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

Magdalena Piasecka,Beata Maciejewska

doi:10.1051/epjconf/20122501073

Abstract

2 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 single- sided 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.

Highlights

Transferring large heat fluxes is one of the most significant issues of today’s technology
The heat transfer considerations presented in this article focus on heat transfer coefficient identification, which belongs to the group of inverse heat conduction problems [1,7,8]
Boiling incipience is recognised as a sudden drop in the heating surface temperature that follows its systematic increase, at constant capacity of the internal heat source

Summary

Introduction

Transferring large heat fluxes is one of the most significant issues of today’s technology. Owing to the change of state that accompanies boiling, it is possible at the same time to meet two contradictory demands: to obtain the largest possible heat flux at small temperature difference between the heating surface and the saturated liquid, and to keep small dimensions of heat transfer systems. The heat transfer considerations presented in this article focus on heat transfer coefficient identification, which belongs to the group of inverse heat conduction problems [1,7,8]. Both the inverse problem and the auxiliary direct problem were solved by means of the Trefftz method. Additional information on the Trefftz method is included in [2,4,6,15]

Objectives

Results

Conclusion