Generalized Heat Transition Matrix for Arbitrarily Shaped Thermal Media and Its Applications to Steady-State Heat Conduction Problems in Large-Scale Systems

Abstract

This article presents a concept of a generalized heat transition matrix (GHTM) used for expressing the steady-state heat conduction characteristics of a thermal block with almost arbitrary shapes and internal structures. A reference surface is defined to separate the thermal block completely from its environment. A generalized heat transition matrix is defined on the reference surface, which associates the equivalence surface heat sources on the reference surface to the temperatures and heat fluxes generated by heat sources outside the concerned thermal block. The generalized heat transition matrix of a thermal block can fully describe its steady-state heat conduction characteristics, and can be reused in a larger system that contains many blocks with identical structures. This property is useful in the analysis of the steady-state heat conduction problem in a multiscale large system using the domain decomposition method.

The Modal Substructuring Method: An Efficient Technique for Large-Size Numerical Simulations

“…Initially developed for mechanical problems [10][11][12], analogous techniques have been used for numerical thermal problems [13]. Concerning the modal reduction methods, the substructuring technique has also been tested: The MIM method [14], for which the modal formulation is used without eigenvectors computation, uses the substructuring technique to link the MIM formulation with another model.…”