The solution of the two-dimensional inverse heat transfer problem with the use of the FEM in combination with Trefftz functions

¹ Kielce University of Technology, Faculty of Mechatronics and Machine Building, Chair of Mechanics, al. 1000-lecia P.P.7, 25-314 Poland
email: tmpmj@tu.kielce.pl
² Kielce University of Technology, Faculty of Management and Computer Modelling, Chair of Mathematics, al. 1000-lecia P.P.7, 25-314 Poland
email: beatam@tu.kielce.pl

Abstract

The aim of this paper is to determine the boiling heat transfer coefficient for the cooling liquid flow in a rectangular minichannel with asymmetric heating. The main part of the test section is made up of a vertical minichannel of 1.0 mm depth. The heating foil on the side of the fluid flowing in the minichannel is singlesided enhanced on the selected area. The experiment is carried out with FC-72. The investigations focus on the transition from single-phase forced convection to nucleate boiling, that is, from the zone of boiling incipience further to developed boiling. Owing to the liquid crystal layer located on the heating surface contacting the glass, it is possible to measure the heating wall temperature distribution while increasing the heat flux transferred to the liquid flowing in the minichannel. The objective of the calculations is to evaluate a heat transfer model and numerical approach to solving the inverse boundary problem, and to calculate the heat transfer coefficient. This problem has been solved by means the finite element method in combination with Trefftz functions (FEMT). Trefftz functions are used to construct base functions in Hermite space of the finite element.