The First Stokes Problem of Radiative-Convective MHD Flow in a Porous Medium

2005 ◽  
Author(s):  
Youn-Jea Kim ◽  
Young-Wan Kim
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Stokes Problem ◽  
Mhd Flow ◽  
Transverse Magnetic ◽  
Magnetic Reynolds Number ◽  
Spherical Particles ◽  
Convection Flow ◽  
Laplace Transform Technique ◽  
The Laplace Transform

Analytic study on the transient mixed radiative convection flow of viscous, incompressible fluids past an impulsively-started infinite vertical plate is performed. The plate is located in the transverse magnetic field embedded in a porous medium. It is assumed that the transversely applied magnetic field and the magnetic Reynolds number are very small and hence the induced magnetic field is negligible. The fluid considered here is a gray, absorbing-emitting radiation but a non-scattering medium. The Rosseland approximation is used to describe radiative heat transfer in the limit of optically thick fluids. It is also assumed here that the porous medium as an assemblage of small identical spherical particles fixed in space. The relevant transformed dimensionless governing equations are solved by using the Laplace transform technique. The obtaining results concerning velocity and temperature across the boundary layer are illustrated graphically for different values of the parameters entering into the problem under consideration. Results show that for an increase in magnetic field parameter, there is a fall in the velocity, whereas there is a rise in the velocity of the fluid for an increase in porous parameter.

scholarly journals Thermal Radiation, Chemical Reaction, Viscous and Joule Dissipation Effects on MHD Flow Embedded in a Porous Medium

2019 ◽  
Vol 24 (3) ◽  
pp. 725-737
Author(s):  
B. Zigta
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Chemical Reaction ◽  
Mhd Flow ◽  
Magnetic Reynolds Number ◽  
Convection Flow ◽  
Joule Dissipation ◽  
Radiation Chemical

Abstract An analysis is presented to study the effects of thermal radiation, chemical reaction, viscous and Joule dissipation on MHD free convection flow between a pair of infinite vertical Couette channel walls embedded in a porous medium. The fluid flows by a strong transverse magnetic field imposed perpendicularly to the channel wall on the assumption of a small magnetic Reynolds number. The governing non linear partial differential equations are transformed in to ordinary differential equations and are solved analytically. The effect of various parameters viz., Eckert number, electric conductivity, dynamic viscosity and strength of magnetic field on temperature profile has been discussed and presented graphically.

scholarly journals Span-Wise Fluctuating MHD Convective Flow of a Viscoelastic Fluid through a Porous Medium in a Hot Vertical Channel with Thermal Radiation

2016 ◽  
Vol 21 (3) ◽  
pp. 667-681 ◽  
Author(s):  
K.D. Singh
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Vertical Channel ◽  
Magnetic Reynolds Number ◽  
Conducting Fluid ◽  
Temperature Fields ◽  
Convection Flow ◽  
Electrically Conducting ◽  
Unsteady Mixed Convection ◽  
Phase Angles

Abstract An unsteady mixed convection flow of a visco-elastic, incompressible and electrically conducting fluid in a hot vertical channel is analyzed. The vertical channel is filled with a porous medium. The temperature of one of the channel plates is considered to be fluctuating span-wise cosinusoidally, i.e., $T^* \left( {y^* ,z^* ,t^* } \right) = T_1 + \left( {T_2} - {T_ 1} \right)\cos \left( {{{\pi z^* } \over d} - \omega ^* t^* } \right)$ . A magnetic field of uniform strength is applied perpendicular to the planes of the plates. The magnetic Reynolds number is assumed very small so that the induced magnetic field is neglected. It is also assumed that the conducting fluid is gray, absorbing/emitting radiation and non-scattering. Governing equations are solved exactly for the velocity and the temperature fields. The effects of various flow parameters on the velocity, temperature and the skin friction and the Nusselt number in terms of their amplitudes and phase angles are discussed with the help of figures.

