Sinc collocation approach through thermal analysis of porous fin with magnetic field

The extended surfaces, known as fins, are of great importance in various industrial applications in electric/electronic devices, heat exchangers, power plants, etc. Recently, it is demonstrated that porous fins, as a potential candidate for traditional fins, may significantly enhance the thermal performance of such equipment. To this end, in the current research work, based upon the Maxwell equations, Rosseland diffusion approximation and Darcy formulation, the impacts of magnetic field, radiation heat transfer and porous medium are incorporated in the problem formulation which is inherently a nonlinear differential equation. It is well-known that particle base methods are accurate enough in dealing with thermal analysis of mechanical structures, however, calculation of interactions between atoms as well as discretization of space and time in these approaches is a time-consuming task leading to high computational costs when the dimension of the structure is sizeable. In order to study such problems, other efficient numerical/asymptotic approaches are preferred. However, it may be also considered as a new introduced approach of particle base methods. In this paper, the Sinc collocation method (SCM) is successfully employed to study the distribution of temperature as well as temperature gradient in porous fin subject to a uniform magnetic field. SCM discretizes the nonlinear boundary value problem to a system of nonlinear equations. The obtained numerical solutions are compared with other existing methods in the literature. The results can support the capability and accuracy of the proposed method.