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 ramin May 3, 2013 06:07

discretisation

Hello
I want to discretise one term of non fourier heat transfer equation with volume control method. I try to do it, but i cant.
this term is: d2(cp u T)/(dt dx)
that we have cp(T),u(x,y,t),T(x,y,t)
T:temperate
t:time
thank you

 FMDenaro May 3, 2013 08:34

I have some doubt about your symbolism, you are referring to as a first time derivative or a second mixed x,t derivative....?

 ramin May 3, 2013 16:40

Quote:
 Originally Posted by FMDenaro (Post 424965) I have some doubt about your symbolism, you are referring to as a first time derivative or a second mixed x,t derivative....?
sorry, d2(cp u T)/(dt dx)

 FMDenaro May 3, 2013 17:52

Quote:
 Originally Posted by ramin (Post 425089) sorry, d2(cp u T)/(dt dx)

what equation you are solving?

 ramin May 4, 2013 03:16

Quote:
 Originally Posted by FMDenaro (Post 425097) what equation you are solving?
I said, non fourier heat transfer equation

 FMDenaro May 4, 2013 04:57

Quote:
 Originally Posted by ramin (Post 425124) I said, non fourier heat transfer equation
I never worked on such model, what about the mathematical classification of this equation?

 ramin May 4, 2013 07:13

Quote:
 Originally Posted by FMDenaro (Post 425130) I never worked on such model, what about the mathematical classification of this equation?
It is a hyperbolic heat transfer equation. It should be discretised base on versteegَ s book(An introduction to computational fluid dynamics) and with volume control method.

 FMDenaro May 4, 2013 13:46

Your question is not clear to me... to the best of my knowledge, a term like d2T/dxdt never appears in the original heat equation....
hybrid time-space derivatives usually appears when you use some time-integration method of the class of the Lax-Wendroff. But in such cases, the original equation is substituted into the derivative.

 ramin May 4, 2013 18:26

Quote:
 Originally Posted by FMDenaro (Post 425231) Your question is not clear to me... to the best of my knowledge, a term like d2T/dxdt never appears in the original heat equation.... hybrid time-space derivatives usually appears when you use some time-integration method of the class of the Lax-Wendroff. But in such cases, the original equation is substituted into the derivative.
I want to write a computer program to solve my equation that one of the itُs terms is d2(cp u T)/(dtdx). Now i want to approximate this term base on my method that i said.
This term is very small, since it has a very small fixed coefficient. This coefficient shows the speed of heat propagation is not infinite.

 FMDenaro May 5, 2013 04:13

Quote:
 Originally Posted by ramin (Post 425245) I want to write a computer program to solve my equation that one of the itُs terms is d2(cp u T)/(dtdx). Now i want to approximate this term base on my method that i said. This term is very small, since it has a very small fixed coefficient. This coefficient shows the speed of heat propagation is not infinite.

Again, the real problem is not in the discretization of a single term (is quite simple to do on a time-space grid) but care in the discretization of the model equation is required.
You said it is hyperbolic, therefore the discretization of the whole model must be stable and accurate, but if the equation is also non-linear other requirements can be necessary.

 ramin May 5, 2013 05:44

Quote:
 Originally Posted by FMDenaro (Post 425278) Again, the real problem is not in the discretization of a single term (is quite simple to do on a time-space grid) but care in the discretization of the model equation is required. You said it is hyperbolic, therefore the discretization of the whole model must be stable and accurate, but if the equation is also non-linear other requirements can be necessary.
Yes, you are right, but the most important of my problem is the discretization of this term. May you send me your email to give whole of my equation.

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