Insulated Pipe Transient Heat Loss

[odc53]

Hello,

I am trying to calculate the cool down time of a stagnant fluid in an insulated pipe exposed to ambient winter conditions. I was wondering if the "lumped capacitance" method is the right approach to solve a problem like this?

The link:

https://www.wbdg.org/design/midg_design.php

provides the following equation to calculate the cool down time:

Where:
Theta = cooling time
RT = insulation heat transfer coefficient
The equation above looks much the same as the solution to a lumped capacitance problem, however, the convective heat transfer coefficient, H, is being replaced with the the thermal resistance of the insulation, RT. My question is whether it is appropriate to do so? The insulation itself will have a temperature gradient which will vary over time, and this equation doesn't seem to account for that (atleast that is my understanding).

If anyone can shed some light on this topic that would be great.

 

[georgeverghese]

Rt could only be the overall htc ; ie it should be a lumped htc which accounts for the internal fluid film htc, the resistance from the metal wall, the insulation resistance and the external htc from the surface of the insulation cladding.

This expression may be ok as a first approximation if it is indeed correct; it doesnt account for the heat content in the metal wall, but this may be small is relation to the heat content of the fluid in your case.

Before you dive headlong into using this equation, would suggest we check this out against a pseudo steady state approximation, by using several short time steps..

 

[IRstuff]

The article clearly states that R_T ignores pipe walls and air film conductance to be conservative.

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