Annular fin exposed to two-dimensional dual oscillating constraints

A two-dimensional analytical model for an annular fin exposed to dual oscillating constraints was developed. The effects of the relevant parameters—including dual frequencies, fin parameter, dual amplitudes, and phase difference—are presented and analysed. Consistent with previous studies, the current work demonstrates that high constraint frequencies lead to a barrier to heat transfer along the fin. Furthermore, regarding the phenomenon of impeded heat transfer, the results clearly show that larger constraint distortions further delay the heat transfer. Additional results reveal several findings. Under equal boundary constraints, an asymmetric temperature distribution in the annular fin is obtained due to the fin parameter effect. Moreover, a larger fin parameter—resulting from higher convection coefficient, lower thermal conductivity, or smaller fin thickness—reduces the absolute temperature level along the fin. The results highlight the critical effect of delayed thermal response under the frequency, and varying peripheral constraints. Momentary adiabatic surfaces form in the longitudinal and peripheral directions, and heat transfer oscillates between two extrema during a full period. Most temperature values converge within the smaller amplitude range. Under a phase difference of $$\pi$$ , the temperature curves do not intersect at a single point, as occurs in a straight fin.