New Galerkin-vector theory and efficient numerical method for analyzing steady-state heat conduction in inhomogeneous bodies subjected to a surface heat flux

Xiujiang Shi, Qian Wang*, Liqin Wang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

This paper reports a new semi-analytical model, together with core analytical solutions, for solving steady-state heat-conduction problems involving materials of a semi-infinite matrix embedded with arbitrarily distributed inhomogeneities, and a novel fast computing algorithm for model construction. The thermal field is analyzed as the summation of the solution to the homogeneous matrix and the variations caused by the inhomogeneities. The former is obtained through the route of discrete convolution and FFT/Influence coefficients/Green's function, and the surface heat flux via the conjugate gradient method (CGM). The eigentemperature gradient of the latter is tackled with the numerical equivalent inclusion method (EIM) based on the new analytical formulas for the disturbed temperature and heat flux from the Galerkin vectors. The influences of inhomogeneity shape, location, and heat-conduction properties are studied, and the thermal fields affected by multi-inhomogeneities in a layered form and with a regular or a random distribution are investigated.

Original languageEnglish (US)
Article number113838
JournalApplied Thermal Engineering
Volume161
DOIs
StatePublished - Oct 2019

Keywords

  • Galerkin vector approach
  • Heat conduction, inhomogeneity
  • Numerical equivalent inclusion method

ASJC Scopus subject areas

  • Energy Engineering and Power Technology
  • Industrial and Manufacturing Engineering

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