Inhomogeneous Stefan problems and underwater discharge
40 0
Keywords:
Stefan problem, heat equation, mobile interface condition, underwater discharge.Abstract
Two-phase physical systems with sources and mobile interfaces are modeled by inhomogeneous parabolic problems which are considered as extensions of the classical problem of Stefan. The solutions in linear, cylindrical and spherical geometrical setups are found as a series in orthogonal (Hermite or Laguerre) polynomials. The deviation of the expansion law of the phase with sources from the classical similarity √t is determined. Underwater discharge is considered and explosion rates are plotted.References
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64
Inhomogeneous Stefan problems and underwater discharge Phys. Sci. Technol., Vol. 1 (No. 2), 2014: 56-64
the under-water spark discharge channel as a Stefan
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Mathematical Functions. – New York: Dover, 1972.
[15] Tao L. N., The Stefan problem with arbitrary initial
and boundary conditions // Quart. Appl. – 1978. – Vol.
36. – P. 223-233.
[16] Tkachenko I. M., DeSilva A. W., and Iserte J.
Strongly coupled Coulomb systems, Eds. Kalman G.J. et
al., – New York: Plenum Press, 1998. – P. 583-585.
[17] Adamyan V.M. et al. High Temp. – 1980. – Vol. 18
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[2] Hill J.M. One-dimensional Stefan Problems: an Introduction. – London: Longman,1987.
[3] Wilson D.G., Solomon A.D., Boggs P.T. Moving Boundary Problems. – New York: Academic Press, 1978.
[4] Gol’dman N.L. Inverse Stefan Problems. – Dordrecht:
Kluwer Academic Publishers, – 1997.
[5] Kharin S.N. The analytical solution of the two-phase
Stefan problem with boundary flux condition //
Matematicheskiy zhurnal. – 2014. – Т. 14(1). – P. 55-76.
[6] Adamyan V.M., Gulyi A.G., Pushek N.L., Starchik
P.D., Tkachenko I.M., Shvets I.S. High Temp. – 1980. – Vol. 18 – 186 p.
[7] DeSilva A. W., Katsouros J. D. Strongly coupled Coulomb systems. Eds. G.J. Kalman et al. – New York: Plenum Press, 1998. – P. 313-318.
[8] Adamjan V.M., Tkachenko I.M., et al. Spreading of
64
Inhomogeneous Stefan problems and underwater discharge Phys. Sci. Technol., Vol. 1 (No. 2), 2014: 56-64
the under-water spark discharge channel as a Stefan
problem.Res.Rep (in Russian, unpublished), 1987.
[9] Korobeynikov S.M. et al. Optical study of
prebreakdown cathode processes in deionized water //
Dielectrics and Electrical Insulation. – 2009. – Vol. 16. –
P. 504-508.
[10] Shafer D.et al. Generation of cumulative jets during
underwater explosion of copper wires in the “X-pinch”
configuration // J. Appl. Phys. – 2013. – Vol. 114. – P.
203301.
[11] Mcnaughton, James L. Underwater Pressure Arc
Discharge System for Disinfection of Food and Food
Products. – United States Patent Application:
20090324786. – 2006. – 6 p.
[12] DeWitt H. E., Slattery W. L. Strongly coupled Coulomb systems. Eds. G.J. Kalman et al. – New York: Plenum Press, 1998. – P. 1-7.
[13] Tikhonov A. N., Samarsky A. A., Mathematical
Physics Equations. – Moscow: Nauka, 1977.
[14] Abramowitz M. and Stegun I. A, eds., Handbook of
Mathematical Functions. – New York: Dover, 1972.
[15] Tao L. N., The Stefan problem with arbitrary initial
and boundary conditions // Quart. Appl. – 1978. – Vol.
36. – P. 223-233.
[16] Tkachenko I. M., DeSilva A. W., and Iserte J.
Strongly coupled Coulomb systems, Eds. Kalman G.J. et
al., – New York: Plenum Press, 1998. – P. 583-585.
[17] Adamyan V.M. et al. High Temp. – 1980. – Vol. 18
– 241 p.
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Arkhipov, Y. V., Askaruly, A., Ferrer, J. R., Santybayev, K., & Tkachenko, I. M. (2015). Inhomogeneous Stefan problems and underwater discharge. Physical Sciences and Technology, 1(2). Retrieved from https://phst.kaznu.kz/index.php/journal/article/view/30
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Plasma Physics and Related Technology
