Numerical solutions are given without the aid of a large Prandtl number assumption for combined forced and free laminar convection in the entrance region of a horizontal pipe with uniform wall temperature. The steady-state solutions have been obtained from the asymptotic time solutions of the time-dependent equations of momentum and energy with the Poisson equation for pressure. Results are presented for the developing primary and secondary velocity profiles, developing temperature fields, local wall shear stress, and local and average Nusselt numbers, which reveal how the developing flow and heat transfer in the entrance region are affected by the secondary flow due to buoyancy forces.
Combined Forced and Free Convection in the Entrance Region of an Isothermally Heated Horizontal Pipe
Hishida, M., Nagano, Y., and Montesclaros, M. S. (February 1, 1982). "Combined Forced and Free Convection in the Entrance Region of an Isothermally Heated Horizontal Pipe." ASME. J. Heat Transfer. February 1982; 104(1): 153–159. https://doi.org/10.1115/1.3245043
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