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[Conduction]
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Embedded Rectangular Volume

Shape factor and heat rate for a rectangular volume 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 Rectangular Volume

Calculates the shape factor S and heat rate Q for a rectangular parallelepiped of dimensions L×W×H buried at depth d in a semi-infinite medium of thermal conductivity k, below an isothermal surface.

Shape Factor

The empirical correlation (Holman, 1990) is:

S=1.685L[log10​(1+Wd​)]−0.59(Hd​)−0.078

where log10​ is the common logarithm (base 10).

Heat Transfer Rate

Q=S⋅k⋅(Tb​−Ti​)

where Tb​ is the body temperature and Ti​ is the isothermal surface temperature.

Thermal Resistance

R=k⋅S1​[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 a rectangular volume 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.