On the motion of a weakly bouyant heat source near an interface

An asymptotic solution to the problem of a slightly bouyant flow, induced by the motion of a submerged point heat source which is governed by the Oseen-Boussinesq approximation, is presented. Two cases are discussed in particular, one which involves a motion of the heat source beneath a free surface and the other near a rigid boundary. The thermal boundary conditions on these two interfaces are assumed to be that of the mixed Cauchy type. Closed-form expressions are obtained for the temperature field as well as for the velocity and the pressure distributions induced in the fluid. The general solution thus obtained is illustrated by calculating both the thermal and kinematic signatures on the free surface for some particular cases.