Effect of heat source on forced convection in a partially-filled porous channel under LTNE condition

Abstract

An analysis of forced convection is presented within a channel partially filled by porous medium inserted in the core, with the inclusion of internal heat source in fluid and solid phases. By employing Brinkman extended Darcy model and local thermal non-equilibrium (LTNE) model in porous region, exact solutions are obtained including fluid velocity, solid and fluid temperatures and Nusselt number, and pertinent parameters' effects on heat transfer enhancement are performed. In addition, the solutions are also compared to that by applying the local thermal equilibrium (LTE) assumption and the LTE validity is discussed. The results find that for a partially-filled porous channel, existed heat source terms can intensify the occurrence of the singularity in Nusselt number, especially with the variation of porous filling ratio more than one singularity points can be observed under both LTE and LTNE conditions. In addition, even if the singularity exists the Nusselt number can reach to LTE condition at a high Biot number (Bi) or at a very high solid to fluid thermal conductivity ratio (K), and at a small K the LTE also holds with the fluid heat source only. Overall, partially-filled porous systems with internal heat source have more rich thermal characteristics.