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.

中文翻译：

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均匀扩展表面热扩散方程的拟解析解

在这项研究中，研究了纵向翅片和销的热传导问题的准解析解。基于泰勒级数展开式的微分变换方法适用于解决方案的开发。所提出的微分变换解决方案使用一组数学运算来将热传导方程式与翅片轮廓一起变换，以产生近似形式的均匀扩展表面热扩散方程式。所提出的差分变换方法解决方案在矩形和三角形轮廓的纵向散热片以及圆柱和圆锥形轮廓的销的导热问题上的应用与精确结果相比，在散热片温度和效率上都显示出极好的一致性。因此，