How this calculator works
Conduction resistance is the temperature difference needed per watt of steady heat flow. It depends on geometry as well as thermal conductivity. Curved shells have changing flow area, so their resistance differs from the plane-wall approximation. The critical radius combines conduction with external convection and identifies maximum heat loss for ideal cylindrical or spherical insulation with constant properties. The conductivity presets are approximate values near 0 C; use a custom value for the relevant temperature and material grade.
Formula
Plate: R = t/(kA). Cylinder: R = ln(ro/ri)/(2 pi k L). Sphere: R = (1/ri - 1/ro)/(4 pi k). Critical radius: k/h for a cylinder; 2k/h for a sphere.
Worked example
A 0.2 m plate with area 2 m² and k = 0.5 W/(m K) has resistance 0.2 K/W. A 1 m long cylinder with radii 1 and e metres and k = 1 has resistance 1/(2 pi) = 0.159155 K/W.
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Frequently asked questions
Is thermal resistance a material property?
No. Conductivity is a material property; resistance also includes size and shape.
Are contact and convection resistances included?
The main result includes conduction only. Add other resistances in series when the same heat rate passes through them.
Can adding insulation increase heat loss?
For a small cylinder or sphere below its critical radius, increasing external area can initially outweigh the added conduction resistance.