Mutual Thermal Resistances between Pipe Layers

Summary
Mutual thermal resistances between layers of a cylinder (either a pipe or a storage tank) in order to obtain heat transfer between these sections (e.g. from water to steel, steel to insulation, insulation to the ground and vice versa).
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:
FIGURE:
244535

FORMULATIONS:
244536


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 such as between water and steel and others. Can any of you help me either by giving formulations or by guiding me to a reference?

More details (Ri and Rg as given in the formulation above (3c)):
244537
 

Mech_Engineer

Science Advisor
Gold Member
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Heat transfer analysis through a multi-layered cylindrical geometry is a common topic, you might just need to look for the right key words.

Here is one paper I found on the subject: https://web2.clarkson.edu/projects/subramanian/ch330/notes/Conduction in the Cylindrical Geometry.pdf

This topic is also covered in college-level heat transfer courses: https://www.sfu.ca/~mbahrami/ENSC 388/Notes/Staedy Conduction Heat Transfer.pdf
Thank you Mech_Engineer. But I don't think that such references are good as answer to my question. I want to find the temperature of (i.e.) insulation so I need this, as termed by the reference, the mutual thermal resistance between the layers (for example between water and insulation (as well as between insulation and the ground). Meanwhile, I need to find the temperature of sorrounding ground (its temperature gets affected by the water temperature as result).
 
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Usually the heat transfer coefficient at the wall (such as between the water and the steel tube) would be found from empirical relation involving Reynolds and Prandtl numbers (see for example, Dittus-Boelter). I'm not sure why that doesn't seem to appear in your referenced text. Maybe (?) the water flowrate is high enough that the heat transfer is conduction limited (so that the convection coefficient isn't significant)?
 

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