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.
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.
Effects of some thermo physical properties on forceAlexander Decker
This document presents research on force convective stagnation point flow over a stretching sheet with convective boundary conditions in the presence of thermal radiation and a magnetic field. Governing equations for the flow are derived and non-dimensionalized. The equations are then solved numerically using a shooting method. Results show that increasing the magnetic field parameter decreases velocity, while increasing the Biot number increases temperature. Temperature is also found to decrease with increasing Eckert number, Prandtl number, and radiation parameter. Skin friction coefficient and local Nusselt number are presented for various parameter values.
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.
Numerical study of mhd boundary layer stagnation point flow and heat transfer...eSAT Publishing House
This document presents a numerical study of magnetohydrodynamic boundary layer stagnation point flow and heat transfer over an exponentially stretching surface with thermal radiation. The governing partial differential equations are transformed into ordinary differential equations using similarity transformations. A Runge-Kutta shooting method is used to solve the coupled non-linear system numerically. The effects of parameters such as the Prandtl number, Grashoff number, Eckert number, and velocity ratio parameter are analyzed through graphs of the velocity and temperature profiles. The results are compared to known solutions to validate the numerical method.
EFFECT OF SLIP PARAMETER OF A BOUNDARY-LAYER FLOW FOR NANOFLUID OVER A VERTIC...IAEME Publication
In this paper we analyze the effect of momentum slip, thermal slip and solutal slip on stagnation point flow of MHD nanofluid towards stretching sheet .The governing partial differential equation of flow, heat and mass transfer on considered flow are converted into the ordinary differential equations by means of similarity trans formations .The resulting equations are solved by the Runge-Kutta fourth order method with efficient shooting technique. Effects of various governing parameters on flow, heat and mass transfer are studied through the plots. The various numerical tables which are calculated and tabulated. A comparison of our present results with a previous study has been done and we found that an excellent agreement is there with the earlier results and of ours.
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.
Unsteady Mhd free Convective flow in a Rotating System with Dufour and Soret ...IOSRJM
This document summarizes numerical analysis of unsteady magnetohydrodynamic (MHD) free convective flow in a rotating system with Dufour and Soret effects. The analysis considers flow through a porous medium along an infinite vertical porous plate. Similarity transformations are used to reduce the governing equations to ordinary differential equations, which are then solved numerically. The effects of varying parameters like the Prandtl number and Dufour number on velocity, temperature, concentration, skin friction, Nusselt number, and Sherwood number are discussed based on graphs of the numerical solutions. Increasing the Prandtl number decreases velocity and temperature but increases concentration, while increasing the Dufour number decreases velocity, temperature,
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.
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.
Effects of some thermo physical properties on forceAlexander Decker
This document presents research on force convective stagnation point flow over a stretching sheet with convective boundary conditions in the presence of thermal radiation and a magnetic field. Governing equations for the flow are derived and non-dimensionalized. The equations are then solved numerically using a shooting method. Results show that increasing the magnetic field parameter decreases velocity, while increasing the Biot number increases temperature. Temperature is also found to decrease with increasing Eckert number, Prandtl number, and radiation parameter. Skin friction coefficient and local Nusselt number are presented for various parameter values.
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.
Numerical study of mhd boundary layer stagnation point flow and heat transfer...eSAT Publishing House
This document presents a numerical study of magnetohydrodynamic boundary layer stagnation point flow and heat transfer over an exponentially stretching surface with thermal radiation. The governing partial differential equations are transformed into ordinary differential equations using similarity transformations. A Runge-Kutta shooting method is used to solve the coupled non-linear system numerically. The effects of parameters such as the Prandtl number, Grashoff number, Eckert number, and velocity ratio parameter are analyzed through graphs of the velocity and temperature profiles. The results are compared to known solutions to validate the numerical method.
EFFECT OF SLIP PARAMETER OF A BOUNDARY-LAYER FLOW FOR NANOFLUID OVER A VERTIC...IAEME Publication
In this paper we analyze the effect of momentum slip, thermal slip and solutal slip on stagnation point flow of MHD nanofluid towards stretching sheet .The governing partial differential equation of flow, heat and mass transfer on considered flow are converted into the ordinary differential equations by means of similarity trans formations .The resulting equations are solved by the Runge-Kutta fourth order method with efficient shooting technique. Effects of various governing parameters on flow, heat and mass transfer are studied through the plots. The various numerical tables which are calculated and tabulated. A comparison of our present results with a previous study has been done and we found that an excellent agreement is there with the earlier results and of ours.
