Effect of thermal boundary conditions on forced convection under LTNE model with no-slip porous-fluid interface condition

Abstract

This paper analytically investigates a fully developed forced convection in a channel partially filled with two porous layers symmetrically arranged at inner walls. The local thermal non-equilibrium (LTNE) model and Brinkman-extended Darcy model are employed as energy and momentum equations respectively in porous region. Three thermal boundary conditions (models A, B and C) and no-slip condition are adopted at porous-fluid interface. Explicit expressions of solid and fluid temperatures and Nusselt number are derived under each thermal boundary condition and variances between the three thermal boundary conditions in predicting thermal behaviors are discussed. It is shown that with present parameters, the temperature bifurcation phenomenon occurs in most cases under model B, while this phenomenon cannot be observed under models A and C. The LTNE model holds in almost any conditions under model B, but under models A and C the LTNE model holds with a low hollow ratio (S) and Biot number (Bi), a large effective thermal conductivity ratio (K) and Darcy number (Da). The increase of interfacial convective heat transfer coefficient (Hs) makes the Nusselt number (Nu) of model C more close to but not exceed the Nu of model A, while the Nu under model B is lower than which under models A and C. By using different thermal boundary conditions, the stress jump coefficient (β) effect on heat transfer can be ignored, and with a high Da, a low β and S the Nu number predicted by stress jump interface condition has slight difference from that by stress continuity interface condition.