IIChE NITR

There are instances when the addition of insulation to the outside surfaces of cylindrical or spherical walls (geometries which have non-constant cross-sectional areas) does not reduce the heat loss.   In cylindrical and spherical coordinates, the addition of insulation also increases the outer surface , which decreases the convection resistance at the outer surface. Moreover, in some cases, a decrease in the convection resistance due to the increase in surface area can be more important than an increase in conduction resistance due to thicker insulation. As a result, the total resistance may actually decrease resulting in increased heat flow. The thickness up to which heat flow increases and after which heat flow decreases is termed as critical thickness . In the case of cylinders and spheres, it is called critical radius . The critical radius of insulation depends on the thermal conductivity of the insulation k and the external convection heat transfer coefficient h.