Temperature distribution, local and total entropy generation analyses in MHD porous channels with thick walls

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Entropy generation rate is an important characteristic of a thermal system. This work aims to study the temperature distribution, and local and total entropy generation rates within a horizontal porous channel under a uniform magnetic field with thick walls. The thermal conductivity of the walls are considered temperature-dependent and viscous dissipation effects are incorporated into the energy equation. Two types of boundary conditions are employed: Case one which has constant but different temperature boundary conditions and Case two which has heat flux boundary condition on the lower wall and convective boundary condition on the upper wall. Using a combined analytical-numerical solution procedure the temperature fields are obtained. Thereafter, the local and total entropy generation rates are achieved. The correctness of the analytical-numerical solution technique is checked against a completely analytical solution, for cases with temperature-independent thermal conductivities of walls. After validation, the general solution procedure, i.e., solution for cases with temperature-dependent thermal conductivities, is used to investigate the effect of various parameters such as Brinkman number, Hartmann number, Darcy number, porous medium to solid parts thermal conductivity ratio, etc. on the temperature field and entropy generation rates. As an interesting result it was found that depending on the boundary conditions of the channel, porous medium to solid parts thermal conductivity ratio may increase or decrease the total entropy generation rate.