The critical and crossover radii on transient heating

For cylindrical and spherical heat transfer systems, it is imperative that the radius of thermal material is matched to the associated heat transfer objective. For systems that intend to maximize heat transfer, the critical radius defines the optimal radius for a specific scenario. For systems that intend to minimize heat transfer, the crossover radius defines the radius required to achieve an equal heat transfer rate to the un-insulated scenario; with any further increase in radii resulting in a monotonic reduction in the associated heat transfer rate. The critical radius is well defined for the steady-state scenario. In recent literature, the steady-state crossover radius has also received attention; however, the literature does not provide clarity for the transient scenario. This work overcomes this identified limitation by quantifying the crossover and critical radii of a transient cylindrical system, allowing novel conclusions to be drawn between the steady-state and transient scenarios. In particular, this work identifies that the cycle-average heat transfer rate can stabilize to a quasi-static value in response to transient heating.