A non-Fourier analysis for transmitting heat in fins with internal heat generation

An analysis is presented to evaluate the temperature response in fins with internal heat generation due to heat conduction described by Fourier and non-Fourier laws. For the influence of non-Fourier heat conduction, the analysis is formulated by considering different boundary conditions in order to understand practical fin design problems. The isothermal base or convection-heated base with a convection tip condition for longitudinal and pin fins with uniform thickness are adopted for the analysis. A method for determining the instantaneous fin efficiency for non-Fourier heat conduction is elaborated. The deviation of the temperature response of the non-Fourier model from the Fourier system is systematically studied with several possible design variables, e.g., Fourier, Vernotte numbers, the effect of boundary conditions, and heat generation parameters. The non-Fourier fin efficiency is always lower than the Fourier value for identical design parameters. This decremented value is dependent upon the Vernotte and Fourier numbers. The heat generation in the fin amplifies both the Fourier and non-Fourier fin efficiency.