An analytical study of heat and mass transfer in multiparticle systems at low Reynolds numbers

Abstract

Abstract This investigation was undertaken to obtain an analytical solution to the problem of predicting particle‐to‐fluid heat and mass transfer rates in multiparticle systems at low Reynolds numbers. The energy equation based on the free surface model was solved by expanding the fluid temperature distribution in even powers of the spherical angle and by assuming that the fluid properties remain relatively constant with temperature. Solutions were obtained for Peclet numbers between 0.1 and 100 and fractional void volumes between 0.4 and 1.0. They show that the average Nusselt or Sherwood number in a bed of particles is a function of both the fractional void volume and the Peclet number, the effect of Peclet number decreasing as the bed becomes more concentrated in the low Peclet number range. A plot of the results in terms of the j factor vs. the Reynolds number shows good agreement with published experimental mass and heat transfer data and indicates that the j factor is not independent of the Schmidt or Prandtl numbers at low Reynolds number, low Peclet number flow.