Reference Temperature in Buosinesq Approximation of free convection flow

alimea · December 14, 2016, 01:51

Hi all
I'm trying to solve the "transient free convection flow of water in a limited box that is driven by a constant heat flux cylinder at the middle of the box". I want to use Buossinesq Approximation in my equations. In this equation we have:

gB(T-Tref)

in infinite fluid domain we get Tref=Tinf.
But my domain is finite! and by passing time, the fluid temperature (Tinf) will be increasing!
What should I get as Tref in my equation?

Thanks

FMDenaro · December 15, 2016, 05:45

could you give more details? Are you working in dimensional form? Tref is the suitable temperature that characterizes your problem, for example the temperature fixed at a wall or the adiabatic temperature.

alimea · December 15, 2016, 05:56

of course...
consider a rectangular 2D box that is full of water in 292 K.
a cylinder is at the middle of the box and there is a fix heat flux on it. I made my equations dimensionless.
My question is the Reference temperature...what should I get that?
you said: "Tref is the suitable temperature that characterizes your problem, for example the temperature fixed at a wall or the adiabatic temperature."
yes, this sentence is correct. but my problem is deferent from what you said.

thanks

FMDenaro · December 15, 2016, 06:30

In non dimensional form you do not have to specify tref but the Rayleigh number. Tref is the constant temperature assumed in the taylor expansion. Use the heat flux to estimate. Give also a look to the book of kundu or white

alimea · December 15, 2016, 06:42

Thanks for your help

But my method to make non-dimensional form, is different! I have this term on my equations!
T*=q".D/k

I should add this point that I solve my problem by openFoam. in this code we have to introduce Tref.

Antanas · December 15, 2016, 07:22

In closed domain you should use average expected temperature.

alimea · December 15, 2016, 07:32

excuse me, could you please explain what's "expected temperature"?

2- Have you seen that in an article? if yes, plz give me the link of that

Thnaks

Antanas · December 15, 2016, 09:15

Quote:

Originally Posted by alimea

excuse me, could you please explain what's "expected temperature"?

2- Have you seen that in an article? if yes, plz give me the link of that

Thnaks

Average temperature that you expect to establish in your domain.

December 14, 2016, 01:51	Reference Temperature in Buosinesq Approximation of free convection flow	#1
alimea Senior Member A. Min Join Date: Mar 2015 Posts: 308 Rep Power: 12	Hi all I'm trying to solve the "transient free convection flow of water in a *limited box* that is driven by a constant heat flux cylinder at the middle of the box". I want to use Buossinesq Approximation in my equations. In this equation we have: gB(T-Tref) in infinite fluid domain we get Tref=Tinf. But my domain is finite! and by passing time, the fluid temperature (Tinf) will be increasing! What should I get as Tref in my equation? Thanks

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December 15, 2016, 05:45		#2
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,849 Rep Power: 73	could you give more details? Are you working in dimensional form? Tref is the suitable temperature that characterizes your problem, for example the temperature fixed at a wall or the adiabatic temperature.

December 15, 2016, 05:56		#3
alimea Senior Member A. Min Join Date: Mar 2015 Posts: 308 Rep Power: 12	of course... consider a rectangular 2D box that is full of water in 292 K. a cylinder is at the middle of the box and there is a fix heat flux on it. I made my equations dimensionless. My question is the Reference temperature...what should I get that? you said: "Tref is the suitable temperature that characterizes your problem, for example the temperature fixed at a wall or the adiabatic temperature." yes, this sentence is correct. but my problem is deferent from what you said. thanks

December 15, 2016, 06:30		#4
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,849 Rep Power: 73	In non dimensional form you do not have to specify tref but the Rayleigh number. Tref is the constant temperature assumed in the taylor expansion. Use the heat flux to estimate. Give also a look to the book of kundu or white

December 15, 2016, 06:42		#5
alimea Senior Member A. Min Join Date: Mar 2015 Posts: 308 Rep Power: 12	Thanks for your help But my method to make non-dimensional form, is different! I have this term on my equations! T*=q".D/k I should add this point that I solve my problem by openFoam. in this code we have to introduce Tref.

December 15, 2016, 07:22		#6
Antanas Senior Member Join Date: Feb 2011 Posts: 496 Rep Power: 18	In closed domain you should use average expected temperature.

December 15, 2016, 07:32		#7
alimea Senior Member A. Min Join Date: Mar 2015 Posts: 308 Rep Power: 12	excuse me, could you please explain what's "expected temperature"? 2- Have you seen that in an article? if yes, plz give me the link of that Thnaks