Editing Thermal insulation (section)

===Insulation of cylinders===
[[File:Plasma sprayed ceramic coating applied onto a part of an automotive exhaust system copy.jpg|thumb|right|A ceramic coating on the exhaust system of a car lowers the surface temperature.]]

For insulated cylinders, a ''critical radius'' blanket must be reached. Before the critical radius is reached, any added insulation increases heat transfer.<ref>{{cite web|url=http://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node123.html|title=17.2 Combined Conduction and Convection|website=web.mit.edu|access-date=29 April 2018|url-status=live|archive-url=https://web.archive.org/web/20171019222743/http://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node123.html|archive-date=19 October 2017}}</ref> The convective thermal resistance is inversely proportional to the surface area and therefore the radius of the cylinder, while the [[Thermal conduction#Cylindrical shells|thermal resistance of a cylindrical shell]] (the insulation layer) depends on the ratio between outside and inside radius, not on the radius itself. If the outside radius of a cylinder is increased by applying insulation, a fixed amount of conductive resistance (equal to 2×π×k×L(Tin-Tout)/ln(Rout/Rin)) is added. However, at the same time, the convective resistance is reduced. This implies that adding insulation below a certain '''critical radius''' actually increases the heat transfer. For insulated cylinders, the critical radius is given by the equation<ref>Bergman, Lavine, Incropera and DeWitt, ''Introduction to Heat Transfer'' (sixth edition), Wiley, 2011.</ref>

:<math>{r_\text{critical}} = {k \over h}</math>

This equation shows that the critical radius depends only on the [[heat transfer coefficient]] and the [[Thermal conductivity and resistivity|thermal conductivity]] of the insulation. If the radius of the insulated cylinder is smaller than the critical radius for insulation, the addition of any amount of insulation will increase heat transfer.