Abstract
Accounting for the fact that thermal conductivity of fluid is much less than the thermal conductivity of solid in most of the porous medium-related applications, this study applies perturbation approach in analyzing forced convection through a parallel plate channel under local thermal nonequilibirum (LTNE) condition by denoting the thermal conductivity ratio of fluid to solid as the small parameter, suggesting leading order solutions to solve the two-equation energy model, by incorporating Darcy model and Brinkman model for large porous medium shape factor, respectively, in the presence of heat generation in both fluid and solid. This study provides important fluid temperatures, solid temperatures, and heat transfer coefficient approximations, which enables further analysis on the fluid and solid temperature gradient at the boundary and hence delineate the roles of thermal conductivities and interfacial heat transfer in LNTE mode. The results signify competition between the heat conduction from the wall through fluid conduction and interfacial heat transfer from solid to fluid in the thermal boundary layer. The effect of thermal boundary layer is intensified with the attendant increase in porous medium shape factor and heat generation in solid. The results for Brinkman model also establish conditions for temperature bifurcations to take place whereby in such cases, an increase in viscous dissipation in fluid attributes to the detachment of thermal boundary layer as the porous medium shape factor, S decreases. The phenomenon caused by insufficient convection rate to overcome viscous dissipation bears much resemblance to the separation point in the momentum boundary layer.
The Onset of Convection in an Unsteady Thermal Boundary Layer in a Porous Medium