To analyze the thermal performance of longitudinal fins made of functionally graded materials, this article studies the transient heat transfer in a longitudinally graded fin with power-law thermal conductivity in a convective ambiance using a fractional heat conduction model. This model has an advantage over the Fourier heat conduction in describing the anomalous heat diffusion and non-Fourier effect, and in avoiding the infinite velocity of heat waves and abrupt change of temperature. For heat shock at the base, instantaneous temperature response in an axially graded fin surrounded by convective fluid is obtained through numerical inversion of the Laplace transform. The effects of non-Fourier parameters such as the fractional order and phase lag of heat flux (relaxation time), and the gradient index of the thermal conductivity on the temperature distribution and fin efficiencies are analyzed and shown graphically. Two definitions of instantaneous fin efficiency are discussed for homogeneous and longitudinally graded fins. The occurrence of heat convection leads to a subdiffusion term, and the temperature change exhibits a significant difference when adopting the fractional-order model and the integer-order model. The obtained results are of great benefit to the design of enhancing the thermal performance of extended surfaces.

为了分析功能梯度材料制成的纵向鳍片的热性能，本文使用分数导热模型研究了对流环境中具有幂律导热率的纵向梯度鳍片的瞬态传热。该模型在描述异常的热扩散和非傅立叶效应方面，以及在避免热波的无限速度和温度的突然变化方面，比傅立叶热传导具有优势。对于基部处的热冲击，通过拉普拉斯变换的数值反演，可以获得由对流流体包围的轴向渐变翅片中的瞬时温度响应。非傅立叶参数的影响，例如热通量的分数阶和相位滞后（松弛时间），并分析了导热系数对温度分布和鳍片效率的梯度指数，并以图形方式显示。对于均质和纵向分级的翅片，讨论了瞬时翅片效率的两种定义。热对流的发生导致了二次扩散项，采用分数阶模型和整数阶模型时，温度变化表现出显着差异。获得的结果对增强延伸表面的热性能的设计非常有益。当采用分数阶模型和整数阶模型时，温度变化表现出显着差异。获得的结果对增强延伸表面的热性能的设计非常有益。当采用分数阶模型和整数阶模型时，温度变化表现出显着差异。获得的结果对于增强延伸表面的热性能的设计非常有用。