Abstract The steady-state, one-dimensional, Cartesian coordinate, non-linear ordinary differential energy equation of heat conduction through a conical spine extended surface of a thermal conductivity temperature dependent property that is proposed by an available quadratic function of a computer fitted model of a published experimental data is solved analytically using Kirchhoff's transformation and numerically using the finite volume method. It is assumed that this extended surface is subjected with a Dirichlet and Neumann's boundary conditions of temperature at its base and tip respectively. The combined convection-radiation mode of heat transfer is imposed along the surface of the conical spine. Three case studies are investigated. The thermal conductivity is assumed constant in the first case and it is variable with temperature in the second and third cases, while the radiation heat transfer is neglected in the first and second cases and it is taken into account in the third case. In addition, the effect of the conical spine aspect ratio on its performance is investigated. Aluminum Alloy (A319) material of extended surface is selected. Excellent agreement between the predicted results of the numerical and analytical solution of the present work (case study 1) when compared with the experimental measurement of previously published paper. In addition, excellent agreement between the analytical and numerical results of the present work for all case studies. It shows a maximum error of temperature difference of less than (0.022%). It is found that the dissipated heat due to combined convection-radiation mode from the surface of the conical spine extended surface to the environment is greater than that due to convection mode only. In addition, increasing the value of aspect ratio of the conical spine extended surface will decrease its efficiency.

中文翻译：

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锥脊扩展面对流-辐射复合传热的解析与数值研究

摘要 热传导通过锥形脊柱扩展表面的热传导的稳态、一维、笛卡尔坐标、非线性常微分能量方程具有热导率温度相关属性，该方程由热导率的计算机拟合模型的可用二次函数提出。已发表的实验数据使用基尔霍夫变换进行解析求解，并使用有限体积法进行数值求解。假设这个扩展表面在其底部和尖端分别受到 Dirichlet 和 Neumann 温度边界条件的影响。传热的组合对流-辐射模式沿锥形脊柱表面施加。研究了三个案例研究。在第一种情况下，假设导热系数是恒定的，在第二种和第三种情况下它是随温度变化的，而在第一种和第二种情况下，辐射传热被忽略，而在第三种情况下被考虑在内。此外，研究了锥形脊柱纵横比对其性能的影响。延展面选用铝合金（A319）材料。与先前发表的论文的实验测量相比，当前工作（案例研究 1）的数值解和解析解的预测结果非常吻合。此外，所有案例研究的当前工作的分析结果和数值结果之间具有极好的一致性。它显示的最大温差误差小于 (0.022%)。研究发现，从锥形脊柱扩展表面的表面到环境的对流-辐射组合模式散发的热量大于仅由对流模式引起的散发热量。此外，增大锥脊延伸面的纵横比值会降低其效率。