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Unsteady Magneto-Hydrodynamic Flow Through Saturated Porous Medium with Thermal Non-equilibrium and Radiation Effects

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Abstract

The effect of thermal non-equilibrium on two-dimensional magnetohydrodynamics flow through a sparsely packed porous medium bounded by two vertical plates has been examined using finite difference approximation. The Rosseland approximation for thermal radiation is incorporated as a pertinent parameter in the liquid phase thermal energy equation. The numerical solutions are used to analyze the effects of Brinkman number, viscosity ratio, porous parameter, magnetic parameter, heat transfer coefficient, and thermal radiation parameter on velocity and temperature profiles. Also, the skin-friction coefficient and Nusselt number are determined at the left boundary of the channel, and results are presented via plots. The results show that the Brinkman number, porous parameter, magnetic parameter, and thermal radiation parameter opposes the liquid flow and enhances the temperature distribution, whereas the interphase heat transfer coefficient, the ratio of thermal diffusivities shows the opposite effect.

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Abbreviations

\(B_{0}\) :

Magnetic field

Bi :

Biot number

\(c_p\) :

Specific heat at constant pressure

d :

Channel width

\(\mathbf {g}\) :

Accelaration due to gravity

h :

Interphase heat transfer coefficient

H :

Dimensionless interphase heat transfer coefficient

k :

Thermal conductivity

\(k^*\) :

Mean absorption coefficient

K :

Permeability

M :

Magnetic parameter

Nr :

Thermal radiation parameter

Nu :

Nusselt number

p :

Fluid pressure

Pr :

Prandtl number

Ra :

Thermal Rayleigh number

T :

Temperature

t :

Time

u, U :

Flow velocity

x, y :

Coordinate elements

\(\beta \) :

Thermal expansion coefficient

\(\gamma \) :

Porosity-modified ratio of thermal conductivities

\(\Gamma \) :

Ratio of thermal diffusitivities

\(\Lambda \) :

Viscosity ratio

\(\mu \) :

Absolute viscosity

\(\epsilon \) :

Porosity (\(0<\epsilon <1\))

\(\tau \) :

Dimensionless time

\(\rho \) :

Liquid density

\(\sigma ^*\) :

Stefan–Boltzman constant

\(\sigma ^2\) :

Porous parameter

\(\theta \) :

Dimensionless temperature

0:

Reference value

l :

Liquid

s :

Solid

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  1. Department of Mathematics, M. S. Ramaiah University of Applied Sciences, Bangalore, Karnataka, 560 058, India

    C. Siddabasappa

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Siddabasappa, C. Unsteady Magneto-Hydrodynamic Flow Through Saturated Porous Medium with Thermal Non-equilibrium and Radiation Effects. Int. J. Appl. Comput. Math 6, 66 (2020). https://doi.org/10.1007/s40819-020-00825-2

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