Analytical study of flow and heat transfer in an annular porous medium subject to asymmetrical heat fluxes

Fully developed forced convective heat transfer in an annulus filled with a porous medium subject to asymmetrical heating is investigated analytically with different models in this work. The classic Darcy and Brinkman models were employed for the fluid flow, while the local thermal equilibrium (LTE) and the local thermal non-equilibrium (LTNE) models were employed to describe the heat transfer process in porous media. An analytical model based on fin theory was also employed for analyzing this problem. Exact solutions with Darcy-LTNE, Darcy-LTE, Brinkman-LTNE, Brinkman-LTE, and the fin models were obtained. Among these solutions, the Brinkman-LTNE solution can be treated as the benchmark, as it is a complete model, which covers the effect of viscous force near the solid wall and the temperature difference between the solid and fluid phases. The basic parameters that affect the velocity and temperature fields were analyzed in depth. The velocity and temperature profiles with these different models were also presented. The effects of some critical parameters on thermal performance of asymmetrically heated annulus fitted with a porous medium were discussed. The cited different analytical models were compared in detail with each other. The critical heat flux (HF) ratios for the inner and outer walls were presented in terms of a Nu-xi curve for the five models. These solutions were developed for an asymmetrically heated annular channel filled with a porous medium, which can predict the thermal performance within a wide range of radii and HF ratios.