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Multi-layer Plane Wall

Far-face temperature for a multi-layer plane wall given known face 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 Plane Wall

Calculates the temperature Tn​ on the far face of a multi-layer plane wall, given the temperature T1​ on the known face and the heat flow Q through the wall. Up to four layers may be specified; layers with zero thickness are ignored.

Layer Resistance

For a plate of height H and depth D, cross-sectional area A=H×D:

Ri​=ki​⋅Ati​​

Series Resistance

Rtotal​=i=1∑N​Ri​

Far-face Temperature

Tn​=T1​+Q⋅Rtotal​

where positive Q means heat flows from the Tn​ side to the T1​ side (Tn​>T1​). End surfaces are assumed adiabatic; only through-thickness conduction is accounted for.

Reference

Holman, J. P., Heat Transfer, 7th ed., McGraw-Hill, 1990, pp. 27–29.

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Frequently asked questions

Far-face temperature for a multi-layer plane wall given known face 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.