Approximate analytic solutions are useful when exact analytic solutions are too difficultor impossible to obtain or when the numerical solution of the problem can not be justified. Furthermore, an analytic solution pr...Approximate analytic solutions are useful when exact analytic solutions are too difficultor impossible to obtain or when the numerical solution of the problem can not be justified. Furthermore, an analytic solution provides a better insight to the physical significanceof various parameters effecting a given problem than a purely nuxnerical solution. Therefore, various approximate methods of analysis have been developed to solve heat-conduction problems, such as the integral method, the Ritz method, the Galerkin method, and so on.However, high accurate approximate solution in large scale is hardly obtained. In this paper a new approximate analytic method for transient heat--conduction problems in an infiniteplane wall was preseoted on the. basis of matrix theory and spline interpolation theory. Casesunder different boundary and initial conditions or heat generation can be conveniently dealtwith in a uniform way with this method. Compared with the exact solutions, this methodcan warrant high accuracy.展开更多
基金Project(52225404)supported by the National Natural Science Foundation for the Distinguished Young Scholars of ChinaProject(BJJWZYJH01201911413037)supported by the Beijing Outstanding Young Scientist Program,China+1 种基金Project(202206430036)supported by the China Scholarship CouncilProject(2022YJSLJ02)supported by the Fundamental Research Funds for the Central Universities,China。
文摘Approximate analytic solutions are useful when exact analytic solutions are too difficultor impossible to obtain or when the numerical solution of the problem can not be justified. Furthermore, an analytic solution provides a better insight to the physical significanceof various parameters effecting a given problem than a purely nuxnerical solution. Therefore, various approximate methods of analysis have been developed to solve heat-conduction problems, such as the integral method, the Ritz method, the Galerkin method, and so on.However, high accurate approximate solution in large scale is hardly obtained. In this paper a new approximate analytic method for transient heat--conduction problems in an infiniteplane wall was preseoted on the. basis of matrix theory and spline interpolation theory. Casesunder different boundary and initial conditions or heat generation can be conveniently dealtwith in a uniform way with this method. Compared with the exact solutions, this methodcan warrant high accuracy.
