Abstract The nonlinear thermal performance of convective and radiative longitudinal cooling fins with temperature-dependent thermal conductivity is studied. For linearly temperature-dependent thermal conductivity, the exact temperature distribution is obtained analytically in an implicit integral form. By converting the resulting integral equation to an algebraic equation, a simpler explicit expression of quadratic polynomials for the temperature excess in the whole convective-radiative fins is derived and the numerical results are compared with the exact one and the previous ones. Additionally, analytical expressions for the temperature change at the fin tip and for the fin efficiency are respectively given in terms of the thermal and geometric parameters of extended surfaces. The accuracy of approximate solution is examined. The influences of nonlinearity and hybrid Biot number on the temperature distribution, the fin-tip temperature change, and the fin efficiency are analyzed.

中文翻译：

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使用积分方程法求解具有温度相关热导率的对流辐射翅片的精确和近似解

摘要 研究了热导率随温度变化的对流和辐射纵向散热片的非线性热性能。对于线性温度相关的热导率，精确的温度分布以隐式积分形式解析获得。通过将得到的积分方程转换为代数方程，推导出了整个对流辐射翅片中温度过剩的二次多项式的更简单的显式表达式，并将数值结果与精确的和以前的结果进行了比较。此外，根据扩展表面的热参数和几何参数分别给出了翅片尖端温度变化和翅片效率的解析表达式。检查近似解的准确性。