An analytical solution is presented for transient heat conduction in a two-layer composite cylinder subjected to outer-surface convection with a general time-dependent ambient temperature. Using Duhamel’s principle, closed-form series expressions are derived and then specialized to harmonic ambient fluctuations, recovering the classical constant-ambient solution in the zero-frequency limit. A parametric study shows that the ratio of the inner layer conductivity to the conductivity of the outer layer strongly shapes interfacial gradients and mean-temperature evolution, with sensitivity concentrated at small ratios and diminishing when the ratio is larger than 0.1. Increasing Biot number accelerates the heat transfer and approaches the isothermal-surface limit as it becomes extremely large. The geometric aspect ratio is most influential when the inner layer is resistive, and becomes weak for large conductivity ratio, supporting thin-coating approximations. Under harmonic ambient fluctuations, the response rapidly reaches a periodic steady state; higher frequency decreases amplitude and increases phase lag, while larger Biot numbers amplify oscillations and reduce delay. The coupled effects of the aspect ratio and the conductivity ratio govern penetration and phase behavior.
Alassar et al. (Thu,) studied this question.