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高校应用数学学报
Applied Mathematics A Journal of Chinese Universities  2020, Vol. 35 Issue (2): 199-210    DOI:
    
A singularly perturbed two parameter solution for the distribution of non Fourier temperature field with a jump in thermal conductivity
BAO Li-ping, LI Wen-yan, WU Li-qun
1.School of science, Hangzhou Dianzi University, Hangzhou 310018;
2. School of Mechanical Engineering, Hangzhou Dianzi University, Hangzhou 310018
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Abstract  In this paper, a temperature field model is constructed by using non-Fourier heat
conduction law, i.e. a class of singularly perturbed hyperbolic equations with small parameters in
an unbounded domain. The singularly perturbed two-parameter hyperbolic nonlinear equations with
discontinuous coefficients are obtained when the heat conduction coefficients jump due to sharp temperature changes. By using the singularly perturbed biparametric expansion method, the asymptotic
solution of the problem is obtained. Firstly, the expansion of the problem is obtained by using the
singularly perturbed method, and the existence and uniqueness of the internal and external solutions
are obtained. The position expression of the jump of the thermal conductivity coefficient is determined
by the method of separating variables, and the slit method is used to connect the slits of the two sides of
the jump position of the thermal conductivity coefficient, thus the asymptotic expansion of the solution
is obtained. Secondly, the uniform validity of the asymptotic solution is obtained by estimating the
residual term, and the distribution of the complete temperature field is obtained.

Key words： singularly perturbed      heat conduction equation      discontinuous coefficient      uniformly valid estimate     
Published: 07 July 2020
CLC:  O175.27  
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BAO Li-ping
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Cite this article:

BAO Li-ping, LI Wen-yan, WU Li-qun. A singularly perturbed two parameter solution for the distribution of non Fourier temperature field with a jump in thermal conductivity. Applied Mathematics A Journal of Chinese Universities, 2020, 35(2): 199-210.

URL:

http://www.zjujournals.com/amjcua/     OR     http://www.zjujournals.com/amjcua/Y2020/V35/I2/199


一类热传导系数跳跃的非Fourier温度场分布的奇摄动双参数解

应用非Fourier热传导定律构建了温度场模型, 即一类在有界域上带小参数的
奇摄动双曲方程, 由于温度急剧变化热传导系数出现跳跃的情况, 得到了非线性的具
有间断系数的奇摄动双参数双曲方程. 通过奇摄动双参数展开方法, 得到了该问题的
渐近解; 其次对热传导系数跳跃位置进行了定性分析, 得到了确定热传导系数跳跃位
置的计算公式, 从而确定了解的形式渐近展开式; 再通过余项估计, 得到了渐近解的一
致有效性, 从而得到了完整温度场的分布.

关键词： 奇摄动,  热传导方程,  间断系数,  一致有效估计 
[1] ZHU Peng, YANG Yu-bo, YIN Yun-hui. Higher order uniform convergent SIPG method for singularly perturbed problem[J]. Applied Mathematics A Journal of Chinese Universities, 2014, 29(2): 233-244.