The plane problem of the theory of convective heat and mass transfer: PMM vol. 42, no. 5, 1978, pp. 848–855

Abstract

An effective solution is obtained for the plane problem of convective heat transfer from a heated body of arbitrary shape in a stream of perfect incompressible heat-conducting fluid. Solution of this problem is of interest in the theory of heat transfer in liquid metals, of the mass transfer of a bubble moving in a fluiidized bed, in the theory of ablation and freezing in a stream of heat-conducting fluid, etc. The input boundary value problem in Heimholtz' variables reduces to the similar problem of convective heat transfer from a heated plate in a longitudinal stream of perfect incompressible fluid, a problem that is solved, after some transformations, by separattag variables in elliptic coordinates. The solution is in the form of series in Matheu's functions. Simple asymptotic formulas are obtained for low and high Péclet numbers. A simple interpolation formula is obtained for the heat flax over a range of Péclet numbers.