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[Heat Transfer]
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Conduction

Six conduction calculators: buried-object shape factors, multi-layer walls and cylinders, and thermal interface conductance — heat rates and temperatures from Holman's correlations.

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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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Steady-state conduction problems rarely need simulation. For the geometries plant engineers actually meet — buried pipes, embedded ducts, layered walls, bolted joints — published shape factors and series-resistance methods give answers within a few percent, instantly. This suite implements six of them.

What's in this suite

  • Embedded Cylinder — shape factor and heat rate for an isothermal cylinder buried in a semi-infinite medium (buried pipes, cables, ground loops). Three validity cases per Holman, selected automatically.
  • Embedded Flat Plate — the same treatment for a buried flat plate, from surface-flush to deeply buried.
  • Embedded Rectangular Volume — empirical shape factor for a buried rectangular parallelepiped (tanks, duct banks, foundations).
  • Multi-layer Plane Wall — far-face temperature of a wall of up to four layers in series, given the known-face temperature and heat load.
  • Multi-layer Cylinder — outer-wall temperature of a concentric multi-layer cylinder (insulated pipe) given the inner temperature and radial heat flow.
  • Thermal Interface Conductance — joint conductance and temperature drop across two rough conforming surfaces with a gap filler (thermal grease, oil).

Method

Every shape-factor tool evaluates

Q=Sk(T1T2)

where the shape factor S (units: metres) captures the full geometry of the conduction path. For the embedded cylinder, for example, the deep-burial case is

S=ln(2d/r)2πLc

Each correlation carries validity limits (such as Lc10r) — the tools check them and report which case was applied.

The multi-layer tools sum series resistances. Plane layers contribute Ri=ti/(kiA); cylindrical layers contribute

Ri=2πLckiln(ri/ri1)

and the unknown temperature follows from ΔT=QRtotal.

The interface tool combines contact conductance (from harmonic-mean solid conductivity, RMS roughness and contact pressure) with gap-fluid conduction, per the standard conforming-rough-surface model.

Assumptions

Steady state, constant properties, isothermal boundary surfaces. Shape-factor cases assume a semi-infinite medium below an isothermal surface. Sources: Holman, Heat Transfer (1990), pp. 74–83, and standard thermal-interface literature.

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Frequently asked questions

A shape factor S condenses the entire geometry of a steady conduction path between two isothermal surfaces into a single number with units of metres. The heat rate is then just Q = S·k·ΔT, where k is the medium conductivity. Published shape factors exist for most practical buried and embedded geometries.

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 (steel, concrete, mineral wool and more); use a measured value when you have one, since soil conductivity especially varies with moisture content.

They assume a semi-infinite medium below an isothermal surface, and each case has geometric validity limits — for the cylinder, length at least ten times the radius, with separate cases for shallow and deep burial. The calculator checks the limits automatically and reports which case it used in the worked solution.

Yes — the multi-layer cylinder and multi-layer plane wall tools take up to four layers in series with individual thicknesses and conductivities. Layers entered with zero thickness are ignored, so two- and three-layer builds work directly.