In the Boussinesq hypothesis, the buoyancy term is added in the momentum equation. Why does not it appear in the energy equation? since energy equation can be derived by dotting momentum equation with velocity, why is this density correction term left out?

Thanks,

CFDtoy

The energy equation in the Boussinesque model is an internal energy (usually temperature) equation and is not affected by the buoiancy term. The equation cited by you, the kinetic energy equation, is alreqady accounted for by the momentum equation.

Thanks paolo. I have another question in this bouss approx.

Lets say the normal body force involved in the momentum eq. is rho*g (rho simply being the incompress fluid dens)

now, mom eqn reads,

d(rhoU)/dt+..conv terms = -gradP + rho*g

if we have bousinesq, => rho = f(T), we get

d(rhoU)/dt+.. = -gradP + g(rho(T)-rho_0)

rho_0 -> reference density.

Now, rho(T) = -rho_0 * beta * (T-Tref).

if the temperatures are almost same etc, T ~ Tref,

the gravity term in the momen equation -> 0. Does it mean that there is no body force?

I was thinking, the body force term be,

rho*g - rho*g*beta*(T-Tref), so even in the case that T->Tref, we retain rho*g. But literature seems otherwise.

So, does it mean that in a incompress heated flow, if the temperatures remain not so elevated, there is no body force effect (gravity) ??

Thanks,

CFDtoy