Combined Forced-Convective and Radiative Heat Transfer in Cylindrical Packed Beds with Constant Wall Temperatures

Hydrodynamically fully developed and thermally developing turbulent forced-convection in cylindrical packed beds heated at constant wall temperatures are numerically studied based on a zero-equation turbulence model accounting for the effect of thermal radiation. The macroscopic momentum equation considers the effects of turbulence and hydrodynamic dispersion in addition to Darcy-Brinkman-Forchheimer flow resistances, while the effects of thermal radiation, turbulence, and thermal dispersion are taken into account in the energy equation. The hydrodynamic dispersion term associated with spatial fluctuations of microscopic time-mean velocity in the momentum equation is modeled in a similar form to Boussinesq's eddy diffusivity model for Reynolds stress. The effective Prandtl numbers for dispersion and turbulence are assumed to be the same as each other and are adjusted so as to reproduce the experimental data of pressure gradient obtained by Fand and Thinakaran (ASME J. Fluids Eng., vol. 112, pp. 84−88, 1990). Radiation heat transfer in packed beds is analyzed based on the P1 approximation to the equation of transfer and the correlated-radiative properties of opaque packed spheres. It is shown that the coupled hydrodynamic dispersion and turbulence term in the momentum equation affects the pressure gradients in packed beds. Moreover, obtained theoretical results of velocity profiles, temperature profiles, and heat transfer characteristics are favorably compared to available experimental data.