General Convection Heat Transfer Coefficient 3

[rjw57]

I am trying to get my arms around the methodology of calculating the subject term (typically, "h") when used in a finite difference scheme (or any other numerical approach to heat transfer) where the boundary includes a convection term. Is it as simple as calculating the convection heat transfer coefficient for a flat plate? Do you assume a constant temperature condition (as opposed to constant flux) due to the nature of the methodology (that is, the discretized cell is of a constant temperature by definition)? Any insight would be greatly appreciated from you numerical computation gurus out there.

See this webpage for an example of what I am talking about. NO, this is NOT homework.

http://courses.ucsd.edu/rherz/mae221a/notes/transimplicit5x5.pdf

 

[IRstuff]

Convection coefficient is dependent on ambient temperature and geometry. But, certainly, within a cell you assume constancy of all conditions.

Beyond that, the question is how accurately do you care to make the model. In cases where you've determined the need to discretize there will be other geometry effects that are more relevant than the convection coefficient.

TTFN

FAQ731-376

 

[rjw57]

Not sure I understand your reply. I am familiar in general terms with discretization techniques, however, I have never been concerned with the specifics of calculating a convection coefficient at a solid-fluid interface WHEN USING NUMERICAL METHODS (I'm not talking here about calculating the empirically derived heat transfer coefficient for, as an example only, the cylinder in cross-flow). As I recall in my (long ago) college days, the heat transfer coefficient was always stated as part of the problem definition. I am on the other side of college now. I want to know how to calculate the local convection transfer coefficient which is a boundary condition for a discretized numerical problem. Is this more clear?

 

[vpl]

rjw57

There is not a simple answer to your question. Calculating the heat transfer coefficient depends on your configuration and there are different formulas depending on the configuration. Depending on your set up, the temperatures may, or may not, be constant (it's easier if they are.) Assuming flow across a flat plate might be appropriate (but generally isn't.)


Patricia Lougheed

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[rjw57]

Maybe I'm not seeing things clearly here. If I discretize the problem of flow perpendicular to and across a cylinder by creating a grid pattern that surrounds the cylinder and represents the fluid, how is there any PARTICULAR method of calculating the heat transfer coefficient at any one of the small linear boundaries surrounding the cylinder. I don't see how it would be appropriate to use the GENERAL calculation for the heat transfer coefficient for this situation. Like I said in a previous post, I know how to calculate the AVERAGE OVERALL heat transfer coefficient for heat transfer from a cylinder in cross-flow. It's (loosely): Konstant * Reynolds^X * Prandtl^Y. This is NOT a local heat transfer coefficient. It represents an integrated average of the local coefficients around the cylinder. I am asking about how to calculate the heat transfer coefficient for one of those tiny little lines on the grid that represents one small portion of the surface of the cylinder where a fluid is in contact with it and removing energy from it via convection.

 

[IRstuff]

You appear to be asking a new question, now. The convective transfer coeffcient is basically a function of air thermal conductivity, Nusselt number, and air temperature. Any decent heat transfer text should have the formulas.

TTFN

FAQ731-376

 

[rjw57]

IRstuff

Appearances can be deceiving. I've been asking the same question all along - just not very well apparently.

 

[Maxham1]

From the little that I remember from my finite-difference studies, the local heat transfer coefficient is determined by considering it's definition (h=q*A*DELTAT) and equating that definition to the conduction occuring at the same surface as where the heat-transfer coefficient is desired. That is, h=q*A*DELTAT is compared to k=qDT/Dy, where y is in the direction perfendicular to the surface.

What I've written above might not be exactly correct, but I hope it helps in getting to the correct answer.

 

[rjw57]

Maxham1

Thanks. I dug a little deeper and found something similar to what you said here on a CFD forum. I was getting confused by the fact that in discretization, we know the flux term out of the solid and into the fluid at the boundary is equivalent. So, yes, I can see that the convective heat transfer coefficient is a RESULT of the equations, not an input to them. I still need to think a little harder here though. Thank you for your help. You've gotten me closer to my goal.

 

[IRstuff]

Yes and no. The heat transfer coefficient is simply the way the heat flow is bookkept. For any given set of heat flows and ambient conditions and geometry, there is one and only one transfer coefficient that will simultaneously satisfy all the conditions.

Your FEA model does the math. You can input the heat flows, conditions, etc., and simultaneously solve for the resultant output flows and transfer coefficients. This is part of the iteration that's done at each time step.

TTFN

FAQ731-376

 

[stanford94]

what are you modeling?

h is a function of:

1.geometry
2.velocity distribution
3.fluid properties
4.temperature boundary condition, and
5.temperature initial condition

 

[ginsoakedboy]

Strictly speaking, a heat transfer coefficient is an empirical construct to keep track of heat transfer across a solid/fluid interface. (As mentioned by IRstuff and also stated by you.) See attached image file showing the formalized definition of the "local" heat transfer coefficient. Also, keep in mind that a heat transfer coefficient is only defined for equilibrium conditions (because that is when the surface temperature and bulk fluid temperature are constant).

The conventional definitions of heat transfer coefficients for various geometries of the forms:

h=(Nu x Kf)/Lc {where Nu=f(Gr,Pr) or Nu=f(Re,Pr)}

are always averaged generalizations obtained by curve-fitting of experimental data. *Again, this data is obtained for equilibrium conditions.* To be really accurate your program should recalculate the heat transfer coefficient at each time step because these temperatures will be varying during a transient simulation.

 

[corus]

You can use CFD which will couple fluid flow with the heat transfer within the solid, which is still part of the Navier Stokes equation. This would give you your discrete heat transfer at specific positions. For generalised heat transfer it is typical to use an empriical formula which has been obtained for general areas, such as horizonatal/vertical plates or cylinders. There is some confusion over which formula to use though when the formula is applicable for either fixed surface temperatures, or for fixed surface heat flux, as quoted in

http://www.cheresources.com.

I use the general expressions quoted in MacAdama, which aren't far off other formulae I've seen.

corus