Hi, there,

Is there anybody who can tell me what is Boussinesq equation? Is it the energy equation + Navier-Stokes equations? Could anybody can tell me where can find some online reference about heat transfer?

Thanks a lot. Have good holiday.

bao

The Boussinesq assumption is that the turbulent stresses are directly proportional to the velocity gradient, ie turbulence can be modeleled as an eddy viscosity.

Jonas, I'm sorry but he was talking about the Boussinesq equations, not the Boussinesq linear stress tensor approximation. The BE may be understood as a simplified version of the full set of Navier-Stokes equations, i.e. continuity, momentum and heat equations. The simplification is attributed to the followings: i) effect of thermal expansion is limited to a linear buoyancy force; ii) usually, viscous dissipation of energy is neglected, and iii) all fluid properties (density, viscosity and thermal diffusivity) are assumed to be constant. In another words, you've got to solve a set of 2*d+1 equations (here d stands for the dimension of the problem). The set is strongly coupled (coupling is stronger than for the NSE for isothermal flows). Good starting would be reading of classical heat transfer books in your local library, not looking for crap on the internet. It's never late to do the latter.

Ah, that's news to me, I'm sorry if I mislead anyone. I never even heard about the Boussinesq Equations. It is not a very common term in CFD. Thanks for correcting me.

Hello Jonas:

I understand the confusion. Boussinesq approximation you were referring to is found in the Turbulence Modeling literature. Boussinesq equation Yangang Bao was reffering to can be found in classical heat transfer text books. I think it refers to the modifications made to momentum equations while dealing with free convection problems. Unfortunately, both carry the same name.

Probably, one needs to be bit specific when talking about the above.

Thanks,

Thomas

Thomas, yeah, it is quite common that we encounter such confusions. For example, even talking about the Navier-Stokes equations, do people imply only momentum equations, or the full set of equations that govern the phenomena? The problem is with the terminology, though... As for your post, I'd like just to add that the Boussinesq equations are valid not only for free convections problems, but also for mixed ones (free+forced). Once stratification is present and conditions (i)-(iii) in my previous post are met, the full set of NSE reduces to the BE's. Otherwise, the equations are more complex. Regards

So.. I would assume that the Boussinesq Equations is the incompressible set of Navier-Stokes equations adding the Boussinesq approximation for the density variation, correct or not? The confusing about Boussinesq isn't total however, since the denotation is Boussinesq hypothesis, or assumption regarding the eddy diffusivity linear relation with velocity gradients. However I maybe adding confusion because this is another Jonas posting this...

There is one equation about the particle motion in multiphase flow called: "Basset-Boussinesq-Oseen equation". I am not sure if it is what you mentioned. Just for referring.