Thermally driven motion of strongly heated fluids

Two sets of approximate equations governing the thermally driven motions of strongly heated fluids are derived by a formal and unified method, taking into account the fluid properties' temperature dependence. After considering the limits of strongly heated shallow and deep fluids, attention is given to weakly heated cases. The resulting equations constitute the Boussinesq approximation, and are valid independent of the relative magnitudes of the nondimensionalized depth of the fluid and the strength of the heat source distribution. In addition, all of the equations are based on a characteristic velocity that is vanishingly small when compared with the speed of sound.