Understanding how to model a non-isothermal flow through a pipe

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The discussion focuses on modeling non-isothermal flow through a pipe using conservation laws for mass, momentum, and total energy, along with an equation for the void ratio. The main challenges include determining appropriate equations for modeling the steel component and how to effectively couple the fluid and solid models. Suggestions include utilizing conjugate heat transfer principles and exploring OpenFOAM's chtMultiRegionFoam solver for insights into simulation handling. The need for more literature on this specific coupling issue is highlighted. Overall, the conversation emphasizes the complexity of integrating fluid and solid dynamics in thermal modeling.
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I want to simulate (using OpenFOAM) a flow of water at an initial temperature (say 300 K) passing through a steel pipe at an initial temperature (say 90 K) and write two sets of equations: one that describes the fluid and other the solid. Then these two sets need to be coupled so that eventually both fluid and solid reach the same temperature.

Please note that the aim of this post is to understand the physics behind the problem (i.e. what equations should be studied and how to couple both sets)
For the fluid, I will use three conservation laws for mixture quantities (mass, momentum and total energy) and an additional equation for the void ratio (as explained in the paper "Modeling for non isothermal cavitation using 4-equation models"). If you want I can share the explicit equations.

I have two main issues:

1) What equations should be used to model the steel? I thought of using essentially the same equations that for the fluid but I do not see how to modify them such that it models a solid.2) How to couple both sets? I have been looking into the literature but I did not find a paper addressing a similar issue.

Any help is appreciated, thank you :)
 
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I’d rather call this conjugate heat transfer since that’s the kind of problem where you account for heat exchange between the fluid and solid. OpenFOAM has a special solver for that - chtMultiRegionFoam. Check its documentation and maybe even source code. This should give you an insight on how such simulations are handled internally.
 
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