Critical radius for radial heat conduction: A necessary criterion but not always sufficient

The use of critical radius as a necessary criterion for radial heat conduction in thermal insulation systems was discussed. For decreasing the heat gain or heat loss in radial thermal insulation system, the critical radius serves as a necessary condition, but it is not sufficient. The crossover radius is utilized to address the design issues of such thermal systems. The crossover radius is the radius greater than the critical radius such that the heat transfer with the corresponding amount of insulating material is equal to that of the bare thermal system.