Analytical solution of the Stefan problem with account for the ablation and the temperature-disturbance front
An approximate analytical solution of the problem on the heat conduction of an infinite plate has been obtained on the basis of the determination of the temperature-disturbance front and the introduction of additional boundary conditions with account for the movement of the melting front in the case where the melted substance is completely removed (Stefan problem with ablation). A method for construction of additional boundary conditions, which allows one to obtain solutions of the indicated problem for engineering applications in the form of simple algebraic polynomials free of special functions, is proposed. The accuracy of these solutions is determined by the number of approximations, which is not limited in the case where additional boundary conditions are used.
Keywordsintegral methods Stefan problem temperature-disturbance front melting front heat of phase transition;ablation additional boundary conditions
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- 1.T. Goodmen, Application of integral methods in nonlinear problems on nonstationary heat transfer, in: Problems of Heat Transfer, Coll. Sci. Papers [in Russian], Atomizdat, Moscow (1967), pp. 41–96.Google Scholar
- 2.V. A. Kudinov and I. V. Kudinov, Methods of Solving Parabolic and Hyperbolic Heat Conduction Equations [in Russian], Knizhnyi Dom "LIBROKOM," Moscow (2011).Google Scholar
- 3.V. A. Kudinov, É. M. Kartashov, and E. V. Stefanyuk, Technical Thermodynamics and Heat Transfer [in Russian], Izd. Yurait, Moscow (2011).Google Scholar
- 4.V. A. Kudinov and I. V. Kudinov, Mathematical simulation of the processes of heat transfer and phase transformations with allowance for ablation, Inzh.-Fiz. Zh., 84, No. 5, 1065–1074 (2011).Google Scholar
- 5.N. M. Belyaev and A. A. Ryadno, Methods of Nonstationary Heat Conduction [in Russian], Vysshaya Shkola, Moscow (1979).Google Scholar
- 6.Yu. T. Glazunov, Variational Methods [in Russian], Research Center "Regular and Chaotic Dynamics," Inst. of Computer Investigations, Moscow–Izhevsk (2006).Google Scholar