A quasi-analytical solution of homogeneous extended surfaces heat diffusion equation

IF 3.4 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY International Journal of Mechanical and Materials Engineering Pub Date : 2017-08-16 DOI:10.1186/s40712-017-0084-4

Ernest Léontin Lemoubou, Hervé Thierry Tagne Kamdem

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Abstract

In this study, a quasi-analytical solution for longitudinal fin and pin heat conduction problems is investigated.

The differential transform method, which is based on the Taylor series expansion, is adapted for the development of the solution. The proposed differential transform solution uses a set of mathematical operations to transform the heat conduction equation together with the fin profile in order to yield a closeform series of homogeneous extended surface heat diffusion equation.

The application of the proposed differential transform method solution to longitudinal fins of rectangular and triangular profiles and pins of cylindrical and conical profiles heat conduction problems showed an excellent agreement on both fin temperature and efficiencies when compared to exact results. Therefore, the proposed differential transform method can be useful for optimal design of practical extended surfaces with suitable profile for temperature response.

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齐次扩展表面热扩散方程的拟解析解

本文研究了纵翅和纵针热传导问题的拟解析解。采用基于泰勒级数展开的微分变换方法求解。所提出的微分变换解使用一组数学运算将热传导方程与翅片剖面进行变换，从而得到一系列紧密的齐次扩展表面热扩散方程。将所提出的微分变换方法应用于矩形和三角形型纵鳍和圆柱形和锥形型销钉的热传导问题，结果表明，与精确结果相比，该方法在翅片温度和效率上都有很好的一致性。因此，所提出的微分变换方法可用于具有适合温度响应的实际扩展曲面的优化设计。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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