The thermal performance of longitudinal radiative–convective fins with rectangular, trapezoidal, and concave parabolic profiles was analyzed by the homotopy perturbation method (HPM). The governing equation of the problem was obtained by establishing the energy balance for a longitudinal element on the longitudinal radiative–convective fin. In addition, thermal conductivity, convective heat transfer coefficient, and surface emissivity were assumed to change with temperature. Given its nonlinear nature, the governing equation was solved relying on the HPM. Validating the results from this method with those of the differential transform method, a good agreement was achieved between the two. In parametric studies, the fins were compared in terms of heat transfer rate, effectiveness, and efficiency. Further, the effects of changes in thermal conductivity, emissivity, convection–conduction parameter, and the radiation–conduction parameter were also investigated on the fin performance. The results were suggestive of the potentials of HPM as a reliable tool for solving nonlinear equations such as the energy equation for radiative–convective fins without compromising accuracy or speed. Further, the concave parabolic fin was found to have a higher heat transfer rate, efficiency, and effectiveness than its rectangular and trapezoidal counterparts.

通过同伦摄动法（HPM）分析了具有矩形，梯形和凹抛物线轮廓的纵向辐射对流散热片的热性能。通过建立纵向辐射-对流散热片上纵向元件的能量平衡，可以得出问题的控制方程。另外，还假设导热系数，对流换热系数和表面发射率会随温度变化。鉴于其非线性特性，依靠HPM求解了控制方程。用微分变换法验证了该方法的结果，两者之间取得了很好的一致性。在参数研究中，比较了散热片的传热速率，有效性和效率。进一步，还研究了热导率，发射率，对流传导参数和辐射传导参数的变化对散热片性能的影响。结果表明，HPM作为解决非线性方程式（如辐射对流散热片的能量方程式）而不影响精度或速度的可靠工具的潜力。此外，发现凹形抛物线翅片比矩形和梯形翅片具有更高的传热速率，效率和效率。结果表明，HPM作为解决非线性方程式（如辐射对流散热片的能量方程式）而不影响精度或速度的可靠工具的潜力。此外，发现凹形抛物线翅片比矩形和梯形翅片具有更高的传热速率，效率和效率。结果表明，HPM作为解决非线性方程式（如辐射对流散热片的能量方程式）而不影响精度或速度的可靠工具的潜力。此外，发现凹形抛物线形翅片比其矩形和梯形翅片具有更高的传热速率，效率和效率。