基于拓展分离变量法的非傅里叶传热研究

doi:10.19596/j.cnki.1001-246x.7772

计算物理 ›› 2018, Vol. 35 ›› Issue (6): 685-692.DOI: 10.19596/j.cnki.1001-246x.7772

基于拓展分离变量法的非傅里叶传热研究

李细霞, 王丽, 戴海燕, 李长玉

华南理工大学广州学院汽车与交通工程学院, 广州 510800

收稿日期:2017-09-25 修回日期:2017-11-16 出版日期:2018-11-25 发布日期:2018-11-25
通讯作者: 李长玉(1981-),男,汉族,湖北老河口人,工学博士,副教授,E-mail:licy@gcu.edu.cn
作者简介:李细霞(1982-),女,汉族,湖北黄冈人,工学硕士,讲师,E-mail:lixx@gcu.edu.cn
基金资助:
广东省青年创新类人才项目基金（2016KQNCX226）资助

Non-Fourier Heat Transfer Based on Extended Separation Variable Method

LI Xixia, WANG Li, DAI Haiyan, LI Changyu

School of Automotive and Traffic Engineering, Guangzhou College of SCUT, Guangzhou 510800, China

Received:2017-09-25 Revised:2017-11-16 Online:2018-11-25 Published:2018-11-25

摘要/Abstract

摘要： 常规的分离变量方法不能求解非傅里叶传热模型问题，本文对常规分离变量法进行拓展，利用拓展后的方法求解热传导的傅里叶模型，单相位滞后（C-V）模型和双相位滞后（DPL）模型，比较利用三种模型计算温度场的差别.研究C-V模型和DPL模型中温度波动的规律，得到温度波动速度和热流量时间滞后值的关系.

关键词: 分离变量法, 非傅里叶模型, 温度场, 双相位滞后

Abstract: Non-Fourier heat transfer model cannot be solved by conventional method of separating of variables. A conventional method of separating variables is developed. Fourier model, Cattaneo-Vernotte (C-V) model and dual phase lag (DPL) model are solved by the method. Differences of temperature fields calculated with three models are compared. Temperature fluctuation in C-V model and DPL model is studied. And relation between temperature fluctuation velocity and time lag of heat flux is studied.

Key words: separation of variables method, non-Fourier model, temperature field, dual-phase-lag models

中图分类号:

李细霞, 王丽, 戴海燕, 李长玉. 基于拓展分离变量法的非傅里叶传热研究[J]. 计算物理, 2018, 35(6): 685-692.

LI Xixia, WANG Li, DAI Haiyan, LI Changyu. Non-Fourier Heat Transfer Based on Extended Separation Variable Method[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2018, 35(6): 685-692.

参考文献

[1] WU Z, LI L, DO Y K. Least squares regularized method for one-dimensional source inverse heat conduction problem[J]. Chinese Journal of Computational Physics, 2016,33(1):49-56.
[2] LIU C, LI Z, LI D. Analysis on heat transfer coefficient of a PCM-glazed unit[J]. Chinese Journal of Computational Physics, 2016,33(4):427-433.
[3] 詹涌强, 张传林.解抛物型方程的一族高精度隐式差分格式[J].应用数学和力学,2014,35(7):790-797.
[4] 刘芳, 施卫平.用格子Boltzmann方法模拟非线性热传导方程[J].应用数学和力学,2015,36(11):1158-1166.
[5] WANG B L, CUI Y J. Transient interlaminar thermal stress in multi-layered thermoelectric materials[J]. Applied Thermal Engineering, 2017,(2):55-67.
[6] XU F, LU T J, SEFFEN K A. Biothermomechanics of skin tissues[J]. Journal of the Mechanics & Physics of Solids, 2008, 56(5):1852-1884.
[7] CAO J, XU X, WANG Y.Parallel algorithms for separable elliptic equation based on GPU[J].Chinese Journal of Computational Physics, 2015,32(4):475-481.
[8] LIN S, LI C. Semi-analytical solution of bio-heat conduction for multi-layers skin subjected to laser heating and fluid cooling[J]. Journal of Mechanics in Medicine & Biology, 2016, 17(2):1-25.
[9] XU F, LU T J, SEFFEN K A, et al. Mathematical modeling of skin bioheat transfer[J]. Applied Mechanics Reviews, 2009, 62(5):1201-1210.
[10] 陈玲红, 左磊, 吴建, 等.微尺度碳粒的激光诱导辐射非傅里叶现象分析[J].中国激光,2014,(4):197-203.
[11] 王颖泽, 徐杰, 许冠杰, 等.热冲击下平面薄板非傅里叶效应的解析分析[J].江苏大学学报(自然科学版),2016,(4):404-408.
[12] 张丽静, 尚新春.由激光辐照固体表面引起的非Fourier三维传热问题的解析解[J].北京理工大学学报,2016,(8):876-880.
[13] 王海东, 刘锦辉, 过增元,等.金属纳米薄膜中稳态非傅里叶导热的实验[J].科学通报,2012,(19):1800-1805.
[14] VERNOTTE P. LES paradoxes DE LA théorie continue DE l'équation DE LA chaleur[J]. Cahiers DE LA Méditerranée, 1958, 41(1):3154-5
[15] TZOU D Y. A unified field approach for heat conduction from macro-to micro-scales[J]. Journal of Heat Transfer, 1995, 117(1):8-16.
[16] VEDAVARZ A, KUMAR S, MOALLEMI M K. Significance of non-Fourier heat waves in conduction[J]. Journal of Heat Transfer, 1994, 116(1):221-224.
[17] KASHCOOLI M, SALIMPOUR M R, SHIRANI E. Heat transfer analysis of skin during thermal therapy using thermal wave equation[J]. Journal of Thermal Biology, 2017, 64(2):7-18.
[18] LIU K C, CHEN H T, CHENG P J. Inverse investigation of non-Fourier heat conduction in tissue[J]. Journal of Thermal Biology, 2016, 21(2):68-73.
[19] RAMADAN K. Semi-analytical solutions for the dual phase lag heat conduction in multilayered media[J]. International Journal of Thermal Sciences, 2009, 48(1):14-25.
[20] LI L, ZHOU L, YANG M. An expanded lattice Boltzmann method for dual phase LAG model[J]. International Journal of Heat & Mass Transfer, 2016, 93(2):834-838.
[21] MA J, SUN Y, YANG J. Analytical solution of non-Fourier heat conduction in a square plate subjected to a moving laser pulse[J]. International Journal of Heat & Mass Transfer, 2017, 115(2):606-610.
[22] LIN S M, LI C Y. Analytical solutions of non-Fourier bio-heat conductions for skin subjected to pulsed laser heating[J]. International Journal of Thermal Sciences, 2016, 110(2):146-158.
[23] JOSEPH D D, PREZIOSI L. Heat waves[J]. Review of Modern Physics, 1989, 61(1):41-73.

基于拓展分离变量法的非傅里叶传热研究

Non-Fourier Heat Transfer Based on Extended Separation Variable Method

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