Wall-to-bed heat transfer in gas-solid bubbling fluidized bed

The wall-to-bed heat transfer in gas-solid fluidized beds is mainly determined by phenomena prevailing in a thermal boundary layer with a thickness in the order of magnitude of the size of a single particle. In this thermal boundary layer the temperature gradients are very steep and the local porosity profile near the wall strongly influences the heat-transfer rate. A two-fluid continuum model based on conservation laws for mass, momentum and thermal energy has been developed accounting for the porosity distribution near the wall. To validate the model, local instantaneous wall-to-bed heat-transfer coefficients were measured along a heated wall kept at constant temperature. The incorporation of a porosity profile by effective conductivities has remarkably improved the prediction of the heat-transfer coefficients compared against that of previous studies. The predicted local instantaneous heat-transfer coefficients are in good agreement with the experimental data for different jet velocities as well as for different particle sizes, provided that the near-wall porosity profile is accounted for. Two sets of closure equations for the solids-phase rheology (that is, the solids-phase stress tensor) have been considered: the constant viscosity model (CVM) and the kinetic Theory of granular flow (KTGF). For lower bed heights both models give good predictions of the wall-to-bed heat-transfer coefficients, but the KTGF predictions at higher bed heights agree better with the experimental data than the predictions by the CVM as the result of a better description of the passage of the bubble along the wall. The influence of an additional kinetic contribution to the effective solids-phase thermal conductivity arising from the fluctuating solids velocity was studied with the KTGF closures. Because of a large overprediction of the kinetic solids-phase thermal conductivity the wall-to-bed heat-transfer coefficients are largely overestimated when accounting for this additional contribution to the effective solids-phase thermal conductivity