Application of adjustment calculus in the nodeless Trefftz method for a problem of two-dimensional temperature field of the boiling liquid flowing in a minichannel

Purpose – The purpose of this paper is to focus on the application of the Trefftz method to the calculation of the two-dimensional (2D) temperature field in the boiling refrigerant flow through an asymmetrically heated vertical minichannel with a rectangular cross-section. The considerations were limited to determining the temperature of the continuous phase – liquid for bubbly and bubbly-slug flow. The numerical solution found with the Trefftz methods was compared with the simplified solution. For nucleate boiling, heat transfer coefficient at the heating foil – liquid contact was determined. Design/methodology/approach – The Trefftz method was used to determine 2D temperature distributions for the glass pane, the heating foil and the boiling liquid. The temperature fields were approximated by the sum of the particular solution and the linear combination of suitable Trefftz functions. Coefficients of linear combination were computed using experimental data, including heating foil temperature measurements obtained with the liquid-crystal method and experimentally determined void fraction. The computations were based on the Trefftz method supplemented with the adjustment calculus. Findings – The way of solving direct and inverse problems of heat conduction in solid bodies (isolating glass, heating foil) and in liquids (boiling refrigerant flowing through the minichannel) was presented. For the first time, both 2D temperature fields for the heating foil and the boiling liquid were calculated while simultaneously using the Trefftz method. The known temperature values of the foil and liquid allowed the calculation of the heat transfer coefficient and the heat flux at the heating foil-liquid contact. Adjustment calculus implemented into the Trefftz method was used to smooth the measurement data and to reduce their errors. Practical implications – The approach proposed in the paper can be applied to determining 2D temperature field, heat flux and heat transfer coefficient in direct and inverse problems concerning two-phase flowing miniature compact heat exchangers. Originality/value – The paper presents a novel implementation of the Trefftz method to simultaneous solving an inverse problem in the heating foil and the contacting flowing liquid.

Download Full-text

Boiling Heat Transfer Characteristics and Film Boiling Collapse Temperature through the Two-Dimensional Temperature Field Measurement

Proceedings of the 15th International Heat Transfer Conference ◽

10.1615/ihtc15.pbl.009511 ◽

2014 ◽

Author(s):

Hiroyasu Ohtake ◽

Koji Hasegawa

Keyword(s):

Heat Transfer ◽

Temperature Field ◽

Field Measurement ◽

Boiling Heat Transfer ◽

Film Boiling ◽

Two Dimensional ◽

Heat Transfer Characteristics ◽

Transfer Characteristics ◽

Collapse Temperature

Download Full-text

Temperature field evaluation of a two-dimensional partial heat flow problem through Green's Functions

10.26678/abcm.cobem2019.cob2019-0381 ◽

2019 ◽

Author(s):

Guilherme Ramalho Costa ◽

José Aguiar santos junior ◽

José Ricardo Ferreira Oliveira ◽

Jefferson Gomes do Nascimento ◽

Gilmar Guimaraes

Keyword(s):

Temperature Field ◽

Heat Flow ◽

Green's Functions ◽

Flow Problem ◽

Green’S Functions ◽

Field Evaluation ◽

Two Dimensional

Download Full-text

An analytical solution of a two-dimensional temperature field in a hollow cylinder under a time periodic boundary condition using Fourier series

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1243/09544062jmes1382 ◽

2009 ◽

Vol 223 (8) ◽

pp. 1889-1901 ◽

Cited By ~ 4

Author(s):

G Atefi ◽

M A Abdous ◽

A Ganjehkaviri ◽

N Moalemi

Keyword(s):

Boundary Condition ◽

Temperature Field ◽

Fourier Series ◽

Temperature Distribution ◽

Analytical Solution ◽

Hollow Cylinder ◽

Periodic Boundary Condition ◽

Periodic Boundary ◽

Separation Of Variables ◽

Two Dimensional

The objective of this article is to derive an analytical solution for a two-dimensional temperature field in a hollow cylinder, which is subjected to a periodic boundary condition at the outer surface, while the inner surface is insulated. The material is assumed to be homogeneous and isotropic with time-independent thermal properties. Because of the time-dependent term in the boundary condition, Duhamel's theorem is used to solve the problem for a periodic boundary condition. The periodic boundary condition is decomposed using the Fourier series. This condition is simulated with harmonic oscillation; however, there are some differences with the real situation. To solve this problem, first of all the boundary condition is assumed to be steady. By applying the method of separation of variables, the temperature distribution in a hollow cylinder can be obtained. Then, the boundary condition is assumed to be transient. In both these cases, the solutions are separately calculated. By using Duhamel's theorem, the temperature distribution field in a hollow cylinder is obtained. The final result is plotted with respect to the Biot and Fourier numbers. There is good agreement between the results of the proposed method and those reported by others for this geometry under a simple harmonic boundary condition.

Download Full-text

Two-dimensional numerical study of temperature field in an anode supported planar SOFC: Effect of the chemical reaction

International Journal of Hydrogen Energy ◽

10.1016/j.ijhydene.2010.07.141 ◽

2011 ◽

Vol 36 (6) ◽

pp. 4228-4235 ◽

Cited By ~ 16

Author(s):

Bariza Zitouni ◽

G.M. Andreadis ◽

Ben Moussa Hocine ◽

Abdenebi Hafsia ◽

Haddad Djamel ◽

...

Keyword(s):

Temperature Field ◽

Chemical Reaction ◽

Numerical Study ◽

Two Dimensional

Download Full-text

Thermal Mapping, via Liquid Crystals, of the Temperature Field near a Heated Surgical Probe

Journal of Heat Transfer ◽

10.1115/1.3450036 ◽

1973 ◽

Vol 95 (2) ◽

pp. 250-256 ◽

Cited By ~ 11

Author(s):

T. E. Cooper ◽

J. P. Groff

Keyword(s):

Blood Flow ◽

Temperature Field ◽

Liquid Crystals ◽

Theoretical Model ◽

Wheatstone Bridge ◽

Visual Display ◽

Two Dimensional ◽

Test Medium ◽

One Dimensional ◽

Water Test

This paper discusses the use of heat for producing clinical lesions in tissue and presents the design and analysis of a resistively heated surgical probe. The probe surface temperature is accurately maintained and controlled by using a Wheatstone bridge. The probe was embedded in a clear agar–water test medium, and the temperature field generated by the probe was measured with liquid crystals, a material that provides a visual display of certain isotherms. Experimental results compare within approximately 10 percent of a two-dimensional numerical solution. A one-dimensional theoretical model is also developed which examines the influence of blood flow on the temperature field.

Download Full-text