A MULTI-SCALE HEAT CONDUCTION ANALYSIS METHOD FOR POROUS MEDIA IN CONSIDERATION OF MICROSCOPIC HEAT TRANSFER

Abstract

We propose a multi-scale analysis method for heat conduction problem of porous media based on the homogenization method. For the implementation of multi-scale heat conduction analysis, we discuss the differences and characteristics of the homogenization for heat conduction problem in comparison with that for deformation problem particularly by focusing our attention to the definition of micro-structure (unit cell). First, we formulate the homogenization method for heat conduction problem considering the heat transfer at porous boundaries in micro-scale and specify the points to notice of the formulation. Secondly, we examine the validity of the proposed method of multi-scale heat conduction analysis based on the homogenization method by carrying out simple several numerical experiments. Finally, a 3-dimensional numerical example for porous medium at elevated temperature is presented to demonstrate the capability of the method.