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=S⋅k⋅(T1−T2)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)2πLcEach correlation carries validity limits (such as Lc≥10r) — 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/ri−1)and the unknown temperature follows from ΔT=Q⋅Rtotal.
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.