# natural convection with high temperature gradient?

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 December 17, 2007, 16:45 natural convection with high temperature gradient? #1 phsieh2005 Guest   Posts: n/a 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

 December 18, 2007, 03:43 Re: natural convection with high temperature gradi #2 Rami Guest   Posts: n/a 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 Amili likes this.

 December 18, 2007, 04:43 Re: natural convection with high temperature gradi #3 Mayur Guest   Posts: n/a Boussinesq approximation is OK in this case. small delta t may be necessary because of heat extraction and natural convection combination.

 December 18, 2007, 08:57 Re: natural convection with high temperature gradi #4 phsieh2005 Guest   Posts: n/a 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

 December 19, 2007, 07:25 Re: natural convection with high temperature gradi #5 Mayur Guest   Posts: n/a I don't think there is any such relation in the present case(apart from what you s/w may calculate on its own).

September 23, 2015, 08:25
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Quote:
 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.

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