Mixed convection plume above a horizontal line source situated in a forced convection approach flow

Abstract

Both analytical and numerical techniques were employed to solve for the velocity and temperature fields in a two-dimensional mixed convection plume for the Prandtl number range from 0.72 to infinity. The method of inner and outer expansions was used for the Pr = ∞ case while a parabolic, finite-difference method yielded the solutions for the other Prandtl numbers. In general, the plume was found to evolve with increasing distance from the line source from one with a basically forced convection character to one which resembles that for pure natural convection. The centerline velocity and temperature variations with distance from the line source were bounded by envelope curves constructed from the asymptotes for pure forced and pure natural convection. Highly accurate algebraic relations valid for all Prandtl numbers and all distances above the line source were developed to generalize the results obtained for the various discrete Prandtl numbers. The plume width increased with distance from the source, but at a slower rate at greater distances. The shapes of the velocity profiles changed both with distance and Prandtl number, whereas all temperature profiles displayed a common bell-like shape.