanto et al [7] also have solved
the problem of the effect of heat generation on mixed convection in nano fluids over a horizontal
circular cylinder numerically by using Keller-Box method. The result of their investigations show that
the velocity increase and temperature decrease when mixed convection parameter increases. In the
present paper, we are interested to develop mathematical modelling of the problem of MHD newtonian
and non-newtonian nano fluid flow passing on a magnetic sphere with mixed convection effect. The
influence of magnetic parameter ( 𝑀), mixed convection parameter ( 𝜆), and volume fraction (𝜒) towards
velocity and temperature in Newtonian and non-Newtonian nano fluid are investigated.
II. MATHEMATICAL FORMULATION
The unsteady MHD Newtonian and non-Newtonian nano fluid flow passing on a magnetic sphere with
mixed convection effect is considered. Fig. 1illustrates the physical model of the problem and the
coordinate system used to develop the mathematical model. The fluid used is Newtonian nano fluid
and non-Newtonian nano fluid. The bluff body used is a magnetic sphere with radius a. The flow of
nano fluid is assumed laminar flow and incompressible. The magnetic Reynolds number is assumed to
be very small. Therefore, there is no electrical voltage which makes electric field. With potential theory,
where the velocity potential is perpendicular with stream function, so the 3D dimensional governing
equations can be transform into 2D dimensional governing equations.
Fig. 1 Physical model and coordinate system
Based on the physical model and coordinate system, unsteady MHD Newtonian and non-Newtonian
nano fluid flow passing on a magnetic sphere is illustrated in Fig. 1. The 2D dimensional governing
equations are developed from the law of conservation mass, the second law of Newton, and the first
law of Thermodynamics. We further obtain continuity equation, momentum equation, and energy
equation, which can be written as follows:
Continuity Equation:
𝜕𝑟 𝑢
𝜕𝑥
+
𝜕𝑟 𝑣
𝜕𝑦
= 0 (1)
Momentum Equation :
at x axis
𝜌𝑓𝑛
𝜕𝑢
𝜕𝑡
+ 𝑢
𝜕𝑢
𝜕𝑥
+ 𝑣
𝜕𝑢
𝜕𝑦
= −
𝜕𝜌
𝜕 𝑥
+ 𝜇 𝑓𝑛
𝜕2 𝑢
𝜕𝑥2 +
𝜕2 𝑢
𝜕𝑦2 + 𝜎𝐵0
2
𝑢 − 𝜌𝑓𝑛 𝛽 𝑇 − 𝑇∞ 𝑔 𝑥 (2)
3. Basuki Widodo et al. “International Journal of Innovation Engineering and Science Research”
Volume 2 Issue 6 November-December 2018 28|P a g e
aty axis
𝜌𝑓𝑛
𝜕𝑢
𝜕𝑡
+ 𝑢
𝜕𝑢
𝜕𝑥
+ 𝑣
𝜕𝑢
𝜕𝑦
= −
𝜕𝜌
𝜕 𝑥
+ 𝜇 𝑓𝑛
𝜕2 𝑢
𝜕𝑥2 +
𝜕2 𝑢
𝜕𝑦2 + 𝜎𝐵0
2
𝑢 − 𝜌𝑓𝑛 𝛽 𝑇 − 𝑇∞ 𝑔 𝑦 (3)
Energy Equation :
𝜕𝑇
𝜕𝑡
+ 𝑢
𝜕𝑇
𝜕𝑥
+ 𝑣
𝜕𝑇
𝜕𝑦
= 𝛼𝑓𝑛
𝜕2 𝑇
𝜕𝑥2 +
𝜕2 𝑇
𝜕𝑦2 (4)
With the initial and boundary condition as follows :
𝑡 = 0: 𝑢 = 𝑣 = 0, 𝑇 = 𝑇∞, for every𝑥, 𝑦
𝑡 > 0: 𝑢 = 𝑣 = 0, 𝑇 = 𝑇𝑤 ,for𝑦 = 0
𝑢 = 𝑢 𝑒 𝑥 , 𝑢 = 𝑣 = 0, 𝑇 = 𝑇∞as𝑦 → ∞
where𝜌𝑓𝑛 is density of nano fluid, 𝜇 𝑓𝑛 is dynamic viscosity of nano fluid, 𝑔is the gravitational
acceleration, and 𝛼𝑓𝑛 is thermal diffusivity of nano fluid. In addition, the value of 𝑟is defined as
𝑟 𝑥 = 𝑎 sin(𝑥 /𝑎).
