Thermal Performance of a Convective Functionally Graded Fin Using Fractional Non-Fourier Heat Conduction

Abstract

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.