Steady laminar natural convection plumes above a horizontal line heat source

Abstract The extensive past publication concerning the calculation of the behavior of laminar natural convection plumes above energy sources contains numerous elements of uncertainty and confusion concerning proper variables, boundary conditions, and governing equations. This paper, for the first time, states the problem in simplest variables, resolves various apparent redundancies in boundary conditions, and indicates the optimum way to formulate this boundary value problem. Results of numerical calculations are given in terms of the present simple formulation for a wide range of values of Prandtl number, some not having been treated before. Results of experiments with plumes are included to emphasize the various properties of plume flow and to indicate that the large thickness of the boundary region in the range of stable laminar plumes (i.e. at relatively low local Grashof numbers) should encourage the calculation of higher order approximations of the flow.