Abstract Present study proposes a methodology and provides computational results for a conjugate heat transfer problem, where one would like to level out the temperature along the solid-fluid interface. Such constraints or needs may emerges in industrial processes such as mold casting and efficient heat exchanger design. In order to describe the methodology, we consider a benchmark problem of heat and mass transfer through a backward facing step duct with a finite thickness of solid wall. We performed computations at two different Reynolds numbers, 200 and 400 by utilizing our in-house lattice Boltzmann method solver. We validated our in-house solver by comparing our results with those obtained from a conventional Navier-Stokes solver and analytical solution. The solver is able to run on graphical processing unit and model conjugate heat transfer problem without any specific treatment at the solid-fluid interface. Utilizing the optimization algorithm based on trust region method and the advantageous of being able to run our solver on graphical processing unit, we reach constant temperature along the solid fluid interface within 1.55% maximum deviation. The methodology we propose here takes the thermal conductivity of the solid as a variable instead of wall thickness. Thereby, the problem turns into a feasible optimization problem since it does not require remeshing. After reaching the goal, one can easily determine required solid wall thickness along the flow direction by taking the reciprocal of the determined local thermal conductivity according to Fouriers Law.

中文翻译：

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平衡共轭传热问题的界面温度

摘要 目前的研究提出了一种方法并提供了共轭传热问题的计算结果，在该问题中，人们希望沿固-流界面保持温度平稳。这种限制或需求可能会出现在工业过程中，例如模具铸造和高效的热交换器设计。为了描述该方法，我们考虑了通过具有有限厚度实心壁的后向阶梯管道传热和传质的基准问题。我们通过使用我们内部的格子玻尔兹曼方法求解器在两个不同的雷诺数 200 和 400 上执行计算。我们通过将我们的结果与从传统 Navier-Stokes 求解器和解析解获得的结果进行比较来验证我们的内部求解器。该求解器能够在图形处理单元上运行，并对共轭传热问题进行建模，而无需在固-流界面进行任何特殊处理。利用基于信任域方法的优化算法和能够在图形处理单元上运行我们的求解器的优势，我们在 1.55% 的最大偏差内沿固体流体界面达到恒定温度。我们在此提出的方法将固体的热导率作为变量而不是壁厚。因此，该问题变成了一个可行的优化问题，因为它不需要重新网格化。达到目标后，根据傅立叶定律，通过取所确定的局部热导率的倒数，可以很容易地确定沿流动方向所需的固体壁厚。