Pipe insulation

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Pipe Insulation is thermal insulation used to prevent heat loss and gain from pipes, to save energy and improve effectiveness of thermal systems.

The benefits include, in addition to reducing costs and environmental impacts of energy consumption:^[1]

• Reducing or eliminating condensation on cold pipes.
• Protection from dangerous pipe temperatures.
• In domestic hot-water systems, the water temperature at the point of use can be closer to the temperature at the water heater, and wait time for hot water can be reduced ^[2].
• Control of noise.
• Reduction of unwanted heat gain to air-conditioned spaces.

[edit] Heat flow calculations and R-value

The heat flow through pipe insulation with outer diameter <math>d_o</math> and inner diameter (of the insulation--equal to outer diameter of the pipe) <math>d_i</math> is

<math> Q=\frac{ \ell 2 \pi k \Delta T}{ \ln(d_o / d_i)}</math>

where <math>\ell</math> is the length of the pipe, <math>k</math> is the thermal conductivity of the insulation material, and <math>\Delta T</math> is the temperature difference between the inner and outer walls of the insulation. If the insulation is sufficiently thick and has sufficiently low thermal conductivity, the outside surface of the insulation will be close to the ambient temperature, and <math>\Delta T</math> may be approximated as the temperature difference between the temperature of the fluid in the pipe and the ambient temperature.

The relationship between heat loss and temperature difference may be may be expressed in terms of a thermal resistance <math>R_{th}</math>, defined by <math>Q = \Delta T/R_{th}</math>. For pipe insulation,

<math> R_{th}=\frac{1}{ \ell 2 \pi k} \ln(\frac{d_o}{ d_i})</math>.

For building envelope insulation in rectangular forms, R-value <math> R_v</math> is the thermal resistance of a unit-area (1 square foot or 1 square meter) section of insulation, such that

<math> R_v = R_{th} \cdot A</math>

where A is the surface area over which the thermal resistance is calculated. Applying this to pipe insulation is not straightforward, however, because the surface area used could be either the area of the inner cylinder

<math> A_i = \ell \pi d_i</math>

or the area of the outer cylinder

<math> A_o = \ell \pi d_o</math>.

The resulting R-values would be

<math> R_{v,i}=\frac{d_i}{2 k} \ln(\frac{d_o}{ d_i})</math>

or

<math> R_{v,o}=\frac{d_o}{2 k} \ln(\frac{d_o}{ d_i})</math>

R-values of pipe insulation are not covered by the US FTC R-value rule. R-values quoted by manufacturers normalize the thermal resistance to the outer diameter of the insulation ^[3], i.e., they provide

<math> R_{v,o}=\frac{d_o}{2 k} \ln(\frac{d_o}{ d_i})</math>.

This allows them to quote a higher number, but it is less useful for comparing different insulations because, for a given pipe that needs insulation, <math>A_i</math> is constant independent of the insulation chosen, whereas <math>A_o</math> depends on the insulation chosen.

From the manufacturer's quoted R-value <math> R_{v,o}</math>, on can calculate thermal resistance

<math> R_{th}=R_{v,o}/A = \frac{R_{v,o}}{\pi d_o \ell}</math>

and heat flow

<math> Q = \Delta T/R_{th}=\frac{\Delta T \pi d_o \ell}{R_{v,o}}</math>

Note that doing any of these calculations in imperial units (BTU, feet, hours, inches and fahrenheit) is hazardous because there is often a mix of inches and feet used, even within the units for one variable (such as k).

The North American Insulation Manufacturers Association provides software for calculating heat loss with and without pipe insulation.

[edit] References