Transient thermal analysis of longitudinal fins with internal heat generation considering temperature-dependent properties and different fin profiles

The present paper aims to study the transient thermal analysis of longitudinal fins with variable cross section considering internal heat generation. The profile shapes of the fins are considered rectangular, convex, triangular and concave. It is assumed that both thermal conductivity and internal heat generation are as linear functions of temperature. The power-law temperature-dependent model is used to simulate different types of heat transfer such as laminar film boiling, natural convection, nucleate boiling and radiation. The governing equation is derived as a nonlinear partial differential equation (PDE) that is solved using a hybrid approximate technique based on the differential transform method (DTM) and finite difference method (FDM). The results are presented to study the effects of some physical parameters such as fin profile shape, thermal conductivity, convection heat transfer coefficient and internal heat generation. 2014 Elsevier Ltd. All rights reserved. Heat transfer has an important role in various engineering problems. The extended surfaces or fins have a significant role in the enhancement of heat transfer from the surfaces. Fins have some applications in small systems such as electronic components and transistors; and large systems such as industrial heat exchangers. A general review on the extended surfaces is reported by Kraus et al. [1]. Heat transfer analysis of the fins has been conducted by numerous scientists and engineers. A significant assumption made in the analysis of fins is based on the simplification that variation of the temperature in the lateral direction is negligible. It means that the temperature at any cross section of the fin is constant. This assumption simplifies the governing equation of the fins since it not only converts the mathematical formulation for steady state from partial differential equation (PDE) to ordinary differential equation (ODE), so it can be obtained an analytical solution of the problem for a number of cases. Most of the scientific and engineering phenomena such as heat transfer problems are naturally nonlinear. Usually some assumptions are used to transform the nonlinear problems to linear cases.

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