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

• JD_PM
In summary, the conversation discusses the use of three conservation laws for mixture quantities and an additional equation for void ratio in modeling non-isothermal cavitation. The person also mentions the need for explicit equations and asks for help in determining which equations to use for modeling steel and how to couple both sets of equations. They suggest looking into conjugate heat transfer and mention a specific solver in OpenFOAM that could provide insight on handling such simulations.
JD_PM
TL;DR Summary
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 :)

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.

JD_PM

## 1. What is a non-isothermal flow through a pipe?

A non-isothermal flow through a pipe refers to the movement of a fluid through a pipe where the temperature is not constant. This means that the temperature of the fluid changes as it moves through the pipe, either due to external factors such as heat transfer or internal factors such as friction.

## 2. Why is it important to model non-isothermal flow through a pipe?

Understanding how to model non-isothermal flow through a pipe is important for a variety of reasons. It can help engineers design more efficient and effective piping systems, predict the behavior of fluids in different temperature conditions, and identify potential issues such as heat loss or pressure drop.

## 3. What factors affect non-isothermal flow through a pipe?

There are several factors that can affect non-isothermal flow through a pipe, including the type of fluid being transported, the temperature difference between the fluid and the pipe walls, the flow rate, and the material and size of the pipe. Other external factors such as heat transfer from the surroundings and changes in elevation can also have an impact.

## 4. How is non-isothermal flow through a pipe modeled?

Non-isothermal flow through a pipe is typically modeled using computational fluid dynamics (CFD) software. This involves creating a 3D model of the pipe and fluid system, inputting the relevant parameters and boundary conditions, and solving the governing equations for fluid flow and heat transfer. The results can then be analyzed to understand the behavior of the fluid and make any necessary design changes.

## 5. What are some challenges in modeling non-isothermal flow through a pipe?

There are several challenges in modeling non-isothermal flow through a pipe, including accurately representing the complex geometry of the pipe and any fittings, choosing appropriate boundary conditions, and selecting the most appropriate numerical methods for solving the governing equations. Additionally, accounting for the various factors that can affect non-isothermal flow, such as turbulence and heat transfer, can also be challenging.

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