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

[JD_PM]

TL;DR

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 :)

 

[FEAnalyst]

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.