The derivation of the critical radius of insulation for a cylinder and a sphere with a variable heat transfer coefficient and including the effect of radiation is presented in a generalized dimensionless form. It is shown that in some of the cases the results can be put in a compact form. Criteria for the existence of a critical radius have been developed. This eliminates the search for a solution to simultaneous equations using an iterative procedure when a critical condition does not exist. Unlike the cylinder, the sphere exhibits a minimum in heat transfer before the usual maximum for a specific range of parameters. This phenomenon is due entirely to the inclusion of radiation.
EckertE. R. G. and DrakeR. M., Heat and Mass Transfer (Kogakusha Co. Ltd., Tokyo, 1959), p. 39.
2.
BejanA., Heat Transfer (Wiley, New York, 1993), pp. 42, 288, 396, 575.
3.
SparrowE. M., ‘Reexamination and correction of the critical radius for radial heat conduction’, AIChE Journal, 16 (1970), 149.
4.
SimmonsL. D., ‘Critical thickness of insulation accounting for variable convection coefficient and radiation loss’, J. Heat Transfer, 98 (1976), 150–152.
