In this paper, the steady/unsteady heat conduction in the longitudinal fins with variable cross sectional area under the periodic thermal conditions is examined. Three different one-dimensional fins are considered and solved numerically by implicit finite difference method. In the hyperbolic equation the heat wave propagates with the finite speed hence the sharp discontinuities appear at the temperature distributions. In the explicit solution oscillations appear at discontinuity point which is greatly improved at the implicit method. In the present study temperature distributions are obtained for non-Fourier fins with different profiles. The effects of frequency of temperature oscillation, relaxation time and fin cross sectional area are studied on the temperature and location of the discontinuity of temperature. In order to validate the obtained results of the present study, these results have been compared to those of numerical solutions of the non-Fourier fin with constant cross sectional area. This comparison confirms the correctness of the current results.

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