Further, the 2D dimensional governing equations (1)-(4) are transformed into non-dimensional
equations by using both non-dimensional parameters and variables. In this problem, the non-
dimensional variables are given as in [7], i.e.:
𝑥 =
𝑥
𝑎
; 𝑦 = 𝑅𝑒1/2
𝑦
𝑎
; 𝑡 =
𝑈∞ 𝑡
𝑎
; 𝑢 =
𝑢
𝑈∞
𝑣 = 𝑅𝑒1/2
𝑢
𝑈∞
; 𝑟(𝑥) =
𝑟(𝑥)
𝑎
where𝑔 𝑥and 𝑔 𝑦are defined as in [7]
𝑔 𝑥 = −𝑔 𝑠𝑖𝑛
𝑥
𝑎
𝑔 𝑦 = 𝑔 𝑐𝑜𝑠
𝑥
𝑎
Boundary layer theory [8] is applied to non-dimensional governing equation. We obtain the following
results
Continuity Equation
𝜕(𝑟𝑢 )
𝜕𝑥
+
𝜕(𝑟𝑣)
𝜕𝑦
= 0 (5)
Momentum Equation
atx axis
𝜕𝑢
𝜕𝑡
+ 𝑢
𝜕𝑢
𝜕𝑥
+ 𝑣
𝜕𝑢
𝜕𝑦
= −
𝜕𝑝
𝜕𝑥
+
𝑣 𝑛𝑓
𝑣 𝑓
∂2 𝑢
∂𝑦2 + 𝑀𝑢 + 𝜆𝑇𝑠𝑖𝑛 𝑥 (6)
aty axis
−
𝜕𝑝
𝜕𝑦
= 0 (7)
Energy Equation
𝜕𝑇
𝜕𝑡
+ 𝑢
𝜕𝑇
𝜕𝑥
+ 𝑣
𝜕𝑇
𝜕𝑦
=
1
𝑃𝑟
𝛼 𝑓𝑛
𝛼 𝑓
𝜕2 𝑇
𝜕𝑦2 (8)
4. Basuki Widodo et al. “International Journal of Innovation Engineering and Science Research”
Volume 2 Issue 6 November-December 2018 29|P a g e
where these nano fluid constants are defined as [9], i.e. :
Density of nanofluid :
𝜌𝑓𝑛 = 1 − 𝜒 𝜌𝑓 + 𝜒𝜌𝑠
Dynamic viscosity :
𝜇 𝑛𝑓 = 𝜇 𝑓
1
(1 − 𝜒)2.5
Specific heat :
(𝜌𝐶𝑝) 𝑛𝑓 = 1 − 𝜒 (𝜌𝐶𝑝) 𝑓 + 𝜒(𝜌𝐶𝑝)𝑠
Heat conductivity :
𝑘 𝑛𝑓 =
𝑘 𝑠 + 2𝑘𝑓 − 2𝜒(𝑘𝑓 − 𝑘 𝑠)
𝑘 𝑠 + 2𝑘𝑓 + 𝜒(𝑘𝑓 − 𝑘 𝑠)
𝑘𝑓
The thermo-physical properties of nano particles and base fluid is given in Table 1 [10].
