In this article, the variational iteration method (VIM) is used to analyze heat transfer in longitudinal fins of various profiles with temperature dependent thermal conductivity and heat transfer coefficient. In order to show the efficiency of the VIM, the results obtained using the VIM are compared with the previously obtained results using the differential transform method (DTM) and Lie group analysis of a fin problem with the rectangular profile. After establishing confidence in VIM, heat transfer is analyzed to determine the temperature profiles in longitudinal fins of various profiles with power law thermal properties. The temperature distribution is compared between various profiles. The effects of some physical parameters such as the thermo-geometric fin parameter and thermal conductivity gradient on temperature distribution are illustrated.
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Ndlovu et al. (2018) studied this question.
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