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

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