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April 27, 1999, 07:05 
Conjugate Heat Transfer

#1 
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Hello Everyone:
I am working on a Conjugate Heat Tranfer problem. The ratio of thermal conductivities between the solid and the fluid is quite high. Is it possible to get a convergence in the energy equation in such situations? Thanks, Thomas 

April 28, 1999, 03:16 
Re: Conjugate Heat Transfer

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Hi, What kind of ratios are you normally encountering? Regards


April 28, 1999, 03:18 
Re: Conjugate Heat Transfer

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Hi Mahesh,
For the current problem, the ratio I am having is a little over 100. Thanks, THOMAS 

April 29, 1999, 10:21 
Re: Conjugate Heat Transfer

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I solved such problems for convective heat transfer through the ribbed channels wher the ribs were conductive. I used a conductive ratio of 700 (copper/water) and managed to get converged solution. I be will happy if I can help.


April 30, 1999, 13:03 
Re: Conjugate Heat Transfer

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Hi Mehrdad,
Thanks for the offer to help. I am very close to getting convergence on the energy equation. It really took a lot of time. The convergence on the flow equations was pretty quick as expected. Thanks, Thomas 

April 30, 1999, 15:23 
Re: Conjugate Heat Transfer

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Hi Thomas;
I have the same experience concerning the convergence time. I think one way to improve the convergence is to try to find an intermidate temperature field using, for example, a constant wall heat flux B.C and then use this solution as an intitial guess for the real problem. Thanks, Mehrdad 

May 3, 1999, 22:13 
Re: Conjugate Heat Transfer

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Hi: Now I am trying to solve a similar porblem(the heat transfer between water and copper, and there is heat source on the interface), so I wonder if your two can give me more detail about the method used to solve the energy equation(I have got the velocity field and assume the heat transfer does not influence the velocity field) and more. Thank you.
Lu zhang 

May 6, 1999, 09:28 
Re: Conjugate Heat Transfer

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Hi Lu,
What do you mean by saying that there is a heat source on the interface? That does not seem like a physical situation. Heat source will be on some part of the solid which is not at the interface between the solid and the fluid. This is more of a physical situation. In the fluid region, continuity, momentum, energy and turbulent equations are solved. In the solid region, only the energy equation is solved. There is no boundary condition applied at the interface between the solid and the fluid. It is left free and is calculated as part of the solution process. Thanks, Thomas 

May 6, 1999, 11:33 
Re: Conjugate Heat Transfer

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Hi, Thomas: Thank you for your reply. For my problem, there are lots of small particles in the liquid and these particle will abrade the solid surface, therefore, heat from abrasion is the heat source on the interface(there are lots of experiment about this). Now, I assume the particles have no influence to the velocity field(the particle is small), maybe in the future, I will worry about it. Now I have the velocity field(laminar flow) and try to solve the energy equation(in solid and liquid). I know the heat source on the interface(some one has measure the friction coefficient on the surface). That is the background of my problem. My problem is unsteady problem. By the way, I have tried to solve the energy equation in the liquid using central difference, however, when Pe is large, solution diverges. And I do not want to use upwind, do you have better about that?
Thank you. Lu Zhang 

May 6, 1999, 14:34 
Re: Conjugate Heat Transfer

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Hi Lu,
Try getting a converged solution first by using a first order upwind scheme. It does create a lot of artificial diffusion. You could then improve the accuracy by going for second order upwind scheme. You might also want to try power law and the quick schemes. When the Peclet number is high, you will definitely have convergence problems with the central difference scheme. Thanks, Thomas 

May 6, 1999, 18:56 
Re: Conjugate Heat Transfer

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Hi;
I think another method for convection terms is Hybrid scheme which , as you know, is a combination of central differencing and upwind schemes. About the energy equation, as Thomas said, you need to solve temperature equation in both solid and fluid regions. (As you know in the solid part the energy equation becomes Laplac equation.) You also need to make sure that you satisfay energy conservation at the interface. If you write down the energy balance at the interface you possibly find a relation between the surface temperature, source term and temperature of the neighbouring cells in the solid and liquid parts which can be useful. Thanks 

May 7, 1999, 10:46 
Re: Conjugate Heat Transfer

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Hi, Thank you two for the help. I really appreciate it. For the Hybird and power law, when Pe is large, both go to the upwind, so I will try upwind first. Thank you.
Lu Zhang 

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