TABLE I. THERMO-PHYSICAL PROPERTIES
Properties Water Oil Cu 𝑨𝒍 𝟐 𝑶 𝟑
density 997.1 884 8933 3970
specific heat of constant
pressure
4179 1900 385 765
thermal conductivity 0.613 0.145 400 40
We substitute those nano fluid constants into (6) and (8). We obtain
Momentum Equation :
𝜕𝑢
𝜕𝑡
+ 𝑢
𝜕𝑢
𝜕𝑥
+ 𝑣
𝜕𝑢
𝜕𝑦
= −
𝜕𝑝
𝜕𝑥
+
1
1−𝜒 2.5
1
1−𝜒 +𝜒
𝜌 𝑠
𝜌 𝑓
∂2 𝑢
∂𝑦2 + 𝑀𝑢 + 𝜆𝑇𝑠𝑖𝑛 𝑥 (9)
And
Energy equation :
𝜕𝑇
𝜕𝑡
+ 𝑢
𝜕𝑇
𝜕𝑥
+ 𝑣
𝜕𝑇
𝜕𝑦
=
1
𝑃𝑟
𝑘 𝑠+2𝑘 𝑓−2𝜒(𝑘 𝑠−𝑘 𝑓)
𝑘 𝑠+2𝑘 𝑓+𝜒(𝑘 𝑠−𝑘 𝑓)
1
1−𝜒 +𝜒
(𝜌𝐶 𝑝 ) 𝑠
(𝜌𝐶 𝑝 ) 𝑓
𝜕2 𝑇
𝜕𝑦2 (10)
Further, by converting (9) and (10) into non-similarity equations using stream function, which is given
as follows [11]
𝑢 =
1
𝑟
𝜕𝜓
𝜕𝑦
𝑣 = −
1
𝑟
𝜕𝜓
𝜕𝑥
Where
𝜓 = 𝑡
1
2 𝑢 𝑒 𝑥 𝑟 𝑥 𝑓 𝑥, 𝜂, 𝑡 ,
𝜂 =
𝑦
𝑡
1
2
,
5. Basuki Widodo et al. “International Journal of Innovation Engineering and Science Research”
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𝑇 = 𝑠 𝑥, 𝜂, 𝑡
The equation (9) and (10) are modified by substituting stream function as follows:
Momentum Equation :
1
1−𝜒 2.5 1−𝜒 +
𝜌 𝑠
𝜌 𝑓
𝜕3 𝑓
𝜕𝜂3 +
𝜂 𝜕2 𝑓
2𝜕𝜂2 + 𝑡
𝜕𝑢 𝑒
𝜕𝑥
1 −
𝜕𝑓
𝜕𝜂
2
+ 𝑓
𝜕2 𝑓
𝜕𝜂2) = 𝑡
𝜕2 𝑓
𝜕𝜂𝜕𝑡
+ 𝑡𝑢 𝑒
𝜕𝑓
𝜕𝜂
𝜕2 𝑓
𝜕𝑥𝜕𝜂
−
𝜕𝑓
𝜕𝑥
𝜕2 𝑓
𝜕𝜂2 −
1
𝑟
𝜕𝑟
𝜕𝑥
𝑓
𝜕2 𝑓
𝜕𝜂2 +
𝑀𝑡 1 −
𝜕𝑓
𝜕𝜂
−
𝜆𝑠𝑡
𝑢 𝑒
sin 𝑥 (11)
Energy Equation :
𝑘 𝑠+2𝑘 𝑓−2𝜒 𝑘 𝑠−𝑘 𝑓