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.
Unsteady Mhd free Convective flow in a Rotating System with Dufour and Soret ...IOSRJM
This document summarizes numerical analysis of unsteady magnetohydrodynamic (MHD) free convective flow in a rotating system with Dufour and Soret effects. The analysis considers flow through a porous medium along an infinite vertical porous plate. Similarity transformations are used to reduce the governing equations to ordinary differential equations, which are then solved numerically. The effects of varying parameters like the Prandtl number and Dufour number on velocity, temperature, concentration, skin friction, Nusselt number, and Sherwood number are discussed based on graphs of the numerical solutions. Increasing the Prandtl number decreases velocity and temperature but increases concentration, while increasing the Dufour number decreases velocity, temperature,
Effects of Variable Viscosity and Thermal Conductivity on MHD free Convection...theijes
This document summarizes a study that numerically investigates the effects of variable viscosity and thermal conductivity on magnetohydrodynamic (MHD) free convection and mass transfer flow over an inclined vertical surface in a porous medium with heat generation. The governing equations are reduced to ordinary differential equations using similarity transformations and then solved numerically using a shooting method. The results show that increasing the viscosity variation parameter, thermal conductivity parameter, magnetic parameter, permeability parameter, or Schmidt number decreases the fluid velocity, while increasing the heat generation parameter, local Grashof number, or mass Grashof number increases the fluid velocity. Skin friction, Nusselt number, and Sherwood number are also computed and presented in tabular form.
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.
Non-NewtonianFluid Flow and Heat Transfer over a Non- Linearly Stretching Sur...IJERA Editor
This paper investigates the MHD flow and heat transfer of an electrically conducting non-newtonian power-law
fluid over a non-linearly stretching surface along with porous plate in porous medium. The governing equations
are reduced to non-linear ordinary differential equations by means of similarity transformations. These
equations are then solved numerically with the help ofRunge – Kutta shooting method. The effect of various
flow parameters in the form of dimensionless quantities on the flow field are discussed and presented
graphically.
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
Effects of conduction on magneto hydrodynamics mixed convection flow in trian...Alexander Decker
This document summarizes research on magnetohydrodynamic (MHD) mixed convection flow in triangular enclosures. Key points:
1) The study investigates the effects of conduction on MHD mixed convection flow in triangular enclosures using a finite element method.
2) Parameters like the Hartmann number, Prandtl number, Reynolds number, and Rayleigh number are found to strongly influence the flow and thermal fields.
3) Validation of the numerical code is done by comparing average Nusselt numbers to previous research on natural convection in triangular enclosures.
This document summarizes a study that analyzes two-dimensional free convection and mass transfer flow of an electrically conducting fluid past a continuously moving infinite vertical porous plate. The study considers the combined effects of heat source and thermal diffusion in the presence of large suction. Similarity transformations are introduced to solve the governing equations, and perturbation techniques are used to obtain local similarity solutions. The results obtained include expressions for velocity, temperature, concentration, drag coefficient, heat transfer rate, and mass transfer rate. These results are discussed through graphs and tables to observe the effects of various parameters.
This document summarizes a journal article that investigates the propagation of surface waves in magneto-thermoelastic materials with voids and initial stress. It begins by providing background on thermoelasticity theories and previous work studying wave propagation in materials with voids, thermal effects, and magnetic fields. The document then presents the governing equations for a generalized magneto-thermoelastic solid with voids, considering the Green-Lindsay model. It solves these equations and applies boundary conditions to obtain a frequency equation for surface waves in this material. Some special cases without certain effects are also considered.
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
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.
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 Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
This document presents a mathematical analysis of the unsteady free convection and mass transfer flow through a porous medium with variable viscosity and thermal conductivity. The governing equations for momentum, temperature, and concentration are non-dimensionalized and solved using an explicit finite difference method. Key aspects include:
1) The flow is induced by an exponentially accelerated vertical plate with variable temperature and concentration.
2) Viscosity and thermal conductivity are assumed to vary linearly with temperature.
3) The resulting non-dimensional equations are nonlinear partial differential equations solved numerically.
4) Skin friction and Nusselt numbers are defined and analyzed graphically.
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.
