This article studies a class of fin problems with two nonlinear terms arising from thermal conductivity and convection heat transfer coefficient. A one-dimensional convective straight fin is analysed for exponentially temperature-dependent thermal conductivity and exponentially temperature-dependent heat transfer coefficient. The exact fin temperature excess, heat transfer rate and fin efficiency are obtained and presented graphically. The obtained results show the strong influences of exponent indexes of thermal conductivity and convection transfer coefficient as well as thermogeometric fin parameter on the fin efficiency and heat flow.

中文翻译：

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热导率和传热系数呈指数关系的非线性翅片问题的精确解

本文研究了一类翅片问题，其具有由导热系数和对流传热系数引起的两个非线性项。分析一维对流直翅片的指数温度相关热导率和指数温度相关传热系数。获得准确的翅片温度过量、传热率和翅片效率并以图形方式显示。得到的结果表明，导热系数和对流传递系数的指数指标以及翅片热几何参数对翅片效率和热流的影响很大。