### Thermal Performance and Optimum Design Analysis of Fin with Variable Thermal Conductivity Using Double Decomposition Method

#### Abstract

In this paper, thermal performance and optimum design analysis of straight fin with variable thermal conductivity is carried out using double decomposition method. The developed heat transfer models are used to analyze the thermal performance, establish the optimum thermal design parameters and also, investigate the effects of thermo-geometric parameters and thermal conductivity (non-linear) parameters on the temperature distribution, heat transfer and thermal performance of the longitudinal rectangular fin. From the results, it shows that the fin temperature distribution, the total heat transfer, the fin effectiveness, and the fin efficiency are significantly affected by the thermo-geometric and thermal parameters of the fin. The analysis revealed that the operational parameters must be carefully chosen to ensure that the fin retains its primary purpose of removing heat from the primary surface. The results obtained in this analysis provides platform for improvement in the design of fin in heat transfer equipment.

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