多孔介质平板通道传热模型的两种求解方法  

Two Decoupling Methods for the Heat Transfer Model of a Plate Channel Filled With a Porous Medium

作　　者：王克用[1,2] 王大中[1] 李培超[1] 

机构地区：[1]上海工程技术大学机械工程学院,上海201620 [2]美国加州大学机械工程系

出　　处：《应用数学和力学》2015年第5期494-504,共11页Applied Mathematics and Mechanics

基　　金：上海高校青年骨干教师国外访问学者计划对本文的资助

摘　　要：基于Brinkman-Darcy扩展模型和非局部热平衡模型,考虑液相和固相含有内热源的情况,建立了多孔介质平板通道传热的一般模型.分别采用直接法和间接法将液相与固相能量方程解耦,进而求得充分发展传热条件下的多孔介质温度场.与直接解耦法相比,间接解耦法可在原始边界条件下求解二阶微分方程,更加简单易行.通过对无量纲温度表达式系数以及温度分布的比较,验证了两种求解方法的等价性.在两种极限情形下,间接法所得温度分布解析解与现有文献结果相当吻合,这也在一定程度上证明了所建模型更具一般性.参数分析表明,液固两相温差随着Biot数或有效导热系数比的增大而减小,Nusselt数随着内热源比的增大而减小.A general heat transfer model of a parallel plate channel filled with a porous medium was constructed based on the Brinkman-Darcy extended model and the local thermal non-equi- librium model in view of the internal heat sources in fluid and solid phases. The temperature field of the porous medium under the fully developed heat transfer condition was respectively formulated with the direct and indirect decoupling methods of solving the fluid-phase and solid- phase energy equations. Compared to the direct decoupling method, the indirect one is more convenient to be employed to solve the 2nd-order differential equations under the original boundary conditions. The equivalence of the 2 decoupling methods was ve^ied through com- parison of the coefficients in the dimensionless temperature expressions and the temperature distributions between them. A good agreement was found between the temperature distributions obtained with the indirect decoupling method and those reported in the previous literatures in 2 limit cases, meanwhile the better generality of the proposed model was also proved to some ex- tent. The parametric study shows that the temperature difference between the fluid and solid phases decreases with the Biot number or the effective thermal conductivity ratio, and the Nus- selt number decreases with the internal heat source ratio.

关 键 词：多孔介质 Brinkman-Darcy扩展模型 非局部热平衡模型 内热源 恒定热流 

分 类 号：O241.82[理学—计算数学] TK124[理学—数学]