Trefftz method for solving two-dimensional temperature field of boiling fluid flowing along the minichannel

¹ Kielce University of Technology, Chair of Mathematics, Al. 1000-lecia PP 7, 25-314 Kielce, Poland
² Kielce University of Technology, Chair of Mechanics, Al. 1000-lecia PP 7, 25-314 Kielce, Poland

Abstract

The paper focuses on the numerical solution to two-dimensional temperature field of boiling liquid flowing along a vertical, asymmetrically heated minichannel with a rectangular cross-section. One of the walls of a minichannel is a DC supplied heating foil. The parallel walls are made of glass panes for thermal insulation and for observation of the fluid flow and the void fraction. A thin layer of thermosensitive liquid crystal paint on the outer side of the heating foil enabled to record two-dimensional temperature distribution of outer foil surface. The paper presents computations based on Trefftz method for finding two-dimensional temperature field of boiling liquid flowing along the minichannel. The presented research is limited only to a liquid phase of the two-phase mixture observed in the minichannel. The velocity of liquid flowing through the minichannel is represented by a piecewise linear approximating function. To solve energy equation for liquid phase, Trefftz functions specially generated for this purpose were employed. Temperature field in the fluid was approximated by a linear combination of Trefftz functions. Temperature at the interface between working fluid and foil amounts to the saturation temperature. Temperature distribution in the foil and the glass pane was also computed using proper Trefftz functions.