THERMAL SCIENCE

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Qianqian Zhang

,

Haopeng Song

,

Cunfa Gao

THE 3-D PROBLEM OF TEMPERATURE AND THERMAL FLUX DISTRIBUTION AROUND DEFECTS WITH TEMPERATURE-DEPENDENT MATERIAL PROPERTIES

ABSTRACT
The analytical solution of 3-D heat conduction problem, including the temperature and thermal flux fields, is one of the important problems that have not been completely solved in solid mechanics. Considering the temperature dependence of material parameters makes the problem more difficult. In this paper, we first reduce the 3-D temperature-dependent heat conduction problem to the solution of 3-D Laplace equation by introducing the intermediate function. Then, the generalized ternary function is proposed, and the general solution of 3-D Laplace equation is given. Finally, the analytical solutions of three specific problems are obtained and the corresponding temperature-thermal flux fields are discussed. The results show that the thermal flux field of 3-D temperature dependent problem is the same as the classical constant thermal conductivity approach result, while the temperature field is different from the classical result. Thermal flux at a planar defect boundary has r–1/2 singularity, and its intensity is proportional to the fourth root of defect width. On the other hand, when blocked by a planar defect, the thermal flux distribution will re-adjusted so that it overflows at the same rate from all parts of the planar defect boundary.
KEYWORDS
temperature-dependent, three-dimensional problem, thermal conductivity, thermal flux, temperature field
PAPER SUBMITTED: 2022-10-03
PAPER REVISED: 2022-12-07
PAPER ACCEPTED: 2022-12-15
PUBLISHED ONLINE: 2023-02-11
DOI REFERENCE: https://doi.org/10.2298/TSCI221003028Z
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2023, VOLUME 27, ISSUE Issue 5, PAGES [3903 - 3920]
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The 3-D problem of temperature and thermal flux distribution around defects with temperature-dependent material properties

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence