(1). If you have a 2-D problem, with one inner convection region, one middle conduction region, and one outer convection region, then it is possible to solve it as one problem using say low Reynolds number model. (2). But most practical problems of interest are 3-D. This makes it not practical to use low Reynolds number model because of memory limitations. This will have bad impact on the accuracy of the flow field and temperature field solutions,especially in the region next to the wall. (3). Since the current low Reynolds number models are still not consistent and accurate, the use of the empirical formula based on the experimental test data in terms of the heat transfer coefficient would be more reliable than the numerical solution near the wall. (4). What I am saying is, the accurate prediction of the of the skin friction and the heat transfer using current turbulent models is still difficult. (This is also true for the 2-D cases) (5). So, perhaps, it is more reliable to use experimental heat transfer coefficient formula as the wall boundary condition, when solving the conduction problem in the solid. In this way, one does not have to solve the convection part at the same time when working on the temperature distribution in the solid. (6). For the incompressible flow without the body force and the temperature effect on the density, then the velocity field can be solved first without the energy equation. Once the velocity field is obtained, it can then be used in the energy equation to obtain the temperature field. So, I think, the velocity field can be solved first alone.

>There is no Heat transfer coefficients involved in the calculations.

I see your point John. I think this (our/my confusion) boils down to a question of thermal wall functions, how to deal with the heat transfer in the boundary layer. Current relationships (for y+<=11ish and >11ish)utilise the Stanton number. For y+<11ish:

Stanton = (Re.Pr.)^-1 where Stanton = Q/(rho u Cp (T-Tw)) e.g. htc = thermal conductivity/distance to wall

For y+>11ish:

Stanton becomes a nice complication little function of skin friction coefficient, Pr lam. and Pr turb. Too complicated to write here!

Launder and Spalding covered this (rather buried the truth by showing the full equation in their famous 1974 paper.

I'm imagining that you are thinking of integration direct to the wall with a particulary fine grid?

It's interesting the different approaches or attitudes I've encountered here and elsewhere. One seems to be the academic "wall functions are a source of error and so should be ignored" the other being a more industrial and pragmatic "well if it's OK for flat plate boundary layers it's not going to be a million miles out for my application". I know this is a shameful oversimplification but it's one that can be applied time and time again.

Hey, I've learnt lots in this discussion thread anyway!

Fred.

(1). I think, you are right. (2). I said it was hard to understand your question, and I didn't want to get directly to that point. (3). So, it was a good exercise. From cfd point of view, the future is to solve the whole flow field all the way to the wall. This is not easy, but it will be here with the future hardware and the modeling effort near the wall. We always have to paint a beautiful and challenging picture to keep people away from killing each other. (4). In the current engineering environment, we have to use wall functions and empirical heat transfer coefficients for the real world problems. (this could be very confusing, because the turbulent kinetic energy,k is always non-zero, thus wall shear stress derived from k is always non-zero even for separated flow problems. ) (5). So, the use of these models and concepts can be quite useful in most engineering applications. But there are always exceptions. The only way to make sure that the solution is reliable is to solve the same problem in different ways, from different angles, I guess.

on the matter of a relation ship between skin friction and heat transfer coefficient, i agree with you that there is no necessary relationship between the two as the temperature field and the velocity field are not necessarily similar. in cases of forced convection though i'd probably guess that the two would trend with one another. but then again i wouldn't stake too much money on it.

John. i understand that todays turbulence models are inadequate for heat transfer i just wanted to know if you thought the formal procedure was computationally and/or theoretically sensible.is it possible for you to comment on the use of commercial packages for conjugate heat transfer (ie have you used any for this purpose?)

(1). I have used a couple of commercial CFD codes extensively in the last few years. (2). I have not checked out these codes in the conjugate heat transfer problems (heat transfer in the solid region and the fluid region at the same time). Even though, this is a very important area in turbomachinery applications, my current interest has been in the loss prediction associated with the viscous flow field itself. (3). I can only say that, it is still very difficult to predict the viscous loss accurately using those commercial cfd codes I have used. But I have not been able to track down the source of inaccuracy, whether it is due to the numerical formulation, the solution algorithm, or the turbulence model used. (4). But in general, from the positive side, these commercial CFD codes have made it possible to obtain solutions to problems with complex geometry. It is the first step in the right direction. (5). So, a lot of research is still required in the areas such as solution convergence, accurate solution algorithm, realistic turbulence modelling, ability to generate good meshes for accurate solutions, etc. Don't use the cfd solution directly on the design, unless you have done a systematic validation through comparison with real world test data. (6). But you also have to realize that CFD is not CAD, it still requires the equivalent power of super-computers, and most of the problems remain in the research domain.