FE2 multi-scale framework for the two-equation model of transient heat conduction in two-phase media

In the study of transient heat conduction in heterogeneous two-phase media, the local thermal non-equilibrium condition calls for the use of a two-equation model to appropriately describe different tem-peratures in the two phases. We propose for the two-equation model an FE2 multi-scale framework that is capable of addressing nonlinear conduction problems. The FE2 framework consists of volume-averaged macroscale equations, well-defined microscale problems, and the information exchange between the two scales. Compared to a traditional FE2 method for the one-equation model, the proposed FE2 framework introduces an additional source term at the macroscale that is upscaled from the microscale interfacial heat transfer. At variance with the tangent matrices (i.e., effective conductivity) of the heat flux, the tan-gent matrices of the interfacial heat transfer depend on the microscopic length scale. The proposed FE2 framework is validated against single-scale direct numerical simulations, and some numerical examples are employed to demonstrate its potential. (c) 2021 The Author(s). Published by Elsevier Ltd.

Automated summary

In the study of transient heat conduction in heterogeneous two-phase media, a FE2 multi-scale framework is proposed to address nonlinear conduction problems by using a two-equation model to describe different temperatures, with an additional source term at the macroscale upscaled from microscale interfacial heat transfer. The tangent matrices of the interfacial heat transfer depend on the microscopic length scale, and the FE2 framework is validated against single-scale direct numerical simulations to demonstrate its potential.