Consider the laminar thermal boundary layer development near the entrance of the tube shown in Figure 8.4. When the hydrodynamic boundary layer is thin relative to the tube diameter, the inviscid flow region has a uniform velocity that is approximately equal to the mean velocity um. Hence the boundary layer development is similar to what would occur for a flat plate.

(a) Beginning with Equation 7.23, derive an expression for the local Nusselt number Nu_D, as a function of the Prandtl number Pr and the inverse Graetz number Gz_D^–1. Plot the expression using the coordinates shown in Figure 8.10a for Pr = 0.7.

(b) Beginning with Equation 7.30, derive an expression for the average Nusselt number Nu_D, as a function of the Prandtl number Pr and the inverse Graetz number Gz_D^–1. Compare your results with the Nusselt number for the combined entrance length in the limit of small x.

Transcribed Image Text:

Nu, = hxx k 0.332 Re2 Prl/3 Pr≥ 0.6