George Oguntala - School of Electrical Engineering, Faculty of Engineering and Informatics, University of Bradford, Bradford, West Yorkshire, UK.
Raed Abd-Alhameed - School of Electrical Engineering, Faculty of Engineering and Informatics, University of Bradford, Bradford, West Yorkshire, UK.
Gbeminiyi Sobamowo - Department of Mechanical Engineering, Faculty of Engineering, University of Lagos, Akoka, Lagos, Nigeria.
Isa Danjuma - School of Electrical Engineering, Faculty of Engineering and Informatics, University of Bradford, Bradford, West Yorkshire, UK.

In this study, we analysed the thermal performance, thermal stability and optimum design analyses of a longitudinal, rectangular fin with temperature-dependent, thermal properties and internal heat generation under multi-boiling heat transfer using Haar wavelet collocation method. The effects of the key and controlling parameters on the thermal performance of the fin are investigated. The thermal stability criteria and optimum design parameter were established. From the investigation, the study reveals that the performance of the fin is enhanced as the boiling condition parameter or the exponent decreases. It is also established that the optimum fin length (at which Q/ζ reaches a maximum value) increases as the non-linear thermal conductivity term β, increases. Furthermore, the study shows that the optimum value of M can be obtained based on the value of the non-linear term. The computational results obtained in this study were compared with established numerical solutions and is found to be in good agreement with the standard numerical solutions.

Haar wavelet collocation method, Multi-boiling heat transfer, Longitudinal fin, Thermal stability, Optimum design, Temperature-dependent thermal conductivity, Internal heat generation