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Embedded Cylinder

Shape factor and heat rate for an isothermal cylinder buried in a semi-infinite medium.

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A buried pipe's heat loss needs no mesh or simulation — a conduction shape factor reduces the whole 3-D problem to one multiplication: Q = S · k · ΔT.

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Figures assume typical conditions and the stated method. For measured, guaranteed numbers on your plant, our engineers run site surveys, heat loss audits, and full process models.

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Embedded Isothermal Cylinder

Calculates the shape factor S and heat transfer rate Q for an isothermal cylinder of length Lc and diameter D buried at depth d (to the cylinder centre) in a semi-infinite medium of conductivity k, below an isothermal surface at temperature T2.

The governing relationship is:

Q=Sk(T1T2)

where T1 is the cylinder temperature and S is selected from three cases.

Shape Factor Cases

Case 1 — Long cylinder (Lc10r), depth ≥ length (dLc):

S=cosh1(d/r)2πLc

Case 2 — Long cylinder (Lc10r), deep burial (d>3r):

S=ln(2d/r)2πLc

This is an approximation valid when d/r1, where cosh1(d/r)ln(2d/r).

Case 3 — Deep slender burial (d10r, Lc10d): not implemented (formula was image-only in source).

Thermal Resistance

R=kS1[K/W]

Reference

Holman, J. P., Heat Transfer, 7th ed., McGraw-Hill, 1990, pp. 74–83.

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Frequently asked questions

Shape factor and heat rate for an isothermal cylinder buried in a semi-infinite medium. Enter your inputs and press Calculate — the worked solution shows every step of the method with your numbers substituted in.

The conductivity of the medium between the two isothermal surfaces — soil or concrete for buried objects, the layer material for walls. The tools include a table of common materials; use a measured value when you have one, since soil conductivity especially varies with moisture content.

For geometries within their validity limits they typically agree with full numerical solutions to within a few percent. The worked solution reports which case or correlation was applied, so you can check the limits against your geometry.