In this article, a new interpolation method is developed for the Lagrangian statistics in the non-isothermal gas-solid flow. The Lagrangian statistics are inseparable from interpolation, especially the optimal interpolation. The new interpolation method in this article is developed based on the smooth Dirac delta function, which is also called delta function interpolation method (DFIM). The performance of DFIM is compared with that of the spectral interpolation method (the interpolation method with the highest precision). The comparison results indicate that the performance of DFIM, especially the DFIM, is superior. The Lagrangian statistics method is one of the most effective methods for heat transfer analysis in the gas-solid flow. For the heat transfer analysis of gas-solid flow in this article, the relevant Lagrangian statistics are evaluated based on the newly developed DFIM, which include the temperature autocorrelation, the velocity autocorrelation, the second-order Lagrangian structure function, and the temperature velocity correlation function. The effect of the particle inertia on the heat transfer of the gas-solid flow is considered based on these Lagrangian statistics. The results show that the particle inertia has a great effect on the heat transfer in the gas-solid flow. As the particle inertia increases, the heat transfer in the gas-solid flow increases obviously. These results are helpful to understand the thermal behavior of the gas-solid flow.
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