A direct solution of temperature field and physical quantities for the nonlinear porous fin problem

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TÜRKYILMAZOĞLU M.

INTERNATIONAL JOURNAL OF NUMERICAL METHODS FOR HEAT & FLUID FLOW, cilt.27, sa.2, ss.516-529, 2017 (SCI-Expanded) identifier identifier

Özet

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.

The solution of nonlinear porous fin problem is targeted in the present paper. 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, we outline 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. As a result of the proposed method, 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. The analytical expressions are very beneficial to the practising engineers in the field. 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. This is approved by testing the method against the exact numerical solutions. The method thus can be safely extended to search for other features of the fin problems involving more challenging nonlinearities owing to complex thermal processes.