This document provides an abstract for a research article on magnetohydrodynamic mixed convection micro polar flow through a porous medium driven by a porous stretching sheet. The following key points are discussed:
- Governing partial differential equations are derived and numerically solved using finite element analysis to study the effects of various parameters on velocity, micro rotation, and temperature profiles.
- Parameters investigated include the Hartmann number, Darcy parameter, surface conditions, and their impact on the fluid flow is explored.
- The study aims to provide insights applicable to processes involving polymer sheet stretching and controlled cooling/heating of strips or filaments during manufacturing.
STEADY FLOW OF A VISCOUS FLUID THROUGH A SATURATED POROUS MEDIUM AT A CONSTAN...Journal For Research
In this paper the Steady flow of a viscous fluid through a porous medium over a fixed horizontal, impermeable and thermally insulated bottom. The flow through the porous medium satisfies the general momentum and energy equations are obtained when the temperature on the fixed bottom and on free surface prescibed. By using Galerkin Method, the expression for Velocity and Drag force are obtained. The Galerkin Method endowed with distinct features that account for its superiority over competing methods. The effect of different parameters on Velocity and Drag force are discussed with the help of graphs.
This document summarizes an analysis of an unsteady magnetohydrodynamic (MHD) flow of a viscoelastic fluid along an infinite vertical porous surface with fluctuating temperature and concentration. The governing equations for fluid motion, energy, and concentration are solved using perturbation techniques. The velocity, temperature, and concentration profiles are shown graphically, and values for skin friction, Nusselt number, and Sherwood number are presented in tables for different flow parameters.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
OSCILLATORY FLOW OF MHD POLAR FLUID WITH HEAT AND MASS TRANSFER PAST A VERTIC...IAEME Publication
The study of unsteady two-dimensional laminar boundary layer flow of a viscous incompressible fluid (polar fluid) through porous medium past a semi-infinite vertical porous stretching plate in the presence of transverse magnetic field is investigated.
The sheet makes with a constant velocity in the longitudinal direction and the free stream velocity follows an exponentially increasing or decreasing small perturbation law. A uniform magnetic field acts perpendicularly to the porous sheet which absorbs the polar fluid with a suction velocity varying with time component. The effects of all parameters encountering in the problem are investigated for velocity and temperature fields across the boundary layer.
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.
Effects of Variable Viscosity and Thermal Conductivity on MHD free Convection...theijes
This document summarizes a study that numerically investigates the effects of variable viscosity and thermal conductivity on magnetohydrodynamic (MHD) free convection and mass transfer flow over an inclined vertical surface in a porous medium with heat generation. The governing equations are reduced to ordinary differential equations using similarity transformations and then solved numerically using a shooting method. The results show that increasing the viscosity variation parameter, thermal conductivity parameter, magnetic parameter, permeability parameter, or Schmidt number decreases the fluid velocity, while increasing the heat generation parameter, local Grashof number, or mass Grashof number increases the fluid velocity. Skin friction, Nusselt number, and Sherwood number are also computed and presented in tabular form.
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.
Non-NewtonianFluid Flow and Heat Transfer over a Non- Linearly Stretching Sur...IJERA Editor
This paper investigates the MHD flow and heat transfer of an electrically conducting non-newtonian power-law
fluid over a non-linearly stretching surface along with porous plate in porous medium. The governing equations
are reduced to non-linear ordinary differential equations by means of similarity transformations. These
equations are then solved numerically with the help ofRunge – Kutta shooting method. The effect of various
flow parameters in the form of dimensionless quantities on the flow field are discussed and presented
graphically.
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
Effects of conduction on magneto hydrodynamics mixed convection flow in trian...Alexander Decker
This document summarizes research on magnetohydrodynamic (MHD) mixed convection flow in triangular enclosures. Key points:
1) The study investigates the effects of conduction on MHD mixed convection flow in triangular enclosures using a finite element method.
2) Parameters like the Hartmann number, Prandtl number, Reynolds number, and Rayleigh number are found to strongly influence the flow and thermal fields.
3) Validation of the numerical code is done by comparing average Nusselt numbers to previous research on natural convection in triangular enclosures.
This document summarizes a study that analyzes two-dimensional free convection and mass transfer flow of an electrically conducting fluid past a continuously moving infinite vertical porous plate. The study considers the combined effects of heat source and thermal diffusion in the presence of large suction. Similarity transformations are introduced to solve the governing equations, and perturbation techniques are used to obtain local similarity solutions. The results obtained include expressions for velocity, temperature, concentration, drag coefficient, heat transfer rate, and mass transfer rate. These results are discussed through graphs and tables to observe the effects of various parameters.
