Variable Temperature Plate Heat Transfer: MHD Fluid Natural Convection Flow in Porous Medium

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The heat transfer from a variable temperature plate has been studied under the presence of porous medium and MHD fluid. Solutions for flat plate in porous medium are usually numeric, in this work an exact solution is found. Free convection governing equations were nondimensionalized and solved using Laplace transform. Exact solutions for the dependent non-dimensional variables were obtained. Velocity and temperature solutions that satisfy the governing equations and exponential boundary conditions were validated with a special case from the existing literature and found to be in good agreement. The temperature and velocity distributions within the porous medium were analysed for different non-dimensional numbers such as Prandtl number and Grashof number and for Newtonian and non-Newtonian fluids. It has been found that the Pr number decreases the velocity variation as a result of the increased viscosity. Higher Grashof number increases the velocity variation for the extra potential it supplies in the momentum equation. Heat generation term raises the dimensionless temperature variation in the energy equation, in its turn the dimensionless temperature increases the velocity variation.