Mutual Thermal Resistances between Pipe Layers

[teknomania]

Ref: Palsson, Halldor | Analysis of Numerical Methods for Simulating Temperature Dynamics in District Heating Pipes - please check pg. 62 at LINK (CLICK!)

INTRO: In this reference, the mutual thermal resistances between layers as water-insulation, ground-surrounding, and insulation-ground are defined for a buried pre-insulated pipe, figure and formulations given below.

QUESTION: I want to improve the model given in this reference by studying the layers as water, steel, insulation, and ground so I need to obtain the mutual thermal resistances between water-steel, steel-insulation, insulation-ground, and ground-surrounding. I couldn't find a reference describing how to find the thermal resistances between layers of a cylinder (e.g. thermal resistance between pipe wall and insulation and others). Can any of you help me either by giving formulations or by guiding me to a reference?

FIGURE:

FORMULATIONS:

DETAILS:

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[IRstuff]

Did you get hit by the Google outage? It seems to be working fine now:

https://web2.clarkson.edu/projects/...es/Conduction in the Cylindrical Geometry.pdf

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[teknomania]

Thank you IRstuff. But this reference is not enough to my question. I need to find this mutual thermal resistance between the cylindrical layers (i.e. between insulation and water). The aim here is to find the temperature of insulation (as well as steel and ground) so to consider the thermal inertia for the flow through a buried insulated pipe.

“In life, the truest guide is science” – Mustafa Kemal Atatürk

 

[LittleInch]

My understanding of this is that with the layers in direct contact there is an assumption that there is no additional boundary resistance to heat transfer from one layer to the next, or if there is that it is negligible.

Heat conduction from water to steel is subject to a transfer coefficient depending on water flow rates etc.

By "thermal inertia" do you mean a transient heat up analysis?

Can be done but needs a transient analysis program.




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[IRstuff]

There is typically considered to be none, for two reasons
> they are usually in intimate contact, so the interface layer is extremely thin
> the area of non-contact is usually small

In general, thermal inertia is dominated by the thermal mass of the object and the bulk thermal resistance.

Furthermore, the particular example you selected, water and pipe, are dominated by convection on the water side, and the bulk conductance of water comes indirectly into the calculation.

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[teknomania]

By "thermal inertia" do you mean a transient heat up analysis?

Can be done but needs a transient analysis program.

The main purpose is with the solution of transient water temperature profile through a pipe segment considering the thermal inertia by the insulation and ground. I simply solve the system of partial differential equations for all sections (water, insulation, and ground) simultaneously. As this reference indicates, there need to be thermal resistances defined between these sections of the buried insulated pipe.

“In life, the truest guide is science” – Mustafa Kemal Atatürk

 

[IRstuff]

You are reading the words, but misinterpreting them and the equations. Look at the equations 1a, 1b, 3a, and 3b; they reference the annulus diameters, so all the terms are describing bulk thermal resistances.

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