This document summarizes a journal article that investigates the propagation of surface waves in magneto-thermoelastic materials with voids and initial stress. It begins by providing background on thermoelasticity theories and previous work studying wave propagation in materials with voids, thermal effects, and magnetic fields. The document then presents the governing equations for a generalized magneto-thermoelastic solid with voids, considering the Green-Lindsay model. It solves these equations and applies boundary conditions to obtain a frequency equation for surface waves in this material. Some special cases without certain effects are also considered.
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
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.
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 Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
This document presents a mathematical analysis of the unsteady free convection and mass transfer flow through a porous medium with variable viscosity and thermal conductivity. The governing equations for momentum, temperature, and concentration are non-dimensionalized and solved using an explicit finite difference method. Key aspects include:
1) The flow is induced by an exponentially accelerated vertical plate with variable temperature and concentration.
2) Viscosity and thermal conductivity are assumed to vary linearly with temperature.
3) The resulting non-dimensional equations are nonlinear partial differential equations solved numerically.
4) Skin friction and Nusselt numbers are defined and analyzed graphically.
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.
This document provides an abstract for a research article on magnetohydrodynamic mixed convection micro polar flow through a porous medium driven by a porous stretching sheet. The following key points are discussed:
- Governing partial differential equations are derived and numerically solved using finite element analysis to study the effects of various parameters on velocity, micro rotation, and temperature profiles.
- Parameters investigated include the Hartmann number, Darcy parameter, surface conditions, and their impact on the fluid flow is explored.
- The study aims to provide insights applicable to processes involving polymer sheet stretching and controlled cooling/heating of strips or filaments during manufacturing.
STEADY FLOW OF A VISCOUS FLUID THROUGH A SATURATED POROUS MEDIUM AT A CONSTAN...Journal For Research
In this paper the Steady flow of a viscous fluid through a porous medium over a fixed horizontal, impermeable and thermally insulated bottom. The flow through the porous medium satisfies the general momentum and energy equations are obtained when the temperature on the fixed bottom and on free surface prescibed. By using Galerkin Method, the expression for Velocity and Drag force are obtained. The Galerkin Method endowed with distinct features that account for its superiority over competing methods. The effect of different parameters on Velocity and Drag force are discussed with the help of graphs.
This document summarizes an analysis of an unsteady magnetohydrodynamic (MHD) flow of a viscoelastic fluid along an infinite vertical porous surface with fluctuating temperature and concentration. The governing equations for fluid motion, energy, and concentration are solved using perturbation techniques. The velocity, temperature, and concentration profiles are shown graphically, and values for skin friction, Nusselt number, and Sherwood number are presented in tables for different flow parameters.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
OSCILLATORY FLOW OF MHD POLAR FLUID WITH HEAT AND MASS TRANSFER PAST A VERTIC...IAEME Publication
The study of unsteady two-dimensional laminar boundary layer flow of a viscous incompressible fluid (polar fluid) through porous medium past a semi-infinite vertical porous stretching plate in the presence of transverse magnetic field is investigated.
The sheet makes with a constant velocity in the longitudinal direction and the free stream velocity follows an exponentially increasing or decreasing small perturbation law. A uniform magnetic field acts perpendicularly to the porous sheet which absorbs the polar fluid with a suction velocity varying with time component. The effects of all parameters encountering in the problem are investigated for velocity and temperature fields across the boundary layer.
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.
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.
DISPERSION OF AEROSOLS IN ATMOSPHERIC FLUID FLOWijscmcj
This document summarizes a research paper that presents a mathematical model to study the dispersion of aerosols with and without chemical reaction in the presence of electric and magnetic fields. Key points:
- The model considers laminar flow of aerosols between two parallel plates with an applied electric and magnetic field.
- Governing equations for momentum, species concentration, electric potential, and Maxwell's equations are presented and solved numerically.
