[hifjur]

Hello, Can anyone help me to get out of this?
I m modeling a natural convection heat transfer through a fin in a closed fluid domain. Base temperature of fin is 400K and ambient temperature is 300K. Can I use boussinesq approximation for this? If i use boussinesq approximation what should be the value of density? And what should be the value of other thermophysical properties like thermal conductivity, thermal expansion coefficient, specific heat? Thank you in advance for your time.

[LuckyTran]

Originally Posted by hifjur

Hello, Can anyone help me to get out of this?
I m modeling a natural convection heat transfer through a fin in a closed fluid domain. Base temperature of fin is 400K and ambient temperature is 300K. Can I use boussinesq approximation for this? If i use boussinesq approximation what should be the value of density? And what should be the value of other thermophysical properties like thermal conductivity, thermal expansion coefficient, specific heat? Thank you in advance for your time.

Note that the average density is specified through the operating pressure and temperature in operating conditions. In my opinion, the unperturbed density should be at the unperturbed temperature and pressure (the ambient 300K and ambient press).

The Boussinesq approximation is a constant property approximation (an incompressible fluid) but allows you to get buoyancy forces. Thus I think all properties should be constant properties when simulating using the Boussinesq model to be consistent with the Boussinesq model. Of course you can still choose variable properties, but if you are going to choose variable thermal conductivities and such, why would you not also choose a variable density, the most basic material property?

In my opinion these are all selected by you. It's up to you how detailed you want your simulation to be. Why not just use constant thermal properties for everything? Do you need variable properties for what you are trying to do or study? What is their added benefit? What do you hope to achieve?

[hifjur]

Originally Posted by LuckyTran

Note that the average density is specified through the operating pressure and temperature in operating conditions. In my opinion, the unperturbed density should be at the unperturbed temperature and pressure (the ambient 300K and ambient press).

The Boussinesq approximation is a constant property approximation (an incompressible fluid) but allows you to get buoyancy forces. Thus I think all properties should be constant properties when simulating using the Boussinesq model to be consistent with the Boussinesq model. Of course you can still choose variable properties, but if you are going to choose variable thermal conductivities and such, why would you not also choose a variable density, the most basic material property?

In my opinion these are all selected by you. It's up to you how detailed you want your simulation to be. Why not just use constant thermal properties for everything? Do you need variable properties for what you are trying to do or study? What is their added benefit? What do you hope to achieve?

Thank you for your reply sir!
I am using constant thermal properties for my simulation. my only confusion is that while using boussinesq approximation, with respect to which temperature should I take the values of thermal properties? density should be should be taken with respect to ambient temperature and pressure i got it. what about the other parameters? Should i take those in film temperature( 400+300/2)K in my case or at 300K?

[LuckyTran]

Originally Posted by hifjur

Thank you for your reply sir!
I am using constant thermal properties for my simulation. my only confusion is that while using boussinesq approximation, with respect to which temperature should I take the values of thermal properties? density should be should be taken with respect to ambient temperature and pressure i got it. what about the other parameters? Should i take those in film temperature( 400+300/2)K in my case or at 300K?

The film or any average temperature is used for making experimental data collapse and using a reference temperature to evaluate your properties is purely for post-processing purposes (like calculating Reynolds number and Nusselt number). If you calculate your thermophysical properties at the film temperature then you will enter a infinite nested loop argument. In a numerical simulation you have the freedom to make all these known constants. In a numerical simulation, there is no ambiguity in the thermophysical properties.

If you want variable properties, then make them truly variable and don't use the Boussinesq approximation since density and hence the buoyancy force is a first order effect (from your equation of state). The other thermophysical properties are higher order.

[hifjur]

But to calculate rayleigh number and nusselt number the fluid properties should be taken at the film temperature. so if take these at the reference temperarue(ambient, 300K in my case) wont it give absurd result? and if I take the film temperature as the reference temperature(360K) will it give accurate result using boussinesq approximation and density values at 360K?

[hifjur]

Originally Posted by LuckyTran

The film or any average temperature is used for making experimental data collapse and using a reference temperature to evaluate your properties is purely for post-processing purposes (like calculating Reynolds number and Nusselt number). If you calculate your thermophysical properties at the film temperature then you will enter a infinite nested loop argument. In a numerical simulation you have the freedom to make all these known constants. In a numerical simulation, there is no ambiguity in the thermophysical properties.

