Hybrid Spline Difference Method for Heat Transfer and Thermal Stresses in Annular Fins

Abstract

This study proposes a high-accuracy numerical method—the hybrid spline difference method—which is as simple as the finite-difference method, and discusses its feasibility by analyzing the internal temperature and thermal stresses of rectangular annular fins changing the heat transfer coefficient. The hybrid spline difference method can simplify the complex computational process of the traditional spline method, and obtain the high accuracy of O(ξ ⁴) regardless of whether the equation and boundary conditions have a first differential term. As compared with other numerical methods, the numerical accuracy of temperature and thermal stresses obtained by internal arithmetic is improved greatly considering the effects of heat transfer, convection, and radiation. The results prove that the proposed method can the replace traditional cubic spline method and finite-difference method directly, as a new simple and high-accuracy numerical method.

Acknowledgments

Thanks for the subsidy of the Outlay NSC 100-2628-E-035-009-MY2 given by the National Science Council, the Republic of China, to help us finish this special research successfully.

Notes

*: A recurrence relation, cannot be expressed directly by adjacent spline function.