ASYMPTOTIC AND NUMERICAL-SOLUTIONS FOR THERMALLY DEVELOPING FLOWS OF NEWTONIAN AND NON-NEWTONIAN FLUIDS IN CIRCULAR TUBES WITH UNIFORM WALLTEMPERATURE

Methods that predict heat transfer rates in thermally developing flows , important in engineering design, are often compared with the classic al Graetz problem. Surprisingly, numerical solutions to this problem g enerally do not give accurate results in the entrance region. This ina ccuracy stems from the existence of a singularity at the tube inlet. B y adopting a fundamental approach based upon singular perturbation the ory, the heat transfer process in the tube entrance has been analyzed to bring out the asymptotic boundary layer structure of the generalize d problem with non-Newtonian flows. Using a standard finite difference method with only 21 radial nodes, results within 0.3% of the exact so lution to the Graetz problem (Newtonian limit of generalized power law fluid flaws) are obtained. Compared with previous numerical solutions reported in the literature, these results are an order of magnitude i mprovement in the accuracy with an order of magnitude decrease in the required number of radial nodes. Also, the number of radial nodes does not have to be increased in the present method to maintain this high level of accuracy as the initial singularity is approached. Solutions for power law, non-Newtonian fluid flows are presented, and generalize d correlations are given for predicting Nusselt numbers in both the th ermal entrance region and fully developed flows with 0 < n less than o r equal to infinity.