A. Introduction

Heat transfer coefficients between particles and fluid in packed beds are one of the basic pieces of information needed for unit operations and chemical reactor design. Heat transfer is of interest, for example, in chemical reactors with fixed beds of catalysts in which large amounts of heat are absorbed or released, or in fixed beds employed as regenerative heat exchangers. Particles of very different shapes, such as spheres, cylinders, Raschig rings, or Berl saddles, are used as packing material. Because of its great importance, many papers in the literature deal with this problem. Review papers (Balakrishnan and Pei, 1979, Barker, 1965) show that there are great differences in the correlating equations. This chapter deals only with packings of spheres of equal size.

B. The calculation process

The measurements of Gillespie et al. (1968) show that the Nusselt number during flow in a packing increases markedly in the first two layers of spheres, and finally reaches a fixed value. Ranz (1952) found that the Nusselt numbers measured in packings are significantly larger than for single spheres at the same approach velocity, and that they fall along a line parallel to that for single spheres when plotted against the Reynolds number.

From these findings, the mean Nusselt numbers for flow through stationary spherical packings with any void fraction can be calculated (Gnielinski, 1981) from the equation