scholarly journals Transient Free Convective MHD Flow Past an Exponentially Accelerated Vertical Porous Plate with Variable Temperature through a Porous Medium

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Ashish Paul
Keyword(s):  
Boundary Layer ◽  
Skin Friction ◽  
Vertical Plate ◽  
Variable Temperature ◽  
Porous Plate ◽  
Mhd Flow ◽  
Transverse Magnetic ◽  
Magnetic Reynolds Number ◽  
Suction Parameter ◽  
Laplace Transform Technique

This paper is concerned with analytical solution of one-dimensional unsteady laminar boundary layer MHD flow of a viscous incompressible fluid past an exponentially accelerated infinite vertical plate in presence of transverse magnetic field. The vertical plate and the medium of flow are considered to be porous. The fluid is assumed to be optically thin and the magnetic Reynolds number is considered small enough to neglect the induced hydromagnetic effects. The governing boundary layer equations are first converted to dimensionless form and then solved by Laplace transform technique. Numerical values of transient velocity, temperature, skin friction, and Nusselt number are illustrated and are presented in graphs for various sets of physical parametric values, namely, Grashof number, accelerating parameter, suction parameter, permeability parameter, radiation parameter, magnetic parameter, and time. It is found that the velocity decreases with increases of the suction parameter for both cases of cooling and heating of the porous plate whereas skin friction increases with increase of suction parameter.

scholarly journals Exact Solutions of Heat and Mass Transfer with MHD Flow in a Porous Medium under Time Dependent Shear Stress and Temperature

2015 ◽  
Vol 2015 ◽  
pp. 1-16 ◽  
Author(s):  
Arshad Khan ◽  
Ilyas Khan ◽  
Farhad Ali ◽  
Asma Khalid ◽  
Sharidan Shafie
Keyword(s):  
Mass Transfer ◽  
Porous Medium ◽  
Shear Stress ◽  
Heat And Mass Transfer ◽  
Fluid Motion ◽  
Mhd Flow ◽  
Convection Flow ◽  
Closed Form Solutions ◽  
Special Cases ◽  
Laplace Transform Technique

This paper aims to study the influence of thermal radiation on unsteady magnetohyrdodynamic (MHD) natural convection flow of an optically thick fluid over a vertical plate embedded in a porous medium with arbitrary shear stress. Combined phenomenon of heat and mass transfer is considered. Closed-form solutions in general form are obtained by using the Laplace transform technique. They are expressed in terms of exponential and complementary error functions. Velocity is expressed as a sum of thermal and mechanical parts. Corresponding limiting solutions are also reduced from the general solutions. It is found that the obtained solutions satisfy all imposed initial and boundary conditions and reduce to some known solutions from the literature as special cases. Analytical results for the pertinent flow parameters are drawn graphically and discussed in detail. It is found that the velocity profiles of fluid decrease with increasing shear stress. The magnetic parameter develops shear resistance which reduces the fluid motion whereas the inverse permeability parameter increases the fluid flow.

scholarly journals Radiation effect on unsteady MHD flow through porous medium past an oscillating inclined plate with variable temperature and mass diffusion in the presence of hall current

2016 ◽  
Vol 12 (2) ◽  
Author(s):  
U. S. Rajput ◽  
Gaurav Kumar
Keyword(s):  
Porous Medium ◽  
Variable Temperature ◽  
Mhd Flow ◽  
Mass Diffusion ◽  
Inclined Plate ◽  
Plate Temperature ◽  
Electrically Conducting ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Variable Wall

In the present paper, we study the effect of radiation on unsteady flow of a viscous, incompressible and electrically conducting fluid past an oscillating inclined plate through a porous medium with variable wall temperature and mass diffusion in the presence of transversely applied uniform magnetic field. The plate temperature and the concentration level near the plate increase linearly with time. The governing equations involved in the present analysis are solved by the Laplace-transform technique. The results obtained are discussed with the help of graphs drawn for different parameters. The numerical values obtained for skin-friction and Nusselt number have been tabulated. The results are found to be in a good agreement and the data obtained is in concurrence with the actual flow phenomenon. 

