Editing Thermal insulation (section)

== Definition ==
{{main|Thermal conductivity}}
Thermal conductivity ''k'' is measured in [[watt]]s-per-meter per [[kelvin]] (W·m<sup>−1</sup>·K<sup>−1</sup> or W/mK). This is because [[heat transfer]], measured as [[Power (physics)|power]], has been found to be (approximately) proportional to 
* difference of temperature <math> \Delta T </math>
* the surface area of [[thermal contact]] <math> A </math>
* the inverse of the thickness of the material <math> d </math>
From this, it follows that the power of heat loss <math> P </math> is given by
<math> P = \frac{k A\, \Delta T }{d} </math>

Thermal conductivity depends on the material and for fluids, its temperature and pressure. For comparison purposes, conductivity under standard conditions (20&nbsp;°C at 1 atm) is commonly used. For some materials, thermal conductivity may also depend upon the direction of heat transfer.
{{See ||List of thermal conductivities}}

The act of insulation is accomplished by encasing an object in material with low thermal conductivity in high thickness. Decreasing the exposed surface area could also lower heat transfer, but this quantity is usually fixed by the geometry of the object to be insulated.

[[Multi-layer insulation]] is used where radiative loss dominates, or when the user is restricted in volume and weight of the insulation (e.g. [[emergency blanket]], [[radiant barrier]])

===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.