Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-23T21:53:57.117Z Has data issue: false hasContentIssue false
  • English
  • Français

Problems of heat, mass and charge transfer with discontinuous solutions

Published online by Cambridge University Press:  04 March 2011

V. F. DEMCHENKO ,
V. O. PAVLYK ,
U. DILTHEY ,
I. V. KRIVTSUN ,
O. B. LISNYI  and
V. V. NAKVASYUK
V. F. DEMCHENKO
Affiliation:
E.O. Paton Electric Welding Institute, National Academy of Sciences of Ukraine11 Bozhenko Str., 03680, Kyiv, Ukraine
V. O. PAVLYK
Affiliation:
ISF - Welding and Joining Institute, RWTH Aachen UniversityPontstrasse 49, D-52062 Aachen, Germany email: [email protected]
U. DILTHEY
Affiliation:
ISF - Welding and Joining Institute, RWTH Aachen UniversityPontstrasse 49, D-52062 Aachen, Germany email: [email protected]
I. V. KRIVTSUN
Affiliation:
E.O. Paton Electric Welding Institute, National Academy of Sciences of Ukraine11 Bozhenko Str., 03680, Kyiv, Ukraine
O. B. LISNYI
Affiliation:
E.O. Paton Electric Welding Institute, National Academy of Sciences of Ukraine11 Bozhenko Str., 03680, Kyiv, Ukraine
V. V. NAKVASYUK
Affiliation:
E.O. Paton Electric Welding Institute, National Academy of Sciences of Ukraine11 Bozhenko Str., 03680, Kyiv, Ukraine
Get access Rights & Permissions [Opens in a new window]

Abstract

Typical problems with solutions characterised by first-kind discontinuities occurring at interfaces of layered inhomogeneous media are considered with respect to second-order differential equations in partial derivatives. Direct, inverse and mixed types of solution discontinuities are considered. Presented are generalised formulations of problems under consideration, having discontinuous solutions and allowing a uniform description of the processes of heat, mass and charge transfer in multilayer media. Homogeneous difference schemes built on the basis of generalised solutions, which are illustrated by test problems with analytical solutions, are given.

Keywords

heat, mass and charge transferdiscontinuous solutionsfinite-difference schemesgeneralized solutions
Type
Papers
Information
European Journal of Applied Mathematics , Volume 22 , Issue 4 , August 2011 , pp. 365 - 380
Copyright
Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Carslaw, H. S. & Jager, J. C. (1959) Conduction of Heat in Solids, Oxford University Press, UK.Google Scholar
[2]Moulton, D. & Pelesko, J. A. (2008) Thermal boundary conditions: An asymptotic analysis. Heat Mass Transfer 44 (7), 795–803.CrossRefGoogle Scholar
[3]Dinulescu, H. A. & Pfender, E. (1980) Analysis of the anode boundary layer of high intensity arcs. J. Appl. Phys. 51, 3149–3157.CrossRefGoogle Scholar
[4]Krivtsun, I. V. (2001) Model of evaporation of metal in arc, laser and laser-arc welding. Paton Weld. J. 3, 2–9.Google Scholar
[5]Horway, G. (1965) Modified Stefan's problem. Inzh.-Fiz. Zh. 8 (6), 12–19.Google Scholar
[6]Schwartz, L. (1950 et 1951) Théorie Des Distributions, T. 1 et 2, Paris, Hermann.Google Scholar
[7]Samarsky, A. A. (1977) Theory of Differential Schemes, Moscow, Nauka.Google Scholar
[8]Makhnenko, V. I. (1975) Calculation of diffusion in two-phase medium with moving phase interface. Avtom. Svarka 12, 1–6.Google Scholar
[9]Nomirovskii, D. A. (2004) Generalized solvability of parabolic systems with nonhomogeneous transmission conditions of nonideal contact type. Differ. Equ. (Differentsial'nye uravneniya) 40 (10), 1390–1399.Google Scholar