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Effect of Mass Transfer and Hall Current on Unsteady MHD Flow with Thermal Diffusivity of a Viscoelastic Fluid in a Porous Medium
1. Anitha. S. et al. Int. Journal of Engineering Research and Application www.ijera.com
ISSN : 2248-9622, Vol. 7, Issue 4, ( Part -2) April 2017, pp.30-36
www.ijera.com DOI: 10.9790/9622-0704023036 30|P a g e
Effect of Mass Transfer and Hall Current on Unsteady MHD
Flow with Thermal Diffusivity of a Viscoelastic Fluid in a Porous
Medium
Anitha. S*, Lavanya. M**, Naganandhini. A***, Poornima. B****
*(Assistant Professor,Department of Mathematics, PSGR Krishnammal college for women, Coimbatore-04
Email: anithamaths21@gmail.com)
**(M.Sc Mathematics, PSGR Krishnammal college for women,Coimbatore-04)
***(M.Sc Mathematics, PSGR Krishnammal college for women, Coimbatore-04)
****(M.Sc Mathematics, PSGR Krishnammal college for women, Coimbatore-04)
ABSTRACT
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.
Key Words:Viscoelastic, Hall Current, Magnetohydrodynamics, Porous medium.
I. INTRODUCTION
Magnetohydrodynamics (MHD) is a field
of study which combines elements of
electromagnetism and fluid mechanics to describe
the flow of electrically conducting fluids. It is
generally regarded as a difficult academic discipline,
both conceptually as well as mechanically. MHD is
the study of electrically conducting fluids,
combining both principles of fluid dynamics and
electromagnetism. Magnetohydrodynamics is the
study of the magnetic properties of electrically
conducting fluids. When a conducting fluid moves
through a magnetic field, an electric field, may be
induced and, in turn the current interacts with the
magnetic field to produce a body force. The science
which deals with this phenomenon is called
Magnetohydrodynamics The subject of MHD is
traditionally studied as a continuum theory, that is to
say, attempts at studying discrete particles in the
flows are not at a level such that computation in
these regards is realistic. To run “realistic
simulations” would require computations of flows
with many more particles than current computers are
able to handle. Aboeldahab and Elbardy (2001)
examined Hall current effect on
Magnetohydrodynamics free
convection flow past a semi infinite vertical plate
with mass transfer. Effect of Heat of Transfer on
Unsteady Mhd Couette Flow Between Two Infinite
Parallel Porous Plates In an Inclined Magnetic Field
was investigated by Daniel Simon. Magaji
investigated Unsteady MHD mixed convective
oscillatory flow through a porous medium filled in a
vertical channel with heat and mass transfer.
Chemical Reaction and Hall Effect on MHD
Convective Flow along an Infinite Vertical Porous
Plate with Variable Suction and Heat Absorption
was examined by Masthanrao, Balamurugan and
Varma along with Raju. Ramana Murthy, Srinivasa
Raju and Anand Rao studied The effects of Heat and
Mass Transfer on MHD Natural Convective Flow
Past an Infinite Vertical Porous Plate with Thermal
Radiation and Hall Current.
Shit and Haldar investigated Combimed
Effects of Thermal Radiation and Hall Current on
MHD Free Convective Flow and Mass Transfer over
a Stretching Sheet with Variable Viscosity. Thermo
Diffusion and Chemical Reaction Effects on a
Steady Mixed Convective Heat and Mass transfer
Flow with Induced Magnetic Field was examined by
Sravanthi, Leela Ratnam and Bhaskar Reddy. Hall
Current Effects on Free Convective Flow of
Stratified Fluid over an Infinite vertical Porous Plate
was studied by Subbaiah Naidu. Radiation and mass
RESEARCH ARTICLE OPEN ACCESS
2. Anitha. S. et al. Int. Journal of Engineering Research and Application www.ijera.com
ISSN : 2248-9622, Vol. 7, Issue 4, ( Part -2) April 2017, pp.30-36
www.ijera.com DOI: 10.9790/9622-0704023036 31|P a g e
transfer effects on unsteady MHD convective flow
past an infinite vertical plate with Dufour and Soret
effects was studied by Vedavathi, Ramakrishna and
Jayarami Reddy.
II. MATHEMATICAL FORMULATION
We consider the unsteady flow of a viscous
incompressible and electrically conducting
viscoelastic fluid over an infinite porous plate with
oscillating temperature and mass transfer. The x-
axis is assumed to be oriented vertically upwards
along the plate and the y-axis is taken normal to the
plane of the plate. It is assumed that the plate is
electrically non – conducting and a uniform
magnetic field of straight 0
B is applied normal to the
plate. The induced magnetic field is assumed
constant. So that 0,,0 BB
,. The plate is
subjected to a constant suction velocity.
