Trefftz method in an inverse problem of two-phase flow boiling in a minichannel

Abstract

The paper discusses the application of the Trefftz method for solving a coupled inverse problem concerning heat conduction and flow boiling. The T-complete functions were derived for a two-dimensional stationary energy equation in a flowing fluid, with a known velocity profile. The properties of these functions are described, with a focus on their relationship to harmonic polynomials. In view of the problem domain (two adjacent regions with different physical parameters), two subsequent inverse problems were formulated. The former was solved by approximating the temperature with a combination of harmonic polynomials while for the latter problem a twin-track approach was taken. The first method employed was the Trefftz method with newly generated functions. For comparison, the calculation was repeated using the Picard iterative process combined with the Trefftz method based on harmonic functions. The numerical calculations were conducted using experimental data concerning flow boiling of a refrigerant through a rectangular vertical minichannel. The computation resulted in obtaining two-dimensional temperature distributions (in each region) and a heat transfer coefficient at the solid-fluid interface versus the distance from the minichannel inlet. Both numerical approaches gave comparable results. The experimental heat transfer coefficient was compared with some correlations known from the literature.