(419h) Wall-to-Particle Heat Transfer in Gas-Solids Flows
In many industrial systems, domain walls or immersed surfaces are utilized as the primary means for heating a gas-solids mixture. Under such circumstances, the heat transfer to solid particles in the near-wall region is of great significance. Predictions for heat transfer in the near-wall region have largely relied upon the use of convection correlations and/or particle-scale models for indirect conduction. However, convection correlations are generally developed for unbounded systems that do not contain walls, and thus, their accuracy will deteriorate in the near-wall region. In addition, particle-scale models for indirect conduction make simplifying assumptions about the fluid flow. Namely, the interstitial fluid between a particle and wall is assumed to be static and the resulting heat transfer to the particle occurs via one-dimensional conduction. Here we utilize a direct numerical simulation (DNS) code to rigorously quantify the heat transfer to a particle in the near-wall region. Uniform flow past a hot plate and static, cold particle is considered in the present work. The heating rates of the particle obtained via DNS are directly compared to unbounded convection correlations and indirect conduction theory. Unbounded convection correlations alone are found to under-predict the heat transfer occurring in the near-wall region, while indirect conduction theory is observed to better capture boundary effects. Nonetheless, despite capturing the first order physics associated with a wall, indirect conduction theory incorrectly identifies the conductive length scale (fluid lens thickness) as being proportional to the particle size. By contrast, it is observed that the key length scale associated with near-wall heat transfer enhancement is the thermal boundary layer thickness. An approximation of the thermal boundary layer thickness from classic boundary layer theory is utilized to develop a Nusselt correlation for the near-wall region. The new correlation accounts for both convection as well as indirect conduction and asymptotically decays to the unbounded convection correlation for large particle-wall separation distances; thereby seaming together the unbounded and near-wall regions.