1. The equation of conservation of charge
0 J , gives constants.
2.
e
e
ee
en
P
BVEJJ
(1)
Equation (1) reduces to
**
2
0
**
2
0
1
1
*
*
mu
m
B
J
mu
m
B
J
y
x
(2)
Where
m= ee
is the Hall parameter.
The governing equations for the momentum, energy
and concentration are as follows;
(3)
*
202
3
12
2
0
1t
u
k
vu
CCgTTg
m
mu
B
ty
u
k
y
u
v
y
u
v
(4)
*
202
3
12
2
0
1t
k
v
m
mu
B
ty
k
y
v
y
v
2
2
0
t y
T
C
K
y
T
v
T
p
T
(5)
2
2
12
2
0
t y
C
D
y
C
D
y
C
v
C
(6)
The boundary conditions of the problem are:
yas0C0,T0,ω0,u
0yateCC
CC,eTTTT0,ω0,u
int
ω
int
ω
(7)
Where u and v are the components of
velocity in the x and y direction respectively, g is the
acceleration due to gravity,
*
βandβ and are the
coefficient of volume expansion, K is the kinematic
viscoelasticity, is the density, is the viscosity,
v is the kinematic viscosity, T
K is the thermal
conductivity, p
C is the specific heat in the fluid at
constant pressure, is the electrical conductivity
of the fluid, e
is the magnetic permeability, D is
the molecular diffusivity, 1
D is the thermal
diffusivity,
T is the temperature of the plane and
T is the temperature of the fluid far away from
plane.
C is the concentration of the plane and
C is the concentration of the fluid far away from
the plane.
And , 0
vv , the negative sign indicate that the
suction is towards the plane.
Introducing the following non-dimensionless
parameters.
(8)
2
2
0
*
2
2
01
1
1
T
p
2
0
2
0
2
0
ω
2
0
ω
ωω
00
00
v
vk
k,
v
vk
K
,
D
v
Sc,
D
v
Sc,
K
μC
Pr,
ρv
vσB
M
,
v
CCvg
Gc,
v
TTvg
Gr
,
CC
CC
C,
TT
TT
θ
,
v
ω
ω,
v
u
u,
4v
tv
t,
v
yv
η
Substituting the dimensionless variables in (8) into
(3) to (6), we get (dropping the bars)
3. Anitha. S. et al. Int. Journal of Engineering Research and Application www.ijera.com
ISSN : 2248-9622, Vol. 7, Issue 4, ( Part -2) April 2017, pp.30-36
www.ijera.com DOI: 10.9790/9622-0704023036 32|P a g e
(9)
22
3
2
2
14t
u
4
1
GcCGr
k
u
m
mu
M
t
uKuu
(10)
22
3
2
2
14t4
1
k
m
mu
M
t
K
2
2
Pr
1
t4
1
(11)
2
2
1
2
2
11
t4
1
C
Sc
C
Sc
CC
(12)
The corresponding boundary conditions are
yas0t,C
,t,ωt,u
0yatet0,C,et0,
0,t0,ω0,t0,u
intint
t
(13)
Equations (9) and (10) can be combined into a single
equation by introducing the complex velocity.
tη,ωitη,uU (14)
Where
1i
Thus,
GcCGr
k
U
m
im
M
t
UKUU
2
2
3
2
2
1
1
4t
U
4
1
(15)
With boundary conditions:
as0t,C,t,U
0at
et0,C,et0,0,t0,U
intint
t
(16)
where Gr, is the thermal Grashof number,
Gc, is the mass Grashof number, Sc, Sc1 is the
Schmidt numbers, Pr, is the Prandtl number, K, is
the viscoelastic Parameter, M, is the Hartmann
number and k, is the pearmeability.
III. METHODS OF SOLUTION
To solve (11), (12) and (15) subject to the
boundary conditions (16), we assume solutions of
the form
int
1
t,U eU (17)
int
1
t, e (18)
int
1
t, eCC (19)
Where ηCandηθ,ηU 111
are to be
determined.
Substituting (17) to (19) into (11),(12) and (15),
comparing harmonic and non harmonic terms, we
obtain
int
1
int
1
3
1
'
''
44
U
eP
GcC
eP
Gr
UP
P
U
(20)
0Pr
4
1
Pr 11
'''
in (21)
0
4
1
11
1
'
1
''
1
CinScSc
CScScCScSc
(22)
And boundary conditions give
ηat
0C0,θ0,U
0ηat10C0θ,0U
111
111
(23)
where the primes represents differentiation with
respect to . Solving (20) to (22) subject to the
boundary conditions (23) and (25) and substituting
the obtained solutions into (17) to (19) respectively.
