Temperature distributions along an annular fin exposed to dual constraints of temperature oscillations

The study investigated the effect of temperature oscillation constraints applied to the inner and outer surfaces of an annular fin. The oscillations were characterized by different frequencies and amplitudes and addressed the phase difference between the constraints. The model describing the phenomenon was formulated using complex numbers. The main finding was a degradation in temperature penetration as the forcing frequency increased. The critical role of frequency was clearly demonstrated and was supported by a complete and physically accurate model formulation. The results indicated a form of “residual memory,” or a delayed thermal response of the fin material to the oscillating constraints, a behaviour that was consistently observed throughout the analysis. Additional results showed that increasing the fin parameter reduced the absolute temperature values along the fin. For most of the fin length, the temperatures fell within the range defined by the smaller forcing amplitude. The influence of the inner surface constraint extended over more than half of the fin length, and the asymmetry of the temperature distributions became clearly pronounced when a phase difference of $$\pi $$ was introduced.