scholarly journals MHD flow past a parabolic flow past an infinite isothermal vertical plate in the presence of thermal radiation and chemical reaction

2016 ◽  
Vol 21 (1) ◽  
pp. 95-105 ◽  
Author(s):  
R. Muthucumaraswamy ◽  
P. Sivakumar
Keyword(s):  
Thermal Radiation ◽  
Chemical Reaction ◽  
Vertical Plate ◽  
Mhd Flow ◽  
Convection Flow ◽  
Grashof Number ◽  
Linear Partial Differential Equations ◽  
Flow Past ◽  
Laplace Transform Technique ◽  
The Laplace Transform

Abstract The problem of MHD free convection flow with a parabolic starting motion of an infinite isothermal vertical plate in the presence of thermal radiation and chemical reaction has been examined in detail in this paper. The fluid considered here is a gray, absorbing emitting radiation but a non-scattering medium. The dimensionless governing coupled linear partial differential equations are solved using the Laplace transform technique. A parametric study is performed to illustrate the influence of the radiation parameter, magnetic parameter, chemical reaction parameter, thermal Grashof number, mass Grashof number, Schmidt number and time on the velocity, temperature, concentration. The results are discussed graphically and qualitatively. The numerical results reveal that the radiation induces a rise in both the velocity and temperature, and a decrease in the concentration. The model finds applications in solar energy collection systems, geophysics and astrophysics, aerospace and also in the design of high temperature chemical process systems.

scholarly journals MHD heat and mass diffusion flow by natural convection past a surface embedded in a porous medium

2009 ◽  
Vol 36 (1) ◽  
pp. 1-27 ◽  
Author(s):  
R.C. Chaudhary ◽  
Arpita Jain
Keyword(s):  
Porous Medium ◽  
Natural Convection ◽  
Analytical Study ◽  
Mass Diffusion ◽  
Convection Flow ◽  
Governing Equations ◽  
Natural Convection Flow ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Flow Variables

This paper presents an analytical study of the transient hydromagnetic natural convection flow past a vertical plate embedded in a porous medium, taking account of the presence of mass diffusion and fluctuating temperature about time at the plate. The governing equations are solved in closed form by the Laplace-transform technique. The results are obtained for temperature, velocity, penetration distance, Nusselt number and skin-friction. The effects of various parameters are discussed on the flow variables and presented by graphs.

Mass Transfer Effects on MHD Flow through Porous Medium past an Exponentially Accelerated Inclined Plate with Variable Temperature and Thermal Radiation

2019 ◽  
Vol 6 (4) ◽  
Author(s):  
B. Shankar Goud ◽  
B. Suresh Babu ◽  
MN Raja Shekar ◽  
G. Srinivas
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Heat Source ◽  
Saturated Porous Medium ◽  
Variable Temperature ◽  
Mhd Flow ◽  
Seepage Flow ◽  
Convection Flow ◽  
Inclined Plate ◽  
Inclined Surfaces

The current paper focuses on unsteady MHD free convection flow with mass and heat transfer past an inclined plate. The inclined plate moves with exponential acceleration and is placed in a saturated porous medium having a uniform permeability but a varying concentration and temperature. The important essence of the study is to analyze the angle of inclination on the flow phenomenon with a heat source or sink alongside a destructive reaction. The governing equations are solved with the help of Galerkin Finite Element Method. A detailed discussion on the effects of pertinent material parameters, magnetic field, and permeability of the porous medium is presented. This reveals the flow reversal with an active magnetic field in porous medium. A retarding velocity is observed with angle of inclination and heat source. Applications of the present study include understanding of drag experienced at the heated/cooled inclined surfaces in a seepage flow.

Sign in / Sign up

Export Citation Format

Share Document