Then the velocity field can be expressed as
(24)
intηm
8
ηm
7
ηm
6
eeAeAeAt,ηU 426
And the temperature field is given by
intηm
eetη,θ 2
(25)
Similarly, the concentration distribution gives
intηm
eetη,C 4
(26)
IV. RESULTS AND DISCUSSION
The effect of mass transfer and Hall current
on unsteady MHD flow of a viscoelastic fluid in a
porous medium has been formulated and solved
analytically. In order to understand the flow of the
fluid, computations are performed for different
parameters such as Gr, Gc, Sc, Pr, n, M, K, and m.
4.1 Velocity profiles
Figures 1-8 represent the velocity profiles,
figures 9 and 10 depict the temperature profiles and
figures 11 and 12 show the concentration profiles
with varying parameters respectively.
The effect of velocity for different values of
(Pr = 0.025, 0.71, 1, 3) is presented in figure 1, the
graph show that velocity decreases with increase in
Pr. The effect of velocity for different values of (Sc
= 0.3, 0.6, 0.8, 1, 2.01) is given in figure 2, the graph
show that velocity decreases with the increase in Sc.
Figure 3 denotes the effect of velocity for different
values of (n =1, 2, 3, 4, 7), it is seen that velocity
decreases with the increase in n.
4. Anitha. S. et al. Int. Journal of Engineering Research and Application www.ijera.com
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The effect of velocity for different values of (m = 1,
2, 3, 4, 7) is shown in figure 4, it depict that velocity
increases with increase in m.
Figure 5 depicts the effect of velocity for (M = 1, 2,
3, 4, 7), the graph show that velocity decreases with
the increase in M.
The effect of velocity for different values of (Gr = 1,
2, 3, 4, 7) is presented in figure 6, it is seen that
velocity increases with the increase in Gr.
The effect of velocity for different values of (Gc = 1,
2, 3, 4, 7) is displayed in figure 7, it is observed that
velocity increases with the increase in Gc.
The effect of velocity for different values of (K =
0.0001, 0.01, 0.05, 0.08, 0.1) is shown in figure 8, it
is observed that velocity increases with the increase
in K.
Figure 1: velocity profiles for different values of Pr.
Figure 2:Velocity profiles for different
values of Sc.
Figure 3: Velocity profiles for different values of n.
Figure 4: Velocity profiles for different
values of m.
Figure 5:Velocity profiles for different v
alues of M.
0 1 2 3 4 5 6
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
y
u
M=1
M=2
M=3
M=4
M=7
0 1 2 3 4 5 6 7
0
0.5
1
1.5
2
2.5
y
u
m=0.5
m=1
m=1.5
m=2
m=2.5
0 1 2 3 4 5 6 7 8
-0.02
0
0.02
0.04
0.06
0.08
0.1
0.12
y
u
n=1
n=2
n=3
n=4
n=7
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
y
u
Sc=0.3
Sc=0.6
Sc=0.8
Sc=1
Sc=2.01
0 1 2 3 4 5 6 7
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
y
u
Pr=0.71
Pr=1
Pr=3
Pr=7
5. Anitha. S. et al. Int. Journal of Engineering Research and Application www.ijera.com
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Figure 6: Velocity profiles for different
values of Gr.
Figure 7: Velocity profiles for different
values of Gc.
Figure 8: Velocity profiles for different values of K.
4.2 Temperature profiles
In figure 9, the effect of temperature for
different values of (Pr = 0.025, 0.71, 1, 3, 7) is
given. The graph show that temperature decreases
with increasing Pr. Figure 10 shows the effect of
temperature for different values of (n = 0.025, 0.71,
1, 3, 7). The graph show that temperature decreases
with decreasing n.
Figure 9: Temperature profiles for different
values of Pr.
Figure 10: Velocity profiles for different values
of n.
4.3 Concentration profiles
Figure 11 depicts the effect of
concentration for (Sc = 0.3, 0.6, 0.8, 1, 2.01), it is
seen that concentration decreases with the increase
in Sc. The effect of concentration for ( n = 0.3, 0.6,
0.8, 1, 2.01) is given in figure 12, it is seen that
concentration decreases with the decrease in n.
Figure 11: Concentration profiles for different
values of Sc.
