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### Heat Loss Insulated Pipe Equation and Calculator

Equations and calculator to determine the conductive heat loss through a cylinder with multiple layers that may include a pipe wall insulation.

The temperature gradient within a homogeneous material results in an energy transfer rate within the medium which can be calculated with the following equation

eq. a

The illustration above depicts a single-layer cylindrical wall of a homogeneous material with constant thermal conductivity and uniform inner and outer surface temperatures. At a given radius the area normal to radial heat flow by conduction is 2 Π r L, where L is the cylinder length. Substituting this into (eq. a) and integrating with q constant gives:

eq. 0

or

eq. 1

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From (eq 1) the thermal resistance of the single cylindrical layer is [ ln (r_{2} / r_{1}) ] / 2rkL. For a two-layered cylinder show below the heat transfer rate is,

Conductive Heat Flow = Overall Temperature Difference / Summation of Thermal Resistance's

eq 2

or

eq 3

Where:

k = thermal conductivity (Btu / h · in· °F)

k_{a} = thermal conductivity inner wall (Btu / h · in· °F)

k_{a} = thermal conductivity outer wall (Btu / h · in · °F)

L = length of cylinder and insulation layer (in)

q = conduction (Btu / h · °F)

The following is the original (pre-7/2016) equations and calculator:

ΔT = (T h |

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