Analytical solution of Fourier and non-Fourier heat transfer in longitudinal fin with internal heat generation and periodic boundary condition

In this paper, the analytical solution of Fourier and non-Fourier model of heat transfer in longitudinal fin in presence of internal heat generation has been studied under periodic boundary condition. The whole analysis is given in dimensionless form. These two mathematical models have been solved analytically, using Laplace transform technique. Temperature distribution in longitudinal fin is measured using residual theorem in complex plane for the inverse Laplace transform technique. Thermal wave nature is appeared for small value of Fo. The longitudinal fin temperature is evaluated for different value of parameters with respect to space coordinate. The effect of variability of different parameters on temperature distribution in fin is studied in detailed. It has been observed that the cooling process is faster in non-Fourier model in comparison to Fourier model.