Effect of Circumferentially Nonuniform Heating on Laminar Combined Convection in a Horizontal Tube

An analytical study has been made of how the circumferential distribution of the wall heat flux affects the forced/natural convection flow and heat transfer in a horizontal tube. Two heating conditions were investigated, one in which the tube was uniformly heated over the top half and insulated over the bottom, and the other in which the heated and insulated portions were reversed. The results were obtained numerically for a wide range of the governing buoyancy parameter and for Prandtl numbers of 0.7 and 5. It was found that bottom heating gives rise to a vigorous buoyancy-induced secondary flow, with the result that the average Nusselt numbers are much higher than those for pure forced convection, while the local Nusselt numbers are nearly circumferentially uniform. A less vigorous secondary flow is induced in the case of top heating because of temperature stratification, with average Nusselt numbers that are substantially lower than those for bottom heating and with large circumferential variations of the local Nusselt number. The friction factor is also increased by the secondary flow, but much less than the average heat transfer coefficient. It was also demonstrated that the buoyancy effects are governed solely by a modified Grashof number, without regard for the Reynolds number of the forced convection flow.