# Cooling of a thick walled pipe transporting water

In summary: You are trying to solve the problem of finding the temperature drop of the outer wall of a pipe as a function of time.
TL;DR Summary
How does the outer temperature of the pipe changes as the water flows through it.
Hi everyone,

I'm trying to solve the following problem but can't quite get my head around it.

I have a pipe of length, L (m), diameter, d (m), the pipe walls are thick (multiple meters). I know the inflow temperature of the pipe, say, Tin (K), and the pipe's external wall temperature, Tw.

I found a solution which answers my question by assuming the pipe is infinitely thick. What it does is it determines the radius in which the temperature will change in the pipe based on the amount of water flowing through it and the time it has been flowing for.

I am happy with that assumption as long as the radius of temperature change is lower than that of the pipe. When that happens it doesn't make sense and the pipe's wall external temperature, Tw, should be dropping cooling markedly.

When that happens I am unsure how I can determine, both by how much Tw, cools, and from there Tout. My flow rate through the pipe is constant.

A) this is a simple problem that can be solved analytically?
B) If so how would you go about it?

I know all the thermal and material properties of the pipe and water.

Thank you.

The key thing you are missing is the heat transfer from the outer wall to the surrounding environment.

If the pipe is surrounded by perfect insulation, then the outer wall temperature will eventually match the inner wall temperature. If the pipe is on the ocean floor, the outer temperature will be very close to water temperature. There are infinite intermediate cases.

Hi anorlunda,

Thank you for your response. You are absolutely correct, and in my case the pipe is surrounded by perfect insulation...(in practice I actually have a network of pipes evenly spaced together, so half way between the pipes the heat transfer is equal but in opposite direction).

Does that help to narrow down the cases?

Also, the flow in the pipe is turbulent.

Wait, is the outer wall temp given or are you trying to find it?

I know the initial outer wall temperature yes. But eventually the cooling will reach the outer wall and then the outer wall's temperature is starting to drop. When that happens I need to figure out both the temperature drop of the outer wall, and the outflow temperature, as function of time. Essentially, I have a finite amount of heat in my thick pipe. I'm not sure that what I'm trying to obtain is possible analytically. It sounds like it should be, but I've been scratching my brain and notepad for hours without any success. Here's a quick sketch to help define the problem:

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## 1. What is the purpose of cooling a thick walled pipe transporting water?

The purpose of cooling a thick walled pipe transporting water is to maintain a safe and optimal temperature for the water being transported. This helps prevent overheating, which can lead to damage or failure of the pipe and potentially cause harm to the surrounding environment.

## 2. How does the thickness of the pipe affect the cooling process?

The thickness of the pipe plays a significant role in the cooling process. Thicker pipes have a larger surface area, which allows for more efficient heat transfer and faster cooling of the water inside. However, thicker pipes also have a higher thermal mass, meaning they can retain heat for longer periods of time.

## 3. What factors influence the cooling rate of water inside a thick walled pipe?

Several factors can influence the cooling rate of water inside a thick walled pipe, including the temperature difference between the water and the surrounding environment, the thermal conductivity of the pipe material, the flow rate of the water, and the thickness of the pipe.

## 4. How can the cooling rate of a thick walled pipe transporting water be increased?

The cooling rate of a thick walled pipe transporting water can be increased by increasing the flow rate of the water, using a pipe material with a higher thermal conductivity, or reducing the temperature of the surrounding environment. Additionally, insulating the pipe can help prevent heat loss and maintain a lower temperature for the water inside.

## 5. What are the potential consequences of inadequate cooling in a thick walled pipe transporting water?

If a thick walled pipe transporting water is not adequately cooled, it can lead to overheating and potential damage or failure of the pipe. This can result in leaks, bursts, or even explosions, which can cause significant damage to the surrounding area and potentially harm individuals in the vicinity.

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