Effects of Variable Fluid Properties and MHD on Mixed Convection Heat Transfer from a Vertical Heated Plate Embedded in a Sparsely Packed Porous Medium

Abstract

The effects of variable Fluid Properties like variation of permeability, porosity, thermal conductivity and magnetic field on Mixed Convection Heat transfer from Vertical Heated Plate Embedded in a Sparsely Packed Porous Medium have been approached numerically. The boundary layer flow in the porous medium is governed by Lapwood - Forchheimer - Brinkman extended Darcy model and the Lorentz force. The natures of these equations are highly non-linear and coupled each other. The non-linear differential equations are non-dimensionalised using the non-dimensional parameter involving Grashoff number Gr, Prandtl number Pr, Hartmann number M, Eckert number E and so on. Similarity transformations are employed and the resulting ordinary differential equations are solved numerically by using shooting algorithm with Runge - Kutta and Newton - Raphson method to obtain velocity and temperature distributions. Besides, skin friction and Nusselt number are also computed for various physical parameters governing the problem under consideration. It is found that the inertial parameter has a significant influence in decreasing the flow field, whereas its influence is reversed on the rate of heat transfer for all values of permeability considered. The effect of Magnetic field is diminution with velocity of the fluid flow. Further, the obtained results under the two limiting conditions were found to be in good agreement with the existing results.