Turbulent heat transfer in the thermal entrance region of a pipe with uniform heat flux

An analysis has been performed using a method similar to Graetz's formulation for the laminar thermal entry region. The fluid is assumed to have a fully developed turbulent velocity profile throughout the length of the pipe. Local and fully developed Nusselt numbers are presented for fluids with Prandtl numbers ranging from 0.7 to 100 for Reynolds numbers between 50000 and 500000. A thermal entrance length is defined as the heated length required to bring the local Nusselt number to within 5 percent of the fully developed value. This length is found to decrease with increasing Prandtl number, dropping from about 10 diameters for a Prandtl number of 0.7 to less than one diameter for a Prandtl number of 100. Comparison is made with the results of Deissler, who used an integral method-boundary layer approach, and also with available experimental data. The effect of the thermal boundary conditions was studied by comparing the present uniform heat flux results with those of previous investigators who considered uniform wall temperature.