Porous fins with temperature-dependent internal heat generation are frequently used to improve performance in a wide range of heat transfer and porous media applications. Thermal analysis of the porous fin fractal model with temperature-dependent heat generation is generated using fractal derivatives and investigated analytically using a novel Maclaurin series method (MSM). Nonlinear temperature distribution in a porous longitudinal fin is produced by the MSM. The porous fin solution is demonstrated using the Sierpinski fractal, which is based on time-dependent heat generation. The effects of the convection parameter, porosity, internal heat production, and generation number parameter on the dimensionless temperature distribution are discussed. MSM results are graphically and tabularly compared to existing solution methods such as HPM, CM, CSCM, LWCM, and GWRM. A comparison study reveals that MSM is a very reliable, accurate, and effective addition in the field of differential equations.

中文翻译：

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随温发热的多孔翅片分形模型及其新解

具有与温度相关的内部热量产生的多孔翅片经常用于提高各种传热和多孔介质应用中的性能。使用分形导数生成具有温度依赖性发热的多孔翅片分形模型的热分析，并使用新的 Maclaurin 级数方法 (MSM) 进行分析研究。多孔纵向翅片中的非线性温度分布由 MSM 产生。多孔翅片解决方案使用基于时间相关发热的谢尔宾斯基分形进行演示。讨论了对流参数、孔隙率、内部产热和生成次数参数对无量纲温度分布的影响。MSM 结果以图形和表格的形式与现有的解决方案方法（如 HPM、CM、CSCM、LWCM 和 GWRM。比较研究表明，MSM 是微分方程领域非常可靠、准确和有效的加法。