Determining 2D temperature field in flow boiling with the use of Trefftz functions

Abstract

The paper proposes the use of Trefftz method to solve the triple coupled heat conduction problem in flow boiling of refrigerant in an asymmetrically heated minichannel. A mathematical model of heat transfer in a rectangular minichannel is suggested. Two sets of Trefftz functions were used to determine 2D temperature fields at a fluid flow in the minichannel tilted at a known angle. The procedure for the calculation of the liquid temperature was coupled with the process of determining temperature fields in two adjacent elements of the experimental stand with the minichannel, i.e. in the glass pane and the heating foil. Heat transfer in the glass, foil and liquid is described using various 2D differential equations with an adequate set of boundary conditions. Solving those equations led to the solving of the triple coupled heat conduction problem made up of one direct and two subsequent inverse problems. The results are presented as: (1) 2D temperature of the glass pane, the heating foil, the flowing liquid, (2) mean square errors between temperature approximations and selected boundary conditions, (3) the heat transfer coefficient versus the distance from the minichannel inlet.