Pipe insulation heat loss
Heat loss, surface temperature and yearly cost for bare and insulated pipes — with a table of insulation thicknesses.
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How this calculator works
Heat flows out through the insulation by conduction, ln(Do/Dp)/(2πk) per metre, and leaves the surface by convection and radiation. The calculator solves for the surface temperature at which these balance. Natural convection uses the Churchill-Chu correlation for a horizontal cylinder, wind uses Churchill-Bernstein (combined with natural convection), and radiation depends on the emissivity of the outer jacket.
The example is a 2" steam line (60.3 mm) at 150 °C, 100 m long, in still air at 20 °C. Bare, it loses about 430 W/m. With 50 mm of mineral wool (k = 0.045) under aluminium it loses 33 W/m, with a surface at 35 °C — saving about USD 11,000 a year at USD 10/GJ.
Limits: steady state; pipe wall and inside film resistance neglected; conductivity constant at the mean temperature (use the maker's value); bare pipe emissivity 0.9. Compare with ASTM C680 software for design. References: Perry's §5 (heat transfer); Incropera and DeWitt (correlations); ASTM C680 and VDI 2055 (method basis); Branan (energy conservation).