A direct solution of temperature field and physical quantities for the nonlinear porous fin problem
International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Article publication date: 6 February 2017
Abstract
Purpose
The purpose of this study is to target the solution of nonlinear porous fin problem. In contrast to the various complicated numerical or analytical approximate procedures existing in the literature used to approximate the temperature field over a porous fin, this study outlines a direct method based on series expansion of the temperature in the vicinity of the mounted surface, eventually requiring no numerical treatment at all to resolve the temperature field.
Design/methodology/approach
This study uses a direct method based on series expansion of the temperature in the vicinity of the mounted surface, eventually requiring no numerical treatment at all to resolve the temperature field.
Findings
Explicit closed-form formulae for the fin tip temperature as well as for the heat transfer rate, hence for the fin efficiency, which are functions of the porosity parameter and Biot number, are provided. The thresholds and the convergence regions regarding the physical parameters of the resulting approximations are easy to determine from the residual formula.
Originality/value
The novelty of the method is that the accuracy of the solution is controllable and can be gained up to any significant digit of desire by increasing the number of terms in the series solution.
Keywords
Citation
Turkyilmazoglu, M. (2017), "A direct solution of temperature field and physical quantities for the nonlinear porous fin problem", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 27 No. 2, pp. 516-529. https://doi.org/10.1108/HFF-11-2015-0475
Publisher
:Emerald Publishing Limited
Copyright © 2017, Emerald Publishing Limited