The use of Trefftz functions for approximation of measurement data in an inverse problem of flow boiling in a minichannel

Abstract

The paper is devoted to a computational problem of predicting a local heat transfer coefficient from experimental temperature data. The experimental part refers to boiling flow of a refrigerant in a minichannel. Heat is dissipated from heating alloy to the flowing liquid due to forced convection. The mathematical model of the problem consists of the governing Poisson equation and the proper boundary conditions. For accurate results it is required to smooth the measurements which was obtained by using Trefftz functions. The measurements were approximated with a linear combination of Trefftz functions. Due to the computational procedure in which the measurement errors are known, it was possible to smooth the data and also to reduce the residuals of approximation on the boundaries. The conducted experiment will be presented here only in brief, more detailed description can be found in (3),(4).The basic element of the experimental stand is a test section containing a minichannel with a refrigerant (R-123) flowing through it. One of the walls of the minichannel is a heating foil supplied with the direct current whose parameters can be controlled. Due to a layer of thermosensitive liquid crystals spread on the foil it is possible to observe (through a glass pane) changes in the foil surface hue. The back wall of the minichannel is kept in constant temperature. The quantities measured during the experiment are: local temperature of the heating foil , inlet and outlet liquid temperature and pressure, current and voltage drop of the electric power supplied to the heater. Velocity, pressure and inlet liquid subcooling do not change in the successive experiments. Wanted parameters include local heat transfer coefficients on the foil-liquid interface.