2015-08-27 11:27:23

Low thermal conductivity (k) materials reduce heat fluxes. The smaller the kvalue, the larger the corresponding thermal resistance (R) value. Thermal conductivity is measured in watts-per-meter per kelvin (W·m−1·K−1), represented as k. As the thickness of insulating material increases, the thermal resistance—or R-value—also increases.

For a cylinder, the convective thermal resistance is inversely proportional to the surface area and therefore the radius of the cylinder, while the thermal resistance of a cylindrical shell (the insulation layer) depends on the ratio between outside and inside radius, not on the radius itself. Suppose for example that we double the outside radius of a cylinder by applying insulation. We have added a fixed amount of conductive resistance (equal to ln(2)/(2πkL)) but at the same time we have halved the value of the convective resistance. Because convective resistance tends to infinity when the radius approaches zero, at small enough radiuses the decrease in convective resistance will be larger than the added conductive resistance, resulting in lower total resistance.

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