In natural-convection problems, the variation of density due to the temperature difference ΔT creates an important buoyancy term in the momentum equation. If a warm gas at T_Hmoves through a gas at temperature T₀and 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.

Transcribed Image Text:

(TH - 1 Dy -VP+ µV?v+ pg| To Dt (-) Тн Lg To