SECOND-ORDER EFFECTS IN A LAMINAR AXISYMMETRIC PLUME SUBJECTED TO AN EXTERNAL COFLOWING UNIFORM STREAM

Abstract

Asymptotic solutions are found for the steady laminar mixed convective flow of a Boussinesq fluid above a point heat source sited in an aligned uniform coflowing stream. The equations are first developed in vorticity-temperature form and then analysed in inner and outer regions using matched asymptotic expansions. Attention is restricted to the case of unit Prandt1 number and consideration is given to the effects of varying the strength of the external stream. When this is zero, analytical solutions are available for the zeroth-order shear-layer flow thus providing useful checks on the numerical procedure employed for non-zero strengths. The higher-order correction, which is of higher order than for the two-dimensional line-source problem, is found up to arbitrary multiples of the leading-edge shift eigensolution. The analysis facilitates the investigation of the non-parallel flow stability of this problem and this will be reported elsewhere.