The critical radius of insulation in thermal radiation environment

Critical radius of insulation for a circular tube subjected to radiative and convective heat transfer has been studied analytically. It is assumed that condensation or evaporation takes place inside the circular tube such that the bulk fluid temperature inside the tube remains constant. As the fluid is transported from one end to the other, either an increase or decrease of heat transfer is desired depending on the application. The variation of the rate of heat transfer with respect to the variation of insulation thickness is studied. It is found that an critical insulation thickness may exist such that the heat transfer between the fluid and the radiative environment becomes a maximum. For certain special cases, explicit solutions to the critical insulation thickness are obtained.