𝑘 𝑠+2𝑘 𝑓+𝜒 𝑘 𝑠−𝑘 𝑓
1
1−𝜒 +𝜒
(𝜌𝐶 𝑝 ) 𝑠
𝜌𝐶 𝑝 𝑓
𝜕2 𝑠
𝜕𝜂2 + 𝑃𝑟
𝜂
2
𝜕𝑠
𝜕𝜂
+ Pr 𝑡
𝜕𝑢 𝑒
𝜕𝑥
𝑓
𝜕𝑠
𝜕𝜂
= 𝑃𝑟 𝑡
𝜕𝑠
𝜕𝜂
+ 𝑢 𝑒
𝜕𝑓
𝜕𝜂
𝜕𝑠
𝜕𝑥
−
𝜕𝑓
𝜕𝑥
𝜕𝑠
𝜕𝜂
−
1
𝑟
𝜕𝑟
𝜕𝑥
𝑓
𝜕𝑠
𝜕𝜂
(12)With the initial and boundary condition are as follows :
𝑡 = 0 ∶ 𝑓 =
𝜕𝑓
𝜕𝜂
= 𝑠 = 0untuksetiap𝑥, 𝜂
𝑡 > 0 ∶ 𝑓 =
𝜕𝑓
𝜕𝜂
= 0 , 𝑠 = 1ketika𝜂 = 0
𝜕𝑓
𝜕𝑦
= 1 , 𝑠 = 0ketika𝜂 → ∞
By substituting local free stream for sphere case [12],𝑢 𝑒 =
3
2
sin 𝑥 into (11) and (12) respectively, we
obtain
Momentum Equation :
1
1−𝜒 2.5 1−𝜒 +
𝜌 𝑠
𝜌 𝑓
𝜕3 𝑓
𝜕𝜂3 +
𝜂 𝜕2 𝑓
2𝜕𝜂2 +
3
2
𝑡 cos 𝑥 1 −
𝜕𝑓
𝜕𝜂
2
+ 2𝑓
𝜕2 𝑓
𝜕𝜂2) = 𝑡
𝜕2 𝑓
𝜕𝜂𝜕𝑡
+
3
2
𝑡 sin 𝑥
𝜕𝑓
𝜕𝜂
𝜕2 𝑓
𝜕𝑥𝜕𝜂
−
𝜕𝑓
𝜕𝑥
𝜕2 𝑓
𝜕𝜂2 +
𝑀𝑡 1 −
𝜕𝑓
𝜕𝜂
−
2
3
𝜆𝑠𝑡 (13)
Energy Equation :
𝑘 𝑠+2𝑘 𝑓−2𝜒 𝑘 𝑠−𝑘 𝑓
𝑘 𝑠+2𝑘 𝑓+𝜒 𝑘 𝑠−𝑘 𝑓
1
1−𝜒 +𝜒
(𝜌𝐶 𝑝 ) 𝑠
𝜌𝐶 𝑝 𝑓
𝜕2 𝑠
𝜕𝜂2 + 𝑃𝑟
𝜂
2
𝜕𝑠
𝜕𝜂
+ 3 𝑐𝑜𝑠 𝑥𝑃𝑟 𝑡 𝑓
𝜕𝑠
𝜕𝜂
= 𝑃𝑟 𝑡
𝜕𝑠
𝜕𝜂
+ Pr 𝑡
3
2
sin 𝑥
𝜕𝑓
𝜕𝜂
𝜕𝑠
𝜕𝑥
−
𝜕𝑓
𝜕𝑥
𝜕𝑠
𝜕𝜂
(14)
III. NUMERICAL PROCEDURES
MHD Newtonian and non-Newtonian nano fluid flow passing on a magnetic sphere with mixed
convection effect have been investigated numerically by using Euler Implicit Finite Difference method.
he set of similarity equation and boundary condition are discretized by a second order central
difference method and solved by a computer program which has been developed.
