A numerical solution to an inverse unsteady-state heat transfer problem involving the Trefftz functions

¹ Faculty of Management and Computer Modelling
² Faculty of Mechatronics and Mechanical Engineering Kielce University of Technology, Al. 1000-lecia P.P. 7, 25-314 Kielce, Poland

^* Corresponding author: beatam@tu.kielce.pl

Published online: 12 May 2017

Abstract

This paper shows the results concerning flow boiling heat transfer in an asymmetrically heated vertical minichannel. The heated element for FC-72 Fluorinert flowing in that minichannel was a thin foil. The foil surface temperature was monitored continuously at 18 points by K-type thermocouples from the outer foil surface. Fluid temperature and pressure in the minichannel inlet and outlet, current supplied to the foil and voltage drop were also monitored. Measurements were carried out at 1 s intervals. The objective was to determine the heat transfer coefficient on the heated foil–fluid contact surface in the minichannel. It was obtained from the Robin boundary condition. The foil temperature was the result of solving the nonstationary two-dimensional inverse boundary problem in the heated foil. Using the FEM combined with Trefftz functions as basis functions solved the problem. The unknown temperature values at nodes were calculated by minimising the adequate functional. The values of local heat transfer coefficients were consistent with the results obtained by the authors in their previous studies when steady-state conditions were analysed. This time, however, these values were analysed as time dependent, which facilitated observation of coefficient changes that were impossible to observe under the steady-state conditions.