Unsteady Hydromagnetic Convective Flow past an Infinite Vertical Porous Plate through a Porous Medium

Abstract

The effect of heat transfer on unsteady hydromagnetic free convective flow of a viscous incompressible electrically conducting fluid flow has been investigated. The fluid flows past an infinite vertical porous plate in presence of constant injection and heat source. The flow is subjected to transverse magnetic field. The partial differential equations governing the flow field has been derived and transformed to non-dimensional form. The equations and their respective initial and boundary conditions are then non-dimensionalized and solved numerically using finite difference method specifically, the Crank-Nicolson method. The effects of varying various flow parameters on the velocity, temperature and concentration profiles have been presented graphically. This has been done when Grashof number for heat transfer, Gr>0 (cooling of the plate) and also when Gr<0 (heating of the plate). It was observed that when the parameters are varied, there is an increase, decrease or no change in velocity, temperature, concentration, skin friction and rate of heat transfer on the surface of the plate. The results of variation of these parameters is very important especially in petroleum engineering where an engineer is able to make various decisions on how to extract fluids as they move through porous medium.

The effect of heat transfer on unsteady hydromagnetic free convective flow of a viscous incompressible electrically conducting fluid flow has been investigated. The fluid flows past an infinite vertical porous plate in presence of constant injection and heat source. The flow is subjected to transverse magnetic field. The partial differential equations governing the flow field has been derived and transformed to non-dimensional form. The equations and their respective initial and boundary conditions are then non-dimensionalized and solved numerically using finite difference method specifically, the Crank-Nicolson method. The effects of varying various flow parameters on the velocity, temperature and concentration profiles have been presented graphically. This has been done when Grashof number for heat transfer, Gr>0 (cooling of the plate) and also when Gr<0 (heating of the plate). It was observed that when the parameters are varied, there is an increase, decrease or no change in velocity, temperature, concentration, skin friction and rate of heat transfer on the surface of the plate. The results of variation of these parameters is very important especially in petroleum engineering where an engineer is able to make various decisions on how to extract fluids as they move through porous medium.