If you want variable properties, then make them truly variable and don't use the Boussinesq approximation since density and hence the buoyancy force is a first order effect (from your equation of state). The other thermophysical properties are higher order.

What is boussinesq operating temperature? Do I need to set the density corresponding to boussinesq operating temperature? What if I set the boussinesq operating temperature at 300K(ambient) and fluid properties like thermal conductivity, thermal expansion coefficient at at film or bulk mean temperature(360K)? And at reference values what temperature I should specify? anbient temp. or film temp.? please do reply

[LuckyTran]

Originally Posted by hifjur

But to calculate rayleigh number and nusselt number the fluid properties should be taken at the film temperature. so if take these at the reference temperarue(ambient, 300K in my case) wont it give absurd result? and if I take the film temperature as the reference temperature(360K) will it give accurate result using boussinesq approximation and density values at 360K?

Again, the film temperature is an empirical technique for making experimental data collapse. Think about what would happen if properties in real-life were constant properties? What meaning is there to the film temperature anymore if the properties are the same everywhere? It serves no purpose.

The film temperature is not an average of ambient and wall temperature but an average of the temperature of the fluid far from the wall and temperature of the fluid right next to the wall. In a constant property simulation, it does not matter what temperature you compute the properties at because they are all the same.

Now the question is where do you get these constant properties? These can be evaluated at the film temperature or whatever, but once they have been chosen you never need to revisit the film temperature again because you have constant properties everywhere.

If you want to be doing accurate simulations with property variables, then do so and stop using Boussinesq. Then the film temperature is applicable.

Originally Posted by hifjur

What is boussinesq operating temperature? Do I need to set the density corresponding to boussinesq operating temperature? What if I set the boussinesq operating temperature at 300K(ambient) and fluid properties like thermal conductivity, thermal expansion coefficient at at film or bulk mean temperature(360K)? And at reference values what temperature I should specify? anbient temp. or film temp.? please do reply

The operating temperature is the nominal temperature. The operating density should also be computed at this temperature. A deviation of the local temperature from the operating temperature is what gives rise to the buoyancy force per the Boussinesq model.

[hifjur]

Is it possible to model natural convection heat transfer using boussinesq approximation for temperature difference of 120K. Ansys tutorial suggests that boussinesq approximation is valid only for low temperature difference. Can anyone know what is the limiting temperature difference for which boussinesq is applicable. If I cant use boussinsq approximation what other method I should use?

[LuckyTran]

Originally Posted by hifjur

Is it possible to model natural convection heat transfer using boussinesq approximation for temperature difference of 120K. Ansys tutorial suggests that boussinesq approximation is valid only for low temperature difference. Can anyone know what is the limiting temperature difference for which boussinesq is applicable. If I cant use boussinsq approximation what other method I should use?

The Boussinesq approximation assumes that the density and hence buoyancy force varies linearly with temperature. The Boussinesq approximation is no longer valid when the real density change is not linear (hence it breaks down at large temperature differences).

All you need is to get the correct density to get the correct buoyancy force. You just need to provide a reasonable equation of state for the density. It can be a table, curve fit, a formal equation like the ideal gas law of real gas law.

I would not worry about these petty details until you've simulated something first, regardless of whether or not it is 100% valid. You were having a lot of trouble before with properties in general.

[Kosmosisy]

Originally Posted by LuckyTran

The Boussinesq approximation assumes that the density and hence buoyancy force varies linearly with temperature. The Boussinesq approximation is no longer valid when the real density change is not linear (hence it breaks down at large temperature differences).

All you need is to get the correct density to get the correct buoyancy force. You just need to provide a reasonable equation of state for the density. It can be a table, curve fit, a formal equation like the ideal gas law of real gas law.

I would not worry about these petty details until you've simulated something first, regardless of whether or not it is 100% valid. You were having a lot of trouble before with properties in general.

Hello.

I am also trying to analysis natural convection in a closed domain. Which solver method should I use? I have tried both boussinesq and ideal gas model with pressure-velocity coupled pseudo transient solver. The ideal gas model is more reasonable than the boussinesq. However, the residuals are very high, continuity is about 10^1 and energy is about 10^-3 . I will refer last case's film temperature and air's properties in corresponding temperature difference. However, as I said , is the pressure-velocity coupled pseudo transient solver good for closed domain?

Best regards.