This paper describes a thermal homogenization approach to the application of a multiscale 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 multiscale formulation has been verified by comparing its results with reference finite element (FE) 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.
Iterative Multiscale Approach for Heat Conduction With Radiation Problem in Porous Materials
Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received December 15, 2017; final manuscript received February 13, 2018; published online April 11, 2018. Assoc. Editor: Laurent Pilon.
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Haymes, R., and Gal, E. (April 11, 2018). "Iterative Multiscale Approach for Heat Conduction With Radiation Problem in Porous Materials." ASME. J. Heat Transfer. August 2018; 140(8): 082002. https://doi.org/10.1115/1.4039420
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