A Similarity Solutions Approach to Forced Convection via a Porous Medium Attached to Flat Plate

Abstract

In the present study, a porous medium adjoining a heated flat plate was modelled by a similarity approach to determine the effect of porosity on the heat transfer phenomena. The momentum and energy equations for porous media transport were transformed using an appropriately determined similarity parameter. The solutions to the momentum equations proved to depend only on the porosity and not the material used. The energy equation however was additionally dependent on the combinations of fluid type and metal matrix used and was solved for four combinations; water/aluminum, air/aluminum, air/copper and SAE 20W-50/stainless. The results show that replacing the clear fluid control volume with a porous matrix altered both the velocity profiles and temperature distribution profiles at all Reynolds numbers. As the porosity of the medium decreased, it resulted in an increase in interfacial area as well as thermal diffusion in the direction normal to the plate, both of which was seen to enhance the heat transfer coefficients. Decreasing porosity also resulted in an increase in thermal storage as well a reduction in volume flow rate going through the medium, which on the other hand tend to inhibit convection. Thus, changing the porosity triggered effects on the heat transfer coefficient. This opposing trend favored convection at porosity greater than 0.5 for low Prandtl number fluids. The clear fluid condition has the lowest heat transfer coefficient and the values increased steeply as porosity changed from 0.99 through 0.7. The heat convection curve reached its maximum turning point at a porosity of 0.5 and then reversed in trend. The dimensionless heat transfer coefficient was found to fit the equation hLL/ReL0.5kfPrf=aebPrmc ( a= 0.51966;b=0.54683;c=-0.665349) . Using Stanton number representation, the relation is StReL>1/2=1/3 aebPrmc , which portrays in relative terms how the convection enhancement and the opposing thermal storage effects vary with porosity. This study concluded that implementing a porous structure in a medium is feasible for enhancing heat transfer performance.