In this paper we derive an exact expression for the mean heat flux at the wall for the compressible turbulent channel flow. In the expression, the heat flux at the wall can be decomposed into four parts, including the contribution from the turbulent heat transfer, the contribution from the molecular heat transfer, the contribution from the pressure work, and the contribution from the work from viscous stress (VW). The decomposition is validated in compressible turbulent channel flows with isothermal walls at three different Reynolds and Mach numbers, and the results match very well with the direct estimations at the wall. The data also show that the VW term dominates the contributions (around $90\%$) in the decomposition while around $90\%$ of VW is from the near-wall region $(y/h<0.2)$, illustrating the importance of the viscous stress work in the near-wall region.

中文翻译：

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粘性应力功对可压缩湍流通道流动中壁热通量的贡献

在本文中，我们得出了可压缩湍流通道壁平均热通量的精确表达式。在表达式中，壁处的热通量可分解为四个部分，包括湍流传热的贡献，分子传热的贡献，压力功的贡献以及粘性应力的功的贡献。 （大众）。在具有三个不同雷诺数和马赫数的等温壁的可压缩湍流通道流中验证了分解，结果与壁上的直接估计非常吻合。数据还显示，大众一词占主要部分（大约$90％$）在周围分解 $90％$ 大众汽车来自近壁地区 $（ÿ/H<0.2）$，说明了在近壁区域中粘性应力工作的重要性。