[shahrooz.omd]

I have written a code to simulate natural convection inside a channel or pipe. to decribe my code I prefer using keywords: finite volume, transient, laminar, SIMPLE, boussinesq approximation, QUICK, non-uniform grid and staggered.

I have 2 problems that require your help fellow CFD-online users:

1- when using boussinesq approximation by decreasing h/b (b is channel width and h is channel height) form ~60 and higher values to 40 or lower the accuracy of calculated average nusselt number reduces from 1% error to 7.5% and above, is this normal? (accuracy is measured based on the work of Elenbaas, Heat dissipation of parallel plates by free convection)

2- my main question as the title suggests is how to simulate natural convection without boussinesq approximation, my current approach is to substitute the term g * beta * (T - T_infinity) * volume with this term g * (rho_infinity - rho) * volume and update rho using the ideal gas equation while p in dp/dy and dp/dx is pressure variation from the hydrostatic pressure field in both approaches. this method results in a slightly different temperature and velocity field with averege Nusselt number errors around 50~60%. is there something else I need to implement?