Momentum Equation :
1
1 − 𝜒 2.5( 1 − 𝜒 + 𝜒
𝜌 𝑠
𝜌 𝑓
)
𝜕2
𝑢
𝜕𝜂2
+
𝜂
2
𝜕𝑢
𝜕𝜂
+
3
2
𝑡 1 − 𝑢 2
+ 𝑓
𝜕𝑢
𝜕𝜂
= 𝑡
𝜕𝑢
𝜕𝑡
+ 𝑀𝑡 1 − 𝑢 −
2
3
𝜆𝑠𝑡
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𝐿𝑖 =
𝑘 𝑠 + 2𝑘𝑓 − 2𝜒(𝑘𝑓 − 𝑘 𝑠)
( 𝑘 𝑠 + 2𝑘𝑓 + 𝜒 𝑘𝑓 − 𝑘 𝑠 )( 1 − 𝜒 +
𝜒 𝜌(𝐶𝑝) 𝑠
𝜌(𝐶𝑝) 𝑓
1
∆𝜂2
𝑠𝑖+1
𝑛
− 2𝑠𝑖
𝑛
+ 𝑠𝑖−1
𝑛
+
1
4
𝑃𝑟
𝜂𝑖
∆𝜂
3𝑠𝑖+1
𝑛
− 4𝑠𝑖
𝑛
+ 𝑠𝑖−1
𝑛
+ 3 Pr
𝑡 𝑛+1
2∆𝜂
𝑓𝑖
𝑛
3𝑠𝑖+1
𝑛
− 4𝑠𝑖
𝑛
+ 𝑠𝑖−1
𝑛
and for
𝐵0 =
1
4
𝜂𝑖
∆𝜂
+
3
2
𝑃𝑟 𝑡 𝑛+1
𝑓𝑖
𝑛
∆𝜂
𝐵1 =
𝑘 𝑠+2𝑘 𝑓 −2𝜒(𝑘 𝑓−𝑘 𝑠)
( 𝑘 𝑠+2𝑘 𝑓 +𝜒 𝑘 𝑓−𝑘 𝑠 )( 1−𝜒 +
𝜒 𝜌 (𝐶𝑝 ) 𝑠
𝜌 (𝐶𝑝 ) 𝑓
∆𝜂2
+ 𝐵0
𝐵2 =
3
2
𝑃𝑟
𝑡 𝑛+1
∆𝑡
+ 2
𝑘 𝑠+2𝑘 𝑓 −2𝜒(𝑘 𝑓−𝑘 𝑠)
( 𝑘 𝑠+2𝑘 𝑓 +𝜒 𝑘 𝑓−𝑘 𝑠 )( 1−𝜒 +
𝜒 𝜌 (𝐶𝑝 ) 𝑠
𝜌 (𝐶𝑝 ) 𝑓
∆𝜂2
+4𝐵0
𝐵3 =
𝑘 𝑠+2𝑘 𝑓 −2𝜒(𝑘 𝑓−𝑘 𝑠)
( 𝑘 𝑠+2𝑘 𝑓 +𝜒 𝑘 𝑓−𝑘 𝑠 )( 1−𝜒 +
𝜒 𝜌 (𝐶𝑝 ) 𝑠
𝜌 (𝐶𝑝 ) 𝑓
∆𝜂2
+ 3𝐵0
IV. RESULTS AND DISCUSSION
In this research, the effect of magnetic parameter (M) to velocity and temperature in Newtonian and
non-Newtonian nano fluid are analyzed.
Fig. 2 Velocity Profile of Cu-Oil and Cu-Water with Magnetic Influence
Water is chosen as Newtonian base fluid and oil is chosen as non-Newtonian base fluid.
Then, Alumina (𝐴𝑙2 𝑂3) and Copper (Cu) are chosen as solid particle in nano fluid. The numerical
results of the velocity and temperature with respect to the position in front of the lower stagnation at
8. Basuki Widodo et al. “International Journal of Innovation Engineering and Science Research”
Volume 2 Issue 6 November-December 2018 33|P a g e
the point 𝑥 = 0°
with value of magnetic parameters 𝑀 = 1 are depicted in Fig. 2 and Fig. 3
respectively.
Fig. 3 Temperature Profile of Cu-Oil and Cu-Water with Magnetic Influence
Fig. 2 shows the velocity profiles of the MHD Newtonian and non-Newtonian nano fluid flow
passing on a magnetic sphere with mixed convection effect. Cu-oil is used as non-Newtonian nano
fluid and Cu-water is used as Newtonian nao fluid. The results show that the velocity of Newtonian
nano fluid is higher than the velocity of non-Newtonian nano fluid. Also, Fig. 3 shows that the
temperature of Newtonian nano fluid is higher than the temperature of non-Newtonian nano fluid.
