边界界面导热系数插值格式的改进  

Modification of interpolation scheme for thermal conductivity at boundary interfaces

作　　者：王辉[1] 徐明海[1] 刘美霞[1] 王龙[2] 

机构地区：[1]中国石油大学(华东)储运与建筑工程学院,山东青岛266555 [2]中国石油管道研究中心,河北廊坊065000

出　　处：《燕山大学学报》2010年第5期411-416,共6页Journal of Yanshan University

基　　金：国家自然科学基金资助项目(50376043)

摘　　要：分析表明现有文献中采用的边界界面导热系数插值格式与内部界面并不一致,仅适用于常系数和弱非线性导热问题,而对于强非线性问题则会产生较大误差。本文根据调和平均法推导出了新的边界界面导热系数插值公式,确保了边界与内部界面导热系数插值格式的一致性。通过几个具有精确解的非线性导热问题对本文插值格式进行了考核并与文献中的格式进行了对比。结果表明,采用本文改进格式可以明显提高非线性导热问题数值计算的精度,尤其对于边界零扩导问题采用改进格式可以得出物理上更为合理的解。The analysis indicates that the interpolation scheme used in literatures for computing thermal conductivity at boundary interfaces is not in accord with that for internal interfaces,and it is only applicable to those constant coefficients and weakly nonlinear conduction problems. As for strongly nonlinear heat conduction problems, big error may occur by using above scheme. A new in- terpolation formula for thermal conductivity at boundary interfaces is derived based on harmonic mean method, which can ensure consistency of interpolation scheme for thermal conductivity at boundary and interior interfaces. The new scheme is evaluated by solving several non-linear conduction problems with exact solutions, and the errors are compared with those obtained through existing scheme in literatures. Result shows that the new scheme proposed in this paper can obviously improve the accuracy of the solutions for non-linear conduction problems. Especially for the case that the thermal conductivity at boundary is zero, more reasonable solutions can be obtained by the new scheme.

关 键 词：导热系数 边界界面 插值格式 调和平均法 

分 类 号：TK124[动力工程及工程热物理—工程热物理]