The stochastic formulation of the Stephan’s roblem in hyperbolic representation
https://doi.org/10.30724/1998-9903-2019-21-3-4-116-126
Abstract
The presented work offers the stochastic description of the Stephan’s problem in hyperbolic representation equation. This description is based on the generalized Fоккеr-Plank-Kolmogorov equation. The basic thesis of this work is that the determined equalizations and their decisions are the average values of stochastic Stephan’s task model. This work considers the problem of phase transition front deformation. The research is performed using the entered position of stability on dispersion of decisions for average values. The conclusion of the study is that Markov’s diffusion coefficient leads to a significant distortion of the originall y flat front of the phase boundary.
About the Authors
E. M. KartashovRussian Federation
Eduard M. Kartashov.
Moscow.
I. A. Soloviev
Russian Federation
Igor A. Solovyev.
Moscow.
References
1. J. Stefan. Under probleme derteorie der warmeletung// Sietzber. Wien. Akad. Mat. Naturw. 1889. Bd. 98. 11a. P. 616–634.
2. Kartashov E.M. Analytical methods in the theory of thermal conductivity of solids. M.: Higher school, 2001. 540
3. S. Kartashov, E. M., Kudinov, V. A., Analytical theory of heat conductivity and thermoelasticity applied. Samara: Publishing house SGTU. 2010. 652 p.
4. Kartashov E.M., Solovyev I.A. Stochastic approach to the problem of Stefan. News of wounds. Energy. 2017. No. 5. From 134–143.
5. I. Solovyev, H.D Dolicanin-Jekic. Stochastic model. M.: 2014. P. 134.
6. Zhirnov I. D.V. D.V.Kotoban , A.V. Gusarov. Evaporation-induced gas-phase flows at selective laser melting. International Journal of Heat and Mass Transfer. Volume 113, October 2017. P. 975–983.
7. Huaxia YAO. Long-Term Study of Lake Evaporation and Evaluation of Seven Estimation Methods: Results from Dickie Lake, South-Central Ontario, Canada. Earth & Environmental Sciences. Vol.1 No.2, August, 2009, PP. 59–77.
8. C. Meier, R.W. Penny, Y. Zou, J.S. Gibbs, A.J. Hart, Thermophysical phenomena in metal additive manufacturing by selective laser melting: Fundamentals, modeling, simulation and experimentation. arXiv:1709.09510v1 [physics.app-ph] 4 Sep 2017.
9. M.J. Matthews, G. Guss, S.A. Khairallah, A. Rubenchik, A.T. Anderson, P.J. Depond, W.E. King, Denudation of metal powder layers in laser powder bed fusion processes. Acta Mater. 114, 2016. P. 33–42.
10. S. Roscani, E.S. Marcus Two equivalent Stefan's problems for the time fractional diffusion equation. Fractional Calculus and Applied Analysis. 2013. Т. 16. № 4. С. 802–815.
Review
For citations:
Kartashov E.M., Soloviev I.A. The stochastic formulation of the Stephan’s roblem in hyperbolic representation. Power engineering: research, equipment, technology. 2019;21(3-4):116-126. https://doi.org/10.30724/1998-9903-2019-21-3-4-116-126