Fig. 4 Velocity Profile of Cu-Water and 𝐴𝑙2 𝑂3-Water with Magnetic Influence
Fig. 4 and Fig. 5 show the velocity profiles and temperature profiles of Cu-Water and 𝐴𝑙2 𝑂3-
water respectively. Alumina (𝐴𝑙2 𝑂3) contains metal oxide and copper (Cu) contains metal. The results
show that the velocity of Cu-Water is higher than the velocity of 𝐴𝑙2 𝑂3-water. Fig. 5 also shows that
the temperature of Cu-water is higher than the temperature of 𝐴𝑙2 𝑂3-water.
9. Basuki Widodo et al. “International Journal of Innovation Engineering and Science Research”
Volume 2 Issue 6 November-December 2018 34|P a g e
Fig. 5 Temperature Profile of Cu-Water and 𝐴𝑙2 𝑂3-Water with Magnetic Influence
The numerical results of the velocity and temperature in Newtonian nano fluid Cu-Water with
respect to the position in front of the lower stagnation at the point 𝑥 = 0°
with various value of
magnetic parameters 𝑀 = 0, 1, 3, and 5are illustrated in Fig. 6 and Fig. 7 respectively.
Fig. 6 shows the velocity profiles of the MHD Newtonian nano fluid Cu-Water flow passing on
a magnetic sphere at various M when mixed convection parameter 𝜆 = 1and volume fraction 𝜒 = 0.1.
The results show that velocity and temperature of Newtonian nano fluid Cu-Water in Fig. 6 and Fig. 7
decrease when magnetic parameter increases. The magnetic parameter represents the presence of
Lorentz force in a magnetic sphere. Therefore, when magnetic parameter increases, then the Lorentz
force also increases. It impacts to decrease of the velocity and temperature in Newtonian nano fluid
Cu-Water.
Fig. 6 Velocity Profile for various M of Cu-Water
The numerical results of the velocity and temperature in non-Newtonian nano fluid Cu-Oil with respect
to the position in front of the lower stagnation at the point 𝜒 = 0.1with various value of magnetic
parameters 𝑀 = 0, 1, 3, and 5 are illustrated in Fig. 8 and Fig. 9 respectively.
10. Basuki Widodo et al. “International Journal of Innovation Engineering and Science Research”
Volume 2 Issue 6 November-December 2018 35|P a g e
Fig. 7 Temperature Profile for various M of Cu-Water
Fig. 8 Velocity Profile for various M of Cu-O
Fig. 8 shows the velocity of the MHD non Newtonian nano fluid Cu-Oil flow passing on a magnetic
sphere at various M when mixed convection parameter 𝜆 = 1 and volume fraction 𝜒 = 0.1. Fig. 9
shows the temperature of the MHD non Newtonian nano fluid Cu-Oil flow passing on a magnetic
sphere at various M when mixed convection parameter 𝜆 = 1and volume fraction 𝜒 = 0.1.The results in
Fig. 8 and Fig. 9 show that velocity profiles and temperature profiles of non-Newtonian nano fluid Cu-
Oil decrease when magnetic parameter increases.
11. Basuki Widodo et al. “International Journal of Innovation Engineering and Science Research”
Volume 2 Issue 6 November-December 2018 36|P a g e
Fig. 9 Temperature Profile for various M of Cu-Oil
V. CONCLUSIONS
MHD Newtonian and non-Newtonian nano fluid flow passing on a magnetic sphere with mixed
convection effect have been investigated numerically by using Euler Implicit Finite Difference method.
We have considered water as Newtonian base fluid and oil is chosen as non-Newtonian base fluid.
