Abstract Heat or mass transfer becomes usually complicated if coupled with fluid flow. To model the process, the mass, heat, and momentum conservation equations have been well established, which are shown in our work not the only governing laws. We analyzed heat transfer entropy generation rate and viscous dissipation of coupled heat and momentum transport phenomena in Rayleigh-Benard convection, and proposed a hypothesis that the velocity and temperature distributions can be governed by the balance between the maximization of entropy generation and the minimization of viscous dissipation. Such a criterion, combined with a multi-scale model, was used to formulate a variational problem, which was then solved to reconstruct the velocity, temperature, and Nusselt number distributions in the Rayleigh-Benard convection. As a result, three parameters obtained can be used to correct the error caused by the computations with low resolution of meshes. We show that the proposed method consumes significantly less computational effort than a traditional DNS, and can hopefully mitigate the limit by computational burden of the traditional conservation equation based simulations.

中文翻译：

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用于复杂传输过程建模的超越守恒方程的标准 - 瑞利-贝纳德对流的案例

摘要 如果与流体流动相结合，传热或传质通常会变得复杂。为了模拟这个过程，质量、热量和动量守恒方程已经很好地建立起来，这些方程在我们的工作中并不是唯一的控制定律。我们分析了 Rayleigh-Benard 对流中耦合热和动量传输现象的传热熵生成率和粘性耗散，并提出了一个假设，即速度和温度分布可以由熵生成的最大化和粘性的最小化之间的平衡来控制。耗散。此类标准与多尺度模型相结合，用于制定变分问题，然后解决该问题以重建瑞利-贝纳德对流中的速度、温度和 Nusselt 数分布。因此，得到的三个参数可用于校正低网格分辨率计算引起的误差。我们表明，与传统的 DNS 相比，所提出的方法消耗的计算工作量要少得多，并且有望通过基于传统守恒方程的模拟的计算负担来减轻限制。