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transient problem with boundary flux that depends on its own time integral
Posted Apr 5, 2010, 12:55 p.m. EDT 2 Replies
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I want to solve a simple transient heat transfer problem where a volume of fluid is fully enclosed by a solid container, all with constant physical properties (see attached). Heat is transferred from outside to the solid then on to the enclosed fluid inside. To avoid solving a fluid flow/convection problem on the inside I can assume that the fluid is very well mixed and is isothermal at any time.
My goal is to calculate the fluid temperature as a function of time. I need to set the problem with a Neumann boundary condition on the inner boundary but the inner (fluid) temperature will need to be determined from solving a separate integral equation of the sort mfluid*Cp_fluid*(Tinside(t)-Tinitial)=time Integral of heat flux on the inner Neumann boundary.
1- How best do I set up this problem with the auxiliary time integral to set the inside temperature?
2- How do I initialize the fluid temperature (remembering that there is really no computational domain associated with it)
Thanks much,
Ozgur
My goal is to calculate the fluid temperature as a function of time. I need to set the problem with a Neumann boundary condition on the inner boundary but the inner (fluid) temperature will need to be determined from solving a separate integral equation of the sort mfluid*Cp_fluid*(Tinside(t)-Tinitial)=time Integral of heat flux on the inner Neumann boundary.
1- How best do I set up this problem with the auxiliary time integral to set the inside temperature?
2- How do I initialize the fluid temperature (remembering that there is really no computational domain associated with it)
Thanks much,
Ozgur
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2 Replies Last Post Apr 5, 2010, 1:32 p.m. EDT
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Posted:
1 decade ago
Ozgur,
If I understant correctly your problem,
I will suggest to use an ODE for the liquid temperature.
initial temperature will be initial condition of the corresponding global equation.
and the ode will just refect the energy balance for your fluid where the thermal energy of the liquid :
Cp_fluid*Masse_fluid *T_fluid will vary according to the heat flux crossing the boundary.
what you have to decide for yourself and it is a complex decision in most practical situation, is how you model the thermal flux between solid and liquid through the liquid/solidinterface:
is it conduction only ? is convection significant..?.... radiation in some case might play a role but not at "normal temperature with a liquid.
but once you have decided how to model this ,
the flux will be just a simple boundary integration coupling variable that you will use in your ODE to track the evolution of the liquid temperature.
Hope this help
jf
If I understant correctly your problem,
I will suggest to use an ODE for the liquid temperature.
initial temperature will be initial condition of the corresponding global equation.
and the ode will just refect the energy balance for your fluid where the thermal energy of the liquid :
Cp_fluid*Masse_fluid *T_fluid will vary according to the heat flux crossing the boundary.
what you have to decide for yourself and it is a complex decision in most practical situation, is how you model the thermal flux between solid and liquid through the liquid/solidinterface:
is it conduction only ? is convection significant..?.... radiation in some case might play a role but not at "normal temperature with a liquid.
but once you have decided how to model this ,
the flux will be just a simple boundary integration coupling variable that you will use in your ODE to track the evolution of the liquid temperature.
Hope this help
jf
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Posted:
1 decade ago
You are right JF. Actually after I posted the question I put together a quick model attempting what I wanted to do and it seemed to work. Including it here for reference.
Cheers
Ozgur
Cheers
Ozgur
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