Three-dimensional problem of temperature and thermal flux distribution around defects with temperature-dependent material properties

IF 1.1 4区工程技术 Q4 THERMODYNAMICS Thermal Science Pub Date : 2023-01-01 DOI:10.2298/tsci221003028z

Qianqian Zhang, Hao Song, Cunfa Gao

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Abstract

The analytical solution of three-dimensional 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 three-dimensional temperature-dependent heat conduction problem to the solution of three-dimensional Laplace equation by introducing the intermediate function. Then, the generalized ternary function is proposed, and the general solution of three-dimensional 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 three-dimensional 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.

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具有温度相关材料性质缺陷的三维温度和热通量分布问题

三维热传导问题(包括温度场和热通量场)的解析解是固体力学中尚未完全解决的重要问题之一。考虑材料参数的温度依赖性使问题变得更加困难。本文首先通过引入中间函数，将三维温度相关的热传导问题简化为三维拉普拉斯方程的求解。然后，提出了广义三元函数，并给出了三维拉普拉斯方程的通解。最后，给出了三个具体问题的解析解，并讨论了相应的温度-热通量场。结果表明，三维温度相关问题的热流场与经典的恒定导热系数方法结果相同，而温度场与经典的结果不同。平面缺陷边界处的热通量具有r-1/2奇点，其强度与缺陷宽度的四次方根成正比。另一方面，当被平面缺陷阻挡时，热通量分布将被重新调整，使其以相同的速率从平面缺陷边界的各个部分溢出。

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来源期刊

Thermal Science 工程技术-热力学

CiteScore

2.70

自引率

29.40%

发文量

399

审稿时长

5 months

期刊介绍： The main aims of Thermal Science to publish papers giving results of the fundamental and applied research in different, but closely connected fields: fluid mechanics (mainly turbulent flows), heat transfer, mass transfer, combustion and chemical processes in single, and specifically in multi-phase and multi-component flows in high-temperature chemically reacting flows processes present in thermal engineering, energy generating or consuming equipment, process and chemical engineering equipment and devices, ecological engineering, The important characteristic of the journal is the orientation to the fundamental results of the investigations of different physical and chemical processes, always jointly present in real conditions, and their mutual influence. To publish papers written by experts from different fields: mechanical engineering, chemical engineering, fluid dynamics, thermodynamics and related fields. To inform international scientific community about the recent, and most prominent fundamental results achieved in the South-East European region, and particularly in Serbia, and - vice versa - to inform the scientific community from South-East European Region about recent fundamental and applied scientific achievements in developed countries, serving as a basis for technology development. To achieve international standards of the published papers, by the engagement of experts from different countries in the International Advisory board.