球体表面受任意周期热扰动时非傅里叶导热的求解与分析

赵伟涛 1; 2; 吴九汇 1; 2

doi:10.7652/xjtuxb201401003

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球体表面受任意周期热扰动时非傅里叶导热的求解与分析

更新时间：2025-07-09

- 球体表面受任意周期热扰动时非傅里叶导热的求解与分析
- Solution and Analysis of Non-Fourier Heat Conduction in a Solid Sphere under Arbitrary Periodic Surface Thermal Disturbance
- 西安交通大学学报 2014年48卷第1期页码：13-18
- 作者机构：
  
  1. 西安交通大学机械学院,西安,710049
  2. 西安交通大学机械结构强度与振动国家重点实验室,西安,710049
- 作者简介：
- 基金信息：
  
  : 2013-05-06。作者简介: 赵伟涛(1986—),男,博士生;吴九汇(通信作者),男,教授,博士生导师。基金项目: 教育部新世纪优秀人才支持计划资助项目(NCET-09-0644);高等学校博士学科点专项科研基金资助项目(20090201120047)
- DOI：10.7652/xjtuxb201401003
  中图分类号： TK124
- 网络首发：2014-01-10，
  
  纸质出版：2014
- 稿件说明：
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赵伟涛 1, 2, 吴九汇 1, 等. 球体表面受任意周期热扰动时非傅里叶导热的求解与分析[J]. 西安交通大学学报, 2014,48(1):13-18.

Solution and Analysis of Non-Fourier Heat Conduction in a Solid Sphere under Arbitrary Periodic Surface Thermal Disturbance[J]. 2014, 48(1): 13-18.
赵伟涛 1, 2, 吴九汇 1, 等. 球体表面受任意周期热扰动时非傅里叶导热的求解与分析[J]. 西安交通大学学报, 2014,48(1):13-18. DOI： 10.7652/xjtuxb201401003.

Solution and Analysis of Non-Fourier Heat Conduction in a Solid Sphere under Arbitrary Periodic Surface Thermal Disturbance[J]. 2014, 48(1): 13-18. DOI： 10.7652/xjtuxb201401003.

摘要

为研究球体表面遭受任意周期温度变化这类非傅里叶传热情形下的热波传播特性

采用双曲线型热传导方程来描述该超急速热传导问题。首先

利用分离变量法和Duhamel积分原理

得到了球体表面温度突然变化时和以简谐规律周期变化时这两种情况下的解析解; 然后

在此基础上应用傅里叶级数展开法和叠加原理

获得了球体表面温度任意周期变化时的非傅里叶热传导的温度场。利用得到的解析表达式进行数值模拟

分析了不同热松弛时间、不同时刻和不同位置对温度响应的影响

讨论了非傅里叶热传导模型所给出的温度响应与傅里叶热传导模型的差别。结果表明:非傅里叶热传导模型所给出的温度响应曲线存在一系列有序的阶跃点

其响应的幅值随着热松弛时间的减小而减小。这种方法能够处理许多在生产实际中具有周期边界条件的非傅里叶热传导问题。

Abstract

In order to investigate the characteristics of thermal wave propagating in a solid sphere under arbitrary periodic surface thermal disturbance

the hyperbolic heat conduction equation was employed to describe this problem involving high-rate change of temperature. When the solid sphere surface is subjected to a sudden temperature change or a harmonic temperature change

the analytic solution of this problem is obtained by using the separation of the variables method and the Duhamel's principle. Then the analytic solution of temperature field is achieved by using the Fourier series and the principle of superposition when the solid sphere surface is subjected to an arbitrary periodic temperature change. Using the obtained analytical solution

the temperature profiles of the solid sphere were analyzed

and the differences between the temperature response obtained by using the non-Fourier heat conduction model and that by using the Fourier model were discussed. The results show that there exists an orderly series of ‘jump points' at temperature response curve which obtained by using the non-Fourier heat conduction model; and the amplitude of the temperature wave attenuates with the decrease of thermal relaxation. This solution can be applied for more realistic periodic boundary conditions occurring in engineering.

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references

TUNG T L, FONG E. Application of solution structure theorem to non-Fourier heat conduction problems: analytical approach[J]. International Journal of Heat and Mass Transfer, 2011, 54(23/24): 4796-4806.

王颖泽, 张小兵, 宋新南. 圆柱外表面受热冲击问题的广义热弹性分析[J]. 力学学报, 2012, 44(2): 317-325.

WANG Yingze, ZHANG Xiaobing, SONG Xinnan. Research on generalized thermoelastic problems of a solid cylinder subjected to thermal shock[J]. Acta Mechanica Sinica, 2012, 44(2): 317-325.

CATTANEO C. Sulla conduzione del calore[J]. Atti del Seminario Matematico e Fisico della Universita di Modena, 1948, 3(3): 83-101.

VERNOTTE P. Les paradoxes de la theorie continue deI'equation de la chaleur[J]. Compute Rendus, 1958, 246(22): 3154-3155

周凤玺, 李世荣. 平板在周期温度激励下的非傅里叶温度响应[J]. 西安交通大学学报, 2006, 40(7): 866-868.

ZHOU Fengxi, LI Shirong. Non-Fourier temperature response in a plate under periodic temperature boundary condition[J]. Journal of Xi'an Jiaotong University, 2006, 40(7): 866-868.

SARKAR D, HAJI-SHEIKH. A view of the thermal wave behaviors in thin plates[J]. International Communications in Heat and Mass Transfer, 2012, 39(8): 1009-1017.

TANG D W, ARAKI N. Non-Fourier heat conduction in a finite medium under periodic surface thermal disturbance[J]. International Journal of Heat Mass Transfer, 1996, 39(8): 1585-1590.

MOOSAIE A. Non-Fourier heat conduction in a finite medium subjected to arbitrary periodic surface disturbance[J]. International Communications in Heat and Mass Transfer, 2007, 34(8): 996-1002.

BARLETTA A, ZANCHINI E. Thermal-wave heat conduction in a solid cylinder which undergoes a change of boundary temperature[J]. Heat and Mass Transfer, 1997, 32(4): 285-291.

ATEFI G, TALAEE M R. Non-Fourier temperature field in a solid homogeneous finite hollow cylinder[J]. Archive of Applied Mechanics, 2011, 81(5): 569-583.

MISHRA S C, SAHAI H. Analyses of non-Fourier heat conduction in 1-D cylindrical and spherical geometry: an application of the lattice Boltzmann method[J]. International Journal of Heat Mass Transfer, 2012, 55(23/24): 7015-7023.

JIANG F. Solution and analysis of hyperbolic heat propagation in hollow spherical objects[J]. Heat and Mass Transfer, 2006, 42(12): 1083-1091.

SHIRMOHAMMADI R, MOOSAIE A. Non-Fourier heat conduction in a hollow sphere with periodic surface heat flux[J]. International Communications in Heat and Mass Transfer, 2009, 36(8): 827-833.

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