In natural-convection problems, the variation of density due to the temperature difference ?T creates an important buoyancy term in the momentum equation. If a warm gas at TH moves through a gas at temperature T0 and if the density change is only due to temperature changes, the equation of motion becomes
Show that the ratio of gravity (buoyancy) to inertial forces acting on a fluid element is
where L and V0 are reference lengths and velocity, respectively.