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INTERNATIONAL JOURNAL OF MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES Multi-dimensional Mathematical Models of Intensive Steel Quenching for Sphere. Exact and Approximate Solutions

By A Blomkalna, Margarita Buike and Andris Buikis


Abstract—In this paper we develop mathematical models for 3-D and 1-D hyperbolic heat equations and construct their analytical solutions for the determination of the initial heat flux for rectangular and spherical samples. Some solutions of time inverse problems are obtained in closed analytical form. We use approximate analytical solutions on the basis of conservative averaging method and compare the difference between polynomial approximations of exact solutions. Some numerical results are given for a silver ball. The influence of relaxation time on solution, linearity of classical and hyperbolic heat equation, linear and non-linear boundary conditions are investigated. Keywords—Intensive quenching, Hyperbolic Heat equation

Topics: Direct problem, Inverse problem, Exact solution, Fredholm integral equation, Conservative averaging method. C
Year: 2013
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