Convective heat transfer in a porous-medium micro-annulus with effects of the boundary slip and the heat-flux asymmetry: An exact solution

Abstract

Flow and heat transfer in a micro-annulus with the porous material is analytically investigated using local thermal equilibrium (LTE) and local thermal non-equilibrium (LTNE) models with effects of flow/thermal slips and asymmetric heat fluxes. Analytical solutions for velocity and temperatures are obtained. Effects of key factors on convective heat transfer are examined. An increase in the Knudsen number and the inverse of a modified Darcy number can homogenize the velocity. When heat flux (HF) ratio is –R2, the temperatures of solid and fluid show linear profiles. LTNE model must be considered for small duct scale, lower effective thermal conductivity ratio or poor local convective heat transfer between solid and fluid phases. A limit exists for heat transfer enhancement by homogenizing the flow field. Critical HF ratios corresponding to the asymptotic line are verified. The opposite effects of flow slip and thermal slip on heat transfer lead to the maximum heat transfer. This analytical solution predicts the thermal performance of porous medium micro-annulus in wide ranges of radius ratio, Knudsen number, and HF ratio.