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Embedded Flat Plate

Shape factor and heat rate for an isothermal flat plate 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 Flat Plate

Calculates the shape factor S and heat transfer rate Q for a flat plate of width W and length L (where W>L) buried at depth d in a semi-infinite medium of conductivity k, below an isothermal surface.

The governing relationship is:

Q=S⋅k⋅(Tp​−Ti​)

where Tp​ is the plate temperature and Ti​ is the surface temperature.

Shape Factor Cases

Case 1 — Plate at the surface (d=0, W>L):

S=ln(4W/L)πW​

Case 2 — Deeply buried wide plate (d≥10W, W>L):

S=ln(4W/L)2πW​

Case 3 — Very wide plate at moderate depth (W≥10L, d≥2W):

S=ln(2πd/L)2πW​

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 an isothermal flat plate 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.