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Multi-layer Cylinder

Outer-wall temperature for a concentric multi-layer cylinder given inner temperature and heat load.

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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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Multi-layer Cylinder

Calculates the outer-wall temperature Tn​ of a concentric multi-layer cylinder, given the inner-wall temperature T0​ and the radial heat flow Q. Up to four concentric layers may be specified; layers with zero thickness are ignored.

Layer Geometry

Each layer i has inner radius ri−1​ and outer radius ri​=ri−1​+ti​:

Ri​=2πLc​ki​ln(ri​/ri−1​)​

Series Resistance

Rtotal​=i=1∑N​Ri​

Outer Temperature

Tn​=T0​−Q⋅Rtotal​

where positive Q denotes heat flowing outward (T0​>Tn​). The end walls of the cylinder are assumed adiabatic; only radial conduction is considered.

Reference

Holman, J. P., Heat Transfer, 7th ed., McGraw-Hill, 1990, pp. 30–32.

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Frequently asked questions

Outer-wall temperature for a concentric multi-layer cylinder given inner temperature and heat load. 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.