Dear CFD experts:

I recently studies a natural convection problem (air) using Boussinesq approximation. This is an enclosure sitting in room temperature (35 degree C). Inside the enclosure, the temperature drops to 6 degree C. The cover of the enclosure is made of plastics, hence, not perfectly insulated.

Initially, everything is at 35 degree C. There is a cooling device (applied negative heat flux) to cool the inside of enclosure.

I need to apply very small delta t to keep the solution converge at each time step.

My questions are:

1. what reference temperature should I use (I used 35 degree C in my study)? 2. With high temperature gradient (29 degree C in this case), is it still a good idea to use Boussinesq approximation? 3. If not using Boussinesq approximation, then, what other alternatives there are?

Thanks for any feedback!

phsieh2005

phsieh2005,

1. I think the choice of a reference temperature is rather arbitrary - it may be the one you chose, the mid-range tetemperature ( (6+35)/2 in your case) or anything within the expected range.

2. The Boussinesq approximation is valid when beta*deltaT << 1, where beta is the volumetric thermal expansion coefficient and deltaT is the temperature difference. In your case, using air at near standard conditions, the ideal gas model is a good approximation for estimating beta as 1/T. Using T~300K and deltaT~30K, you get beta*deltaT ~0.1 << 1, so that the Boussinesq approximation may be used.

3. If this is not the case, you may use the ideal gas equations of state to directly calculate the density as a function of the temperature and pressure (although the latter will change little in your case, I suppose).

Being myself a beginner in the natural convection area, please read my comments with some careful examination.

Rami

Boussinesq approximation is OK in this case. small delta t may be necessary because of heat extraction and natural convection combination.

Hi, Rani and Mayur,

Thanks a lot for the explanation on Boussinesq approximation!

I realized that, the problem mostly lies in the coupling between heat equation and N-S eq. This is a conjugate heat transfer problem that involves both solids and fluids. Heat equation and N-S are coupled explicitly. Is there a way to estimate delta t in a explicitly coupled case?

phsieh2005

I don't think there is any such relation in the present case(apart from what you s/w may calculate on its own).

[Amili]

Originally Posted by Rami
;53114

phsieh2005,

1. I think the choice of a reference temperature is rather arbitrary - it may be the one you chose, the mid-range tetemperature ( (6+35)/2 in your case) or anything within the expected range.

2. The Boussinesq approximation is valid when beta*deltaT << 1, where beta is the volumetric thermal expansion coefficient and deltaT is the temperature difference. In your case, using air at near standard conditions, the ideal gas model is a good approximation for estimating beta as 1/T. Using T~300K and deltaT~30K, you get beta*deltaT ~0.1 << 1, so that the Boussinesq approximation may be used.

3. If this is not the case, you may use the ideal gas equations of state to directly calculate the density as a function of the temperature and pressure (although the latter will change little in your case, I suppose).

Being myself a beginner in the natural convection area, please read my comments with some careful examination.

Rami

I think the value of T0 is related to Ro0(density)? for example for air, if the density (Ro0) is selected 1.225 kg/m3, the value of T0 is around 288 K.