Iterative Multi-Scale Approach for Heat Conduction with Radiation Problem in Porous Materials

[+] Author and Article Information
Ronen Haymes

The Energy Engineering division Ben-Gurion University of the Negev, Beer-Sheva, Israel, 84105

Erez Gal

Department of Structural Engineering Ben-Gurion University of the Negev, Beer-Sheva, Israel, 84105
erezgal@ bgu.ac.il

1Corresponding author.

ASME doi:10.1115/1.4039420 History: Received December 15, 2017; Revised February 13, 2018


This paper describes a thermal homogenization approach to the application of a multi-scale formulation for heat conduction with radiation problems in a porous material. The suggested formulation enables to evaluate the effective macroscopic thermal conductivity, based on the microscopic properties such as porosity, and can also provide the microscopic radiosity heat flux, based on the macroscopic temperature gradient field. This is done by scaling up and down between the microscopic and macroscopic models according to the suggested methodology. The proposed methodology involves a new iterative upscaling procedure, which uses heat conduction at macroscopic problem and heat transfer by conduction and radiation at microscopic problem. This reduces the required computational time, while maintaining the required level of accuracy. The suggested multi-scale formulation has been verified by comparing its results with reference finite element solutions of porous (filled with air) materials examples, the results shows excellent agreement (up to 5% discrepancy) with reference solutions. The efficiency of the suggested formulation was, demonstrated by solving a full scale engineering transient problem.

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