LI Xixia, DAI Haiyan, LI Changyu. A New Method for Solving Heat Transfer Problems of Laminate Materials Based on the Differential Theory[J]. Applied Mathematics and Mechanics, 2018, 39(6): 728-736. doi: 10.21656/1000-0887.380116
Citation: LI Xixia, DAI Haiyan, LI Changyu. A New Method for Solving Heat Transfer Problems of Laminate Materials Based on the Differential Theory[J]. Applied Mathematics and Mechanics, 2018, 39(6): 728-736. doi: 10.21656/1000-0887.380116

A New Method for Solving Heat Transfer Problems of Laminate Materials Based on the Differential Theory

doi: 10.21656/1000-0887.380116
  • Received Date: 2017-05-02
  • Rev Recd Date: 2017-07-17
  • Publish Date: 2018-06-15
  • A new analytical method for solving heat transfer problems of laminate materials was proposed based on the differential theory. The curves of temperature variation at the interface of the laminate material were approximately linear in a small time interval. With the method of separation of variables, the analytical solution containing unknown coefficients of each layer in a small time interval was obtained. According to the continuous condition of energy at the interface, the unknown coefficients of each layer were determined. Then the temperature field in the whole time domain was obtained. Finally, the analytical method was used to solve the heat transfer problem of a 3-layer structure. The analytical results were compared with those of the finite element method, and the influences of several parameters on the temperature field were discussed, with the correctness of the proposed method verified.
  • loading
  • [1]
    WANG B L, CUI Y J. Transient inter laminar thermal stress in multi-layered thermoelectric materials[J]. Applied Thermal Engineering,2017(2): 55-67.
    [2]
    KUMAR D, KUMAR P, RAI K N. A study on DPL model of heat transfer in bi-layer tissues during MFH treatment[J]. Computers in Biology & Medicine,2016,75(2): 160-172.
    [3]
    MATSUMOTO N, OKUNO T, OBARA H, et al. Multi-layer heat conduction analysis using SPH method[J]. Transactions of the Japan Society of Mechanical Engineers,2016,82(3): 77-82.
    [4]
    LU S, LIU J, LIN G, et al. Modified scaled boundary finite element analysis of 3D steady-state heat conduction in anisotropic layered media[J]. International Journal of Heat & Mass Transfer,2017,108(1): 2462-2471.
    [5]
    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.(LIU Fang, SHI Weiping. Simulation of the nonlinear heat conduction equation with the lattice Boltzmann method[J]. Applied Mathematics and Mechanics,2015,36(11): 1158-1166.(in Chinese))
    [6]
    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.(ZHAN Yongqiang , ZHANG Chuanlin. A family of high accuracy implicit difference schemes for solving parabolic equations[J]. Applied Mathematics and Mechanics,2014,35(7): 790-797.(in Chinese))
    [7]
    盛宏玉, 李和平, 叶建乔, 等. 介质热传导瞬态分析的一种新半数值解法[J]. 合肥工业大学学报(自然科学版), 2010,33(5): 709-712.(SHENG Hongyu, LI Heping, YE Jianqiao, et al. A new semi-numerical approach for the transient heat conduction analysis of laminated medium[J]. Journal of Hefei University of Technology(Natural Science),2010,33(5): 709-712.(in Chinese))
    [8]
    蓝林华, 富明慧, 刘祚秋. 结构瞬态热传导方程的一种精细解法[J]. 中山大学学报(自然科学版), 2011,50(5): 1-6.(LAN Linhua, FU Minghui, LIU Zuoqiu. A precise solution of transient heat conduction equation for laminate structure[J]. Acta Scientiarum Naturalium Universitatis Sunyatseni,2011,50(5): 1-6.(in Chinese))
    [9]
    李金娥, 王保林, 常冬梅. 材料的非傅里叶热传导及热应力[J]. 固体力学学报, 2011,32(S1): 248-253.(LI Jin’e, WANG Baolin, CHANG Dongmei. Non-Fourier heat conduction and thermal stress of non-Fourier heat conduction an thermal stress of layered materials[J]. Chinese Journal of Solid Mechanics,2011,32(S1): 248-253.(in Chinese))
    [10]
    富明慧, 陈焯智. 层合圆柱三维温度场分析的半解析-精细积分法[J]. 应用力学学报, 2012,29(1): 15-20.(FU Minghui, CHEN Chuozhi. The semi-analytical precise integration method for the analysis of three dimensional temperature field of laminated cylinders[J]. Chinese Journal of Applied Mechanics,2012,29(1): 15-20.(in Chinese))
    [11]
    LIU K C, WANG Y N, CHEN Y S. Investigation on the bio-heat transfer with the dual-phase-lag effect[J]. International Journal of Thermal Sciences,2012,58: 29-35.
    [12]
    MOVAHEDIAN B, BOROOMAND B. The solution of direct and inverse transient heat conduction problems with layered materials using exponential basis functions[J]. International Journal of Thermal Sciences,2014,77: 186-198.
    [13]
    BANDOPADHYAY A, CHAKRABORTY S. Combined effects of interfacial permittivity variations and finite ionic sizes on streaming potentials in nanochannels[J]. Langmuir,2012,28(50): 17552-17563.
    [14]
    XU F, LU T J, SEFFEN K A. Bio-thermomechanics of skin tissues[J]. Journal of the Mechanics & Physics of Solids,2008,56(5): 1852-1884.
    [15]
    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: 146-158.
    [16]
    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.
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (761) PDF downloads(918) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return