[Conduction]

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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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Inputs

Inner radius r₀ (m)

Layer 1 thickness (m)

Layer 1 conductivity (W/m·K)

Layer 2 thickness (m)

Layer 2 conductivity (W/m·K)

Layer 3 thickness (0=off) (m)

Layer 3 conductivity (W/m·K)

Layer 4 thickness (0=off) (m)

Layer 4 conductivity (W/m·K)

Cylinder length (m)

Inner wall temperature (°C)

Heat flow (W)

Results

Outer wall temp.

—°C

Total resistance

—K/W

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Results are indicative

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 $T_{n}$ of a concentric multi-layer cylinder, given the inner-wall temperature $T_{0}$ 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 $r_{i - 1}$ and outer radius $r_{i} = r_{i - 1} + t_{i}$ :

R_{i} = \frac{ln ( r _{i} / r _{i - 1} )}{2 π L _{c} k _{i}}

Series Resistance

R_{total} = i = 1 \sum N R_{i}

Outer Temperature

T_{n} = T_{0} - Q \cdot R_{total}

where positive $Q$ denotes heat flowing outward ( $T_{0} > T_{n}$ ). 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.