Abstract A one-dimensional convective-radiative fin with temperature-dependent thermal conductivity is studied. The temperature field is determined for a fin in convective and radiative environments but with an insulated tip. A novel method is proposed to find an approximate solution of the temperature field of a conductive-convective-radiative fin. Based on the first-order Taylor's expansion, we transform the nonlinear ordinary differential equation into an algebraic equation. Solving the algebraic equation gives the desired temperature field. The effectiveness of the approximate solution is illustrated by comparing the evaluated results with the previous ones. The influence of convection and radiation heat transfer coefficients on the temperature distribution and the Nusselt number is examined.

中文翻译：

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具有温度相关热导率的传导-对流-辐射翅片的温度分布

摘要 研究了一种热导率随温度变化的一维对流辐射翅片。温度场是针对在对流和辐射环境中但带有绝缘尖端的翅片确定的。提出了一种求解导电-对流-辐射翅片温度场近似解的新方法。基于一阶泰勒展开式，我们将非线性常微分方程转化为代数方程。求解代数方程给出了所需的温度场。通过将评估结果与先前的结果进行比较来说明近似解的有效性。检查对流和辐射传热系数对温度分布和努塞尔数的影响。