Homotopy perturbation method combined with Trefftz method in numerical identification of liquid temperature in flow boiling

The paper is focused on numerical identification of 2D temperature fields in flow boiling of the liquid through a horizontal minichannel with a rectangular cross-section. The heat transfer process in the minichannel is described by a two-dimensional energy equation with the corresponding boundary conditions. Liquid temperature is determined using the homotopy perturbation method (HPM) with Trefftz functions for Laplace’a equation. The numerical solution to the energy equation found with the HPM is compared with the solution obtained for the simplified form of the energy equation. Considering that only the thermal sublayer is taken into account, both solutions give similar results

Radial basis functions in mathematical modelling of flow boiling in minichannels

The paper addresses heat transfer processes in flow boiling in a vertical minichannel of 1.7 mm depth with a smooth heated surface contacting fluid. The heated element for FC-72 flowing in a minichannel was a 0.45 mm thick plate made of Haynes-230 alloy. An infrared camera positioned opposite the central, axially symmetric part of the channel measured the plate temperature. K-type thermocouples and pressure converters were installed at the inlet and outlet of the minichannel. In the study radial basis functions were used to solve a problem concerning heat transfer in a heated plate supplied with the controlled direct current. According to the model assumptions, the problem is treated as twodimensional and governed by the Poisson equation. The aim of the study lies in determining the temperature field and the heat transfer coefficient. The results were verified by comparing them with those obtained by the Trefftz method

Homotopy perturbation method combined with Trefftz method in numerical identification of liquid temperature in flow boiling

The paper is focused on numerical identification of 2D temperature fields in flow boiling of the liquid through a horizontal minichannel with a rectangular cross-section. The heat transfer process in the minichannel is described by a two-dimensional energy equation with the corresponding boundary conditions. Liquid temperature is determined using the homotopy perturbation method (HPM) with Trefftz functions for Laplace’a equation. The numerical solution to the energy equation found with the HPM is compared with the solution obtained for the simplified form of the energy equation. Considering that only the thermal sublayer is taken into account, both solutions give similar results

Determination of two-dimensional temperatuure field of boiling liquid flowing in a vertical minichannel

Celem pracy jest zastosowanie metody Trefftza do wyznaczenia dwuwymiarowego pola temperatury wrzącego czynnika chłodniczego płynącego przez asymetrycznie ogrzewany prostokątny minikanał. Dla równania zachowa¬nia energii przy znanym profilu prędkości wyprowadzono funkcje Trefftza. Obliczenia przeprowadzono dla fazy ciekłej. Wyniki porównano z uproszczonym modelem, gdzie rozwiązanie metodą Trefftza połączono z metodą operacji odwrotnych. W obu podejściach otrzymano zbieżne wyniki.Application of the Trefftz method in the determination of two-dimensional temperature field of boiling liquid flowing through an asymmetrically heated rectangular minichannel is presented in the paper. The Trefftz functions for a known velocity profile were introduced in the energy balance equation Calculations were performed for liquid phase only. The results were compared with a simplified model where the Trefftz method was combined with inverse operations. Both approaches gave similar results

The application of Fourier transform to the identification of temperature distribution in HFE-7100 flow boiling in an annular minigap

In the paper the results of investigations into HFE-7100 flow boiling heat transfer in a cylindrical minigap a 1 mm wide created between the external glass pipe and the copper pipe were discussed. A cartridge heater located axially heated fluid flowing along the minigap. The cooling fluid temperature and pressure at the inlet and the outlet to/from the minigap and temperature of the heater in 18 points were measured. Two-dimensional mathematical model for heat transfer coefficient determination was proposed. It was assumed that in the test section the heat transfer process was in steady state and the fluid flow was laminar. The temperature of the metal pipe near the heater was assumed to satisfy Laplace’s equation. The problem formulated in this way was solved by two methods: the Fourier transform and the Trefftz method. The working fluid temperature was calculated depending on the flow type: for single phase flow with boiling incipience and for two-phase flow, respectively. The heat transfer coefficient at the fluid – copper pipe interface was calculated due to the Robin condition. Local heat transfer coefficient values obtained from the Fourier transform and from the Trefftz method were similar. Results were presented and discussed

Modelling of flow boiling heat transfer in a cylindrical annulus mini gap

This paper presents the results of investigations into flow boiling heat transfer in a mini gap 1 mm wide. The mathematical approaches of the heat transfer coefficient determination were also proposed. It was considered two ways of describing layers in a measurement module with a cylindrical annulus mini gap. In the first approach, the measurement module was treated as a planar multilayer wall and in the second approach - as a multilayer cylindrical wall. The values of the local heat transfer coefficients, determined from two approaches, were compared. Both approaches gave similar results

Trefftz method in solving Fourier-Kirchhoff equation for two-phase flow boiling in a vertical rectangular minichannel

This paper presents the results of investigations into flow boiling heat transfer in an asymmetrically heated vertical minichannel of 1.7 mm depth. The heated element for FC-72 flowing in the minichannel was an alloy plate 0.45 mm thick, microstructured on one side, in direct contact with the flowing fluid. The computational part of the study contains approximate steady state solutions of the heat transfer problems described by Poisson.s equation and the energy equation for the heated plate and the fluid, respectively. For both equations, the boundary conditions were specified on the basis of experimental data. Temperature of the outer plate surface, measured by infrared thermography, and heat losses to ambient air were included in the calculations. For the energy equation we assumed parabolic profile of fluid velocity and the equality of temperatures and heat fluxes at the interface between the heated surface and the fluid. The void fraction was taken from a single-phase flow model. Two-dimensional temperature distributions were obtained by the Trefftz method and, due to the Robin condition at the interface between them, it was possible to calculate the heat transfer coefficient. Its values were compared to those obtained by other correlations known from literature