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 to 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 the 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 the 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 the aspect ratio of the conical spine extended surface will decrease its efficiency.
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