Mixed convection in a vertical micro-porous channel with radiation and magnetic field. A thermal non-equilibrium perspective

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The present work addresses a numerical approach to the fully developed magnetohydrodynamic mixed convection of a viscous, incompressible, electrically conducted fluid, with the radiation parameter in the vertical micro-porous channel filled with porous medium and thermal nonequilibrium conditions being considered. Governing differential equations are solved numerically by using spectral collocation techniques. The aim of this study is to understand the effect of the inter-phase heat transfer coefficient (H), porosity-scaled thermal conductivity ratio γ, radiation parameter Rd , and Darcy number Da on the velocity, magnetic field, and heat transfer rate Nu profile. The present study revealed that the magnitude of flow was reduced for the higher value of Rd for all three cases (ζ=1,ζ−0,ζ=−1). The Darcy number (Da) reduces the velocity as well as the magnetic field. The velocity profile for ζ=1 (when both walls are heated) decreases as the inter-phase heat transfer coefficient H increases, while for the other two cases, the reverse effect has been observed. The present study also revealed that there exists a threshold value H0 of H for ζ=1 and ζ=0 where the heat transfer rate Nu becomes the decreasing function of H in the interval [0,H0] when radiation parameter Rd increases from 1 to 5. Overall, the inter-phase heat transfer coefficient H makes the flow profile smooth (stabilizes the flow) and recovers the system to equilibrium.