Invited Lectures

Abstract

A new type of analogy between frictional pressure drop and heat transfer has been discovered that may be used in chevron-type plate heat exchangers, in tube bundles, in crossed-rod matrices, and in many other internal flow situations. It is based on the Generalized Lévêque Equation (GLE). This is a generalization of the well known asymptotic solution for thermally developing, hydrodynamically developed tube flow, which was first derived by A. Lévêque in 1928. Nusselt or Sherwood numbers turn out to be proportional to the cubic root of the frictional pressure drop (ξRe 2) under these conditions. It was found that using a friction factor ξ= x f. ξ total leads to a very reasonable agreement between the analogy predictions and the experimental results. The fraction x f of the total pressure drop coefficient ξ total that is due to fluid friction only, turned out to be a constant over the whole range of Reynolds numbers in many cases. For the packed beds of spheres, Ergun's equation, or more appropriate equations from the literature may be used to calculate the total pressure drop. The new method can also be used in external flow situations, not only for internal flow as shown so far. This is demonstrated here for a single sphere as well as for a single cylinder in cross flow. In these cases, however, the frictional fraction x f of the total drag coefficient is not a constant over the range of Reynolds numbers. Nevertheless it is easily obtained from standard correlations of drag coefficients. The successful application of the GLE also in cases of external flow seems to confirm, that this new type of analogy has a broad range of applications and may lead to a better understanding of the interrelation between fluid flow and heat or mass transfer in general.