IJMMP (2018) 12-22 © JournalsPub 2018. All Rights Reserved Page 12 International Journal of Manufacturing and Materials Processing Vol. 4: Issue 2 www.journalspub.com Galerkin Method of Weighted Residual to Study on Enhanced Heat Transfer in Cylindrical Micro-Fins Heat Sink Using Artificial Surface Roughness M.G. Sobamowo 1* , K.F. Dukor 1 , G.A. Oguntala 2 1 Department of Mechanical Engineering, University of Lagos, Akoka, Lagos, Nigeria 2 Faculty of Engineering and Informatics, School of Electrical Engineering and Computer Science, University of Bradford, West Yorkshire, United Kingdom ABSTRACT In this paper, a theoretical investigation is carried out on the use of artificial surface roughness for enhanced heat transfer and thermal management of cylindrical micro-fins with artificial surface roughness. The developed thermal models which are solved using Galerkin method of weighted residual, considered variable thermal properties according to linear, exponential and power laws. The approximate analytical solutions are used to carry out parametric studies and to establish the thermal performance enhancement of the rough fins over the existing smooth fins. Following the results of the simulations, it is established that the thermal efficiency of the micro-fin is significantly affected by the geometric ratio, nonlinear thermal conductivity parameter, thermo-geometric parameter and the surface roughness of the micro-fin. The results showed that geometric ratio and the surface roughness of the fin enhance the thermal performance of the micro-fin. The fin efficiency ratio as established in this present study is found to be greater than unity when the rough and the smooth fins are subjected to the same operations with the same geometrical, physical, thermal and material properties. Therefore, enhanced heat transfer and improved thermal management of electronic and thermal systems can be achieved through the use of artificial rough surface heat sink fins. Keywords: artificial surface roughness, convective–radiative environment, enhanced heat transfer, heat sink, improved thermal management, micro-fin *Corresponding Author E-mail: mikegbeminiyiprof@yahoo.com INTRODUCTION The quest and the production of high- performance electronic systems come with inherent thermal challenges. Considering the thermal challenges for the present and the next-generation electronics systems [1], the need for combating the heat generation has been increasing. Effective cooling technology or thermal management of microprocessors in most electronic devices including notebook and computers and in various thermal devices or componens in thermal equiptment has been one of the ultimate goals of the present advanced technology designers in electronics productions and design of thermal systems. To achieve the goals, both active and passive modes of cooling technologies have been deployed. However, the active modes of heat transfer enhancement or augmentation such as fans, blowers, fluid vibration, surface vibration, suction and jet impingement and electrostatic fields have proved not to be economically viable due to their operating costs. As alternative means of thermal cooling, the applications of passive methods such as extended surfaces and treated surfaces have shown to be very effective thermal management technology [2]. As one of the passive modes of the