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- 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.

Can I ask if:

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.

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.

Can I ask if:

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.