A SEMI-ANALYTICAL APPROACH TO INVESTIGATE THE VALIDITY OF THE THERMAL EQUILIBRIUM ASSUMPTION IN THE ANALYSIS OF UNSTEADY FREE CONVECTION IN POROUS MICRO-CHANNEL

Abstract

Exploring the transient thermal dynamics of a porous micro-channel, this study delves into a uniform composite substrate governed by the parabolic heat–conduction model. The composite structure comprises a fluid domain (matrix) and solid inserts, each crafted from distinct materials. The research defines the parameter range within the application of the thermal equilibrium assumption (TEA) is suitable for analyzing transient free convection flow in the porous micro-channel, as characterized by the parabolic heat-conduction model. The investigation also scrutinizes the influence of various parameters on the validity of the local thermal equilibrium assumption (LTEA)) within the framework of the parabolic heat conduction model. The most significant impact on the LTEA is observed for the volumetric Biot number, thermal conductivity ratio, Knudsen number, and total thermal capacity ratio. Specifically, large values of the Knudsen number and thermal capacity ratio, along with small values of the Biot number and thermal conductivity ratio, contribute to securing the LTEA.