Modeling heat transfer in gas-particle mixtures: Calculation of the macro-scale heat exchange in Eulerian–Lagrangian approaches using spatial averaging

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Heat transfers in dilute gas-particle mixtures are often modeled using hybrid Euler–Lagrange descriptions, treating the carrier fluid via an Eulerian representation and following each particle in a Lagrangian framework. One of the focal issues in these models is the calculation of the macro-scale heat transfer between the continuous phase and particles. In the standard approach, the heat transfer for each particle is considered to vary linearly with the average temperature difference between the particle and the fluid. Here, we use the method of volume averaging with closure to filter the heat transfer equations at the micro-scale and derive a closed form of the heat transfer rate, which is significantly different from the standard case. The primary difference is that the heat transfer for a given particle does not only depend on the temperature of the particle but also depends on the temperatures of all other particles within the averaging volume. This yields a matrix of heat exchange coefficients that captures indirect particle–particle exchanges at macro-scale. Using simple model cases, we validate our approach, compare it to the standard heat transfer model and show that it degenerates toward the standard model only in specific cases.