Laminar flow induced by a point source of heat

An asymptotic description of the laminar flow pattern generated by a point source of heat is derived. Existing solutions of the boundary layer equations are shown to be valid in a limited domain where buoyancy forces are dominant. These solutions are supplemented by new results for the buoyant plume and are matched asymptotically to solutions valid everywhere outside the plume. Composite analytical formulae for the pressure, enthalpy and velocity fields are obtained and applied to the computation of the streamline pattern, pressure, and enthalpy distribution for Prandtl numbers 0.7 and 1.0.