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.
Highlights
Progress in the miniaturization of modern components and systems, rendered possible by technological advances, has led to the development of methods ensuring their functionality and proper performance
The designing process faces the problem of the selection of suitable calculation procedures that will allow the identification of processes governing heat transfer in the small-sized channels
Determined using the Trefftz functions, the temperature approximations for the glass plate TG, heating foil TF and liquid TL are continuous functions that satisfy equations (1), (2) and (5) exactly and the boundary conditions adopted for these equations approximately
Summary
Progress in the miniaturization of modern components and systems, rendered possible by technological advances, has led to the development of methods ensuring their functionality and proper performance. One of the ways to intensify heat transfer and satisfy the criteria above is associated with the phase change of refrigerants, in particular in flow boiling in minichannels This creates the idea of the so-called compact heat exchangers (evaporators and condensers) within cooling systems. The idea of the Trefftz method consists in an approximation of an unknown solution of a linear partial differential equation by a linear combination of functions satisfying this governing equation exactly. The boundary conditions reported for each of the equations led to the solution of a triple coupled heat conduction problem made up of one direct (in the glass) and two subsequent inverse problems (in the foil and the liquid). To model the temperature field in the third region – the liquid – the Trefftz functions given for the energy equation were used [3], at the velocity profile adopted to take into account the minichannel tilt angle
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