Introduction of a new crossover radius for radial heat conduction, Part I: cylindrical systems

Use of the critical radius for radial heat conduction in thermal insulation systems has been widely reported in the literature. When it is desirable to increase heat dissipation, this critical radius can be used in a definitive manner to maximize the heat dissipation. However, if it is desirable to decrease heat gain or heat loss, the critical radius only serves as a necessary condition, but it is not sufficient. To address design of such thermal systems, a new crossover radius is introduced. A crossover radius is a radius greater than the critical radius and is defined such that the heat transfer with the corresponding amount of insulating material is equal to that of the bare thermal system. In order to make effective use of insulation (to prevent heat loss or heat gain) the outside radius of the insulated pipe must correspond to values greater than the crossover radius. In Part I cylindrical systems are considered while spherical systems are considered in Part II.