非均匀变厚度圆盘的定常热传导
Steady Heat Conduction of a Disc with Non-Homogeneity and Variable Thickness
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摘要: 本文采用阶梯折算法,求得了任意非均匀变厚度圆盘定常热传导问题的一般解.并通过算例,对阶梯折算法的误差进行了分析.结果表明,该方法对于求解各类变系数常微分方程是十分有效的.Abstract: In this paper,we use the stepped reduction method suggested by Yeh Kai-yuan in 1965 to obtain the general oslution of steady heat conduction of a disc with nonhomogeneity and variable thickness. Through an illustrative example,the error of Yeh's method is analysed. The result shows that it is effective for solving ordinary differential equation with variable coefficients.
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[1] 叶开沅、许剑云,非均匀变厚度弹性体力学的若干问题的一般解 Ⅰ.在非均匀定常温度场下的非均匀变厚度高速度旋转圆盘的弹塑性应力分析.兰州大学学报(自然科学版).力学专号,1(1979).60-74;力学学报.专号.(1981).78-89. [2] 王竹溪、郭敦仁,《特殊函数概论》,科学出版社,(1979). [3] 竹内洋一郎,《热应力》.科学出版社,(1977). [4] Carslaw,H,S,and J,C,Jaeger,Conduction of Head in Solids,Oxford(1959). -
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