This work establishes a procedure to accurately compute heat transfer between an Eulerian fluid and Lagrangian point-particles. Recent work has focused on accurately computing momentum transfer between fluid and particles. The coupling term for momentum involves the undisturbed fluid velocity at the particle location which is not directly accessible in the simulation. Analogously, in the context of thermal coupling, the undisturbed fluid temperature at the particle location is not directly accessible in simulations and must be estimated. In this paper, we develop a scheme to accurately estimate the undisturbed fluid temperature of a point-particle exchanging thermal energy with a surrounding fluid. The temperature disturbance is correlated with the enhanced temperature curvature in the vicinity of the particle and is formally valid in the low heating, low convection limit. We conduct extensive verification of the correction procedure for a settling particle subject to radiation. This setup allows the simultaneous testing of thermal and momentum corrections. By considering equations of drag and Nusselt number extended to finite Péclet and Boussinesq numbers, we establish a large range over which the correction procedure can be applied.

这项工作建立了一个程序来准确计算欧拉流体和拉格朗日点粒子之间的热传递。最近的工作重点是准确计算流体和粒子之间的动量传递。动量的耦合项涉及在模拟中无法直接访问的粒子位置处的未受干扰流体速度。类似地，在热耦合的情况下，粒子位置处未受干扰的流体温度在模拟中无法直接获得，必须进行估计。在本文中，我们开发了一种方案来准确估计与周围流体交换热能的点粒子的未受干扰流体温度。温度扰动与粒子附近增强的温度曲率相关，并且在低加热、低对流限制下正式有效。我们对受辐射的沉降粒子的校正程序进行了广泛的验证。此设置允许同时测试热和动量校正。通过考虑扩展到有限 Péclet 和 Boussinesq 数的阻力方程和 Nusselt 数，我们建立了一个可以应用校正程序的大范围。