Further, Alumina (𝐴𝑙2 𝑂3) and Copper (Cu) are chosen as solid particle in nano fluid. We further obtain
numerical results that when effects of magnetic parameter, mixed convection parameter, and volume
fraction are included, the velocity and temperature profiles change. It is concluded that the velocity
and temperature of Newtonian nano fluid Cu-water are higher than the velocity and temperature of
non-Newtonian nanofluid Cu-Oil. The velocity and temperature of copper-water Cu-Water also are
higher than the velocity and temperature of Alumina-water 𝐴𝑙2 𝑂3-Water. Further, the velocity profiles
and temperature profiles of Newtonian Cu-Water and non-Newtonian nano fluid Cu-Oil decrease
when magnetic parameter increases.
ACKNOWLEDGMENT
This research is supported by the Institute for Research and Community Services,
InstitutTeknologiSepuluhNopember (ITS) Surabaya, Indonesia with Funding Agreement Letter number
970/PKS/ITS/2018. We further are very grateful to LPPM-ITS for giving us a chance to submit this
paper in an International Journal.
REFERENCES
[1] Y. Ding, Y. Chen, Y. He, A. Lapkin, M.Yeganeh, L.Siller, Y. V.Butenko, “Heat Transfer Intensification Using Nanofluids”,
Advanced Powder Technol, 2007, pp.813-24.
[2] S. Das, S. Chakraborty, R. N. Jana, O. D. Makinde, “Entropy analysis of unsteady magneto-nanofluid flow past
accelerating stretching sheet with convective boundary condition” Appl. Math. Mech., 2015, pp.1593-610.
[3] Putra N, Roetzel W, Das S K , “Natural convection of nano-fluids”, Heat and Mass Transfer,2003, pp.775-84.
[4] D. Wen and Y. Ding, “Experimental Investigation into Convective Heat Transfer of Nanofluids at the Entrance Region
under Laminar Flow Conditions”,International journal of heat and mass transfer, 2004, pp.5181-8.
[5] M. Z. Akbar, M. Ashraf, M. F. Iqbal, K. Ali,“Heat and mass transfer analysis of unsteady MHD nanofluid flow through a
channel with moving porous wall and medium.”, AIP Conf Proc, 2016, 045222.
12. Basuki Widodo et al. “International Journal of Innovation Engineering and Science Research”
Volume 2 Issue 6 November-December 2018 37|P a g e
[6] R. Mahat, N. A. Rawi, A. R. M. Kasim, S. Shafie, “Mixed convection boundary layer flow past a horizontal circular
cylinder in viscoelastic nanofluid with constant wall temperature”,Malaysian Journal of Fundamental and Applied
Sciences, 2017, 13(4-1).
[7] B. Juliyanto, B. Widodo, C. Imron, “The effect of heat generation on mixed convection flow in nano fluids over a
horizontal circular cylinder”,IOP Conf. Series, 2018, 012001
[8] B. Widodo,I. Anggriani, C. Imron, “The Characterization of Boundary Layer Flow in The Magnetohydrodynamic
Micropolar Fluid Past A Solid Sphere”, ,International Journal of Advances in Science Engineering and Technology,
2016, pp. 2321-9009.
[9] A. Karimipour, A. H. Nezhad, A. D'Orazio, E. Shirani, “The effects og inclinatipn angle amd Prandtl number on the
mixed convection in the inclined lid driven cavity using lattice Boltzmann method”, Journal of Theoretical and Applied
Mechanics, 2013, pp.447-62.
[10] A. Zaib, A. R. M. Kasim, N. F. Mohammad, S. Shafie, “Unsteady MHD Mixed Convection Stagnantion Point Flow in A
Micropolar Fluid on A Vertical Surface in A Porous Medium with Soret and Dufour Effects”,Heat Transfer Research,
2013, pp.603-20.
[11] B. Widodo, D. K. Arif, D. Aryany, N. Asiyah, F. A. Widjajati,Kamiran, “The effect of magnetohydrodynamic nano fluid
flow through porous cylinder”, AIP Conference Proceedings, 2017, 020069.
[12] N.Freidoonimehr, M. M. Rashidi, S. Mahmud, “Unsteady MHD free convective flow past a permeable stretching vertical
surface in a nano-fluid”, International Journal of Thermal Sciences, 2015, pp.136-45.