Numerical Heat Transfer
 

How to choose temperature boundary condition for simulation with cfd if they don't specify a accuracy number ?
I read more numerical heat transfer paper. Although i found that the exp which they use don't have a accuracy number, authors still can choose a value to validate. So how to do that ?
Thanks all.

Even if the experimental uncertainty is stated, what would be different? Besides, the uncertainty isn't even certain. They're just estimates.

I don't understand what u means. But if they can't specify a reasonable number for boundary condition, how can they use it to choose turbulent model or something else ?

I'm sorry I thought you were referring to experimental accuracy. You are talking about neither experiments nor accuracy.

You mean how to do simulations where the temperature BC is just temperature and not any number?

If material properties are constant then the heat equation is linear in temperature. If the boundary conditions are simple like fixed temperature or fixed flux, you can always recast the problem into a non-dimensional temperature variable and use any numbers that you like. Superposition. Superposition. Superposition.

So for example. If you have a rectangular heated slab initially at a uniform temperature. And one or more surfaces are suddenly raised to a different temperature. It really doesn't matter what the initial temperature is and what the new temperature is. It can be 0 K, 1 K, 1 million K, the temperature evolution in time follows the same behavior if you just non-dimensionalize it.

Could you detail better your question? First, the BCs to be prescribed depends on the mathematical character of the equation. I suppose you have a parabolic or elliptic equation. Then, Dirichlet/Neumann BCs are generally prescribed. Often, you have from the experiment some value for the heat flux that you use as Neumann BC.

My question is why cfd authors can choose a number for BC if exp don't specify a concrete conditions.
For example, exp said: "The experiment was conducted over a Reynolds number range from 5000 to 125,000. The fluid temperature ranged from 260 to 290 K, and the surface to fluid temperature difference from about 20 to 40 K. The system pressure ranged from 100 to 600 kPa".
with CFD authors: inlet 298.15 K, heat flux on heat surfaces 260 W/m^2

If some input range is given, boundary condition value will be chosen depends up on the condition to be simulated like normal operating condition, worst condition etc.,

You have to ask yourself this question before you start the CFD simulation.

Because using non dimensional equations you don't have a unique concrete conditions. For example, if you have a simulation at a Rayleigh number = 10^3 that can correspond to "infinite" concrete conditions.
Conversely, if you have an experiment at one physical condition you can extract the corresponding non dimensional numbers.

U're right. But something non-dimensional (like density ratio Tw-Ti/Tw) is rarely used. I almost see they plot Nusselt/htc. Do u have any experiment ?

Nusselt number and htc is a flow property (up to the linear limit). The heat equation itself is also linear. In CFD, you have even the option of using running simulations with constant properties to force the linearity even when the real world experiment is not.

The people running the heat transfer experiment even don't care what particular temperature it is. It has to be measured of course, but all they care about is the driving temperature difference. Just look at the definition of heat transfer coefficient. If it matters, I've done thousands of heat transfer experiments in my past life.

If you are trying to benchmark your entire velocity field and temperature field in CFD with experiments then yes the devil is in the details. But if all you want is to compare htc's and Nusselt numbers, it doesn't matter. Newton figured this out some 400 years ago.

So u means Nu/htc doesn't depend on temperature inlet/heat flux on the wall, just depend on something else like reynolds number and geometry. So we can choose whatever we want and the results is still not different

You should consider that a common BC at a wall is the value of the heat flux q. Then, you have q= -k dT/dn at the wall. Now we introduce the non dimensional BC assuming T= T0+ (T1-T0)*Tad so that




q= -k [(T1-T0)/L]*dTad/dn -> dTad/dn=-Nu


A local dependence of Nu is linked to the local dependence of q (of course, by assuming k = constant)