VISCOUS DISSIPATION IN NON-NEWTONIAN FLOWS - IMPLICATIONS FOR THE NUSSELT NUMBER

This article considers the effects of viscous dissipation on convection heat transfer rates in thermally developing, power-law fluid flows in constant wall temperature tubes. The finite difference solution is based upon the use of asymptotic boundary-layer scales, and the results maintain high accuracy (errors less than or equal to 0.3% using 31 radial nodes) throughout the entrance region all the way to the fully developed condition. With viscous dissipation and hydrodynamically developed now, the inlet temperature distribution is not uniform. Viscous dissipation effects are measured by the Brinkman number Br (ratio of viscous heating to convective heat transfer rates through the tube wall). Surprisingly, Br effects are found to be important primarily in a transition region between the inlet and fully developed flow condition. A very dramatic problem with the classical definition of Nusselt number Nu is also illuminated. Because Nu is based upon the bulk temperature, it exhibits local minima and may even show point discontinuities (Nu --> +/- infinity as z --> finite nonzero value). At the same axial locations, the wall temperature gradient remains well-behaved. This demonstrates that Nu, as usually defined, is an extremely poor measure of the local heat transfer rate in this region.