Analysis of Conductive, Convective and Radiative Heat Transfer in Longitudinal Fins of Variable Profiles

Abstract

The heat transfer enhancement by conduction, convection and radiation is still a topic of considerable attention in a number of areas and applications such as fin design despite the fact that numerous studies already exist in literature. In this study, the non-linear steady state heat equation is numerically solved for various fin surface profiles using the combined convection and the radiation modeling approach. The numerical solution is obtained using the Matlab® bvp4c package that is based on the shooting method. The results of this study indicate that the energy transfer by radiation is generally small compared to the transfers by conduction and convection but in situations where the fin base temperature is high, the radiation contribution can be significant and should be included when modeling the extended surface problems. However, it is acceptable to exclude the radiation energy transfer in some applications particularly when the fin thickness is small. The concept of Diminished Radiation Length (DRL) is introduced in this paper, which determines the length of the fin from the base at which the heat dissipation by radiation drops down to 0.4 Watts or less. The results presented in this paper can help the fin designers to select the appropriate fin parameters and decide whether the radiative heat loss is small enough to be neglected from the analysis.
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