广义矩阵法在求任意曲线坐标系的导热方程的应用

APPLICATION OF GENERALIZED MATRIX METHOD FOR DERIVATION OF HEAT CONDUCTION EQUATIONS IN AN ARBITRARY COORDINATES

本文基于非笛卡儿张量分析的广义矩阵法,导出了推求任意曲线坐标的导热方程的张量表达式,并将它转化为矩阵式,借以得出正交曲线坐标系及非正交曲线坐标系的导热方程,并用示例加以说明.实践证明,这种方法是准确、简便的,从而拓宽了非笛卡儿张量的应用领域.

By means of the generalized matrix method based on non-Cartesian tensor analysis, in an arbitrary coordinates the heat conduction equations are derived. And according to the boundary geometric figure of a given problem it proves to be simple and convenient. To find the analytic expressions in a selected 3-D space system by this method. An example of deriving basic formulae of heat conduction equations in an arbitrary coordinates system is presented. This method can be further used to derive the expressions of other mathematical models, etc. Keywords non-Cartesian tensor arbitrary curvilinear coordinates heat conduction equations generalized matrix method