0 1 2 3 4 5 6 7 8 9 10
0
0.2
0.4
0.6
0.8
1
1.2
1.4
y
C
Sc=0.3
Sc=0.6
Sc=0.8
Sc=1
Sc=2.01
0 2 4 6 8 10
0
0.2
0.4
0.6
0.8
1
1.2
1.4
y
n=1
n=5
n=10
n=50
0 1 2 3 4 5 6 7 8 9 10
0
0.2
0.4
0.6
0.8
1
1.2
1.4
y
Pr=0.025
Pr=0.71
Pr=1
Pr=3
Pr=7
0 1 2 3 4 5
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
y
u
K=0.001
K=0.01
K=0.05
K=0.08
K=0.1
0 1 2 3 4 5 6
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
y
u
Gc=1
Gc=2
Gc=3
Gc=4
Gc=7
0 1 2 3 4 5 6 7
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
y
u
Gr=1
Gr=2
Gr=3
Gr=4
Gr=7
6. Anitha. S. et al. Int. Journal of Engineering Research and Application www.ijera.com
ISSN : 2248-9622, Vol. 7, Issue 4, ( Part -2) April 2017, pp.30-36
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Figure
12: Concentration profiles for different values of n.
V. SUMMARY AND CONCLUSION
We have examined and solved analytically
the governing equations for the effect of mass
transfer and Hall current on unsteady MHD flow of
a viscoelastic fluid in a porous medium analytically.
In order to point out the effect of physical
parameters namely; 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. We observe that, the velocity increases
with the increase in Gc, Gr, m, and K, and it
decreases with increase in Sc, n,M and Pr.
Temperature decreases with increase in Pr and n,
and concentration decreases with the increase in Sc
and n.
REFERENCES
[1]. Aboeldahab, E. M. and Elbarby, E. M. E.
(2001). Hall current effect on
Magnetohydrodynamics free convection flow
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39. 1641 – 1652.
[2]. Daniel Simon (2014). Effect of Heat of
Transfer on Unsteady Mhd Couette Flow
Between Two Infinite Parallel Porous Plates
In An Inclined Magnetic Field. International
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[3]. Magaji AS. (2016).Unsteady MHD mixed
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[4]. Masthanrao. S, Balamurugan. K. S, Varma. S.
V. K, and Raju.V. C. C. (2013). Chemical
Reaction and Hall Effects on MHD
Convective Flow along an Infinite Vertical
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AppliedMathematics: An International
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[5]. Ramana Murthy. M. V, Srinivasa Raju. R,
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[6]. Shit.G .S and Haldar. R. (2012). Combined
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[7]. MHD Free-Convective Flow and Mass
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[8]. Sravanthi .C. S. Leela Ratnam. A. and
Bhaskar Reddy. N. (2013). Thermo-Diffusion
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International Journal of Innovative Research
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2(9). 2319-8753
[9]. Subbaiah Naidu. K.Ch. V. (2016). Hall
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Stratified Fluid over an Infinite vertical
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(IOSR-JM). 12(5). 2278-5728
[10]. Vedavathi. N, Ramakrishna. K, Jayarami
Reddy. K. (2015). Radiation and mass
transfer effects on unsteady MHD convective
flow past an infinite vertical plate with
Dufour and Soret effects. Ain Shams
Engineering Journal. 6. 363–371
[11]. Takhar (2006). Unsteady flow free convective
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Journal of Heat and Mass Transfer. 39, 823 –
834.
APPENDIX
4
PrPr
2
in
a
, am
2
Pr
2
, 1
ScScd
11
ScScd , 2
1
1
2
4 d
inddd
b
,
2 1
4
b
d
d
m ,
4
11
inK
P
22
1
11
4 m
imM
k
in
P ,
1
2
3
P
P
P
2
1
3
2
1
4
41
P
PP
c
, ,
2
1
1
6
c
P
m
0 2 4 6 8 10
0
0.2
0.4
0.6
0.8
1
1.2
1.4
y
C
n=1
n=5
n=10
n=50
7. Anitha. S. et al. Int. Journal of Engineering Research and Application www.ijera.com
ISSN : 2248-9622, Vol. 7, Issue 4, ( Part -2) April 2017, pp.30-36
www.ijera.com DOI: 10.9790/9622-0704023036 36|P a g e
876
AAA
3
1
42
41
8
P
P
m
mP
Gc
A
3
1
22
21
7
P
P
m
mP
Gr
A