Geodesic
Universal equations of unsteady two-dimensional MHD boundary layer whose temperature varies with time
Theoretical and applied mechanics, Tome 36 (2009) no. 2, p. 119 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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This paper concerns with unsteady two-dimensional temperature laminar magnetohydrodynamic (MHD) boundary layer of incompressible fluid. It is assumed that induction of outer magnetic field is function of longitudinal coordinate with force lines perpendicular to the body surface on which boundary layer forms. Outer electric field is neglected and magnetic Reynolds number is significantly lower then one i.e. considered problem is in induction-less approximation. Characteristic properties of fluid are constant because velocity of flow is much lower than speed of light and temperature difference is small enough (under 50oC). Introduced assumptions simplify considered problem in sake of mathematical solving, but adopted physical model is interesting from practical point of view, because its relation with large number of technically significant MHD flows. Obtained partial differential equations can be solved with modern numerical methods for every particular problem. Conclusions based on these solutions are related only with specific temperature MHD boundary layer problem. In this paper, quite different approach is used. First new variables are introduced and then sets of similarity parameters which transform equations on the form which don't contain inside and in corresponding boundary conditions characteristics of particular problems and in that sense equations are considered as universal. Obtained universal equations in appropriate approximation can be solved numerically once for all. So-called universal solutions of equations can be used to carry out general conclusions about temperature MHD boundary layer and for calculation of arbitrary particular problems. To calculate any particular problem it is necessary also to solve corresponding momentum integral equation.
DOI : 10.2298/TAM0902119B
Classification : 76D10 80A20
Keywords: MHD, magnetic field, electroconductivity, temperature, similarity parameters, universal equations, Prandtl number, Eckert number. 
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     author = {Zoran Bori\v{c}i\'c and Dragi\v{s}a Nikodijevi\'c and Branko Obrovi\'c and \v{Z}ivojin Stamenkovi\'c},
     title = {Universal equations of unsteady two-dimensional {MHD} boundary layer whose temperature varies with time},
     journal = {Theoretical and applied mechanics},
     pages = {119 },
     year = {2009},
     volume = {36},
     number = {2},
     doi = {10.2298/TAM0902119B},
     zbl = {1265.76021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/TAM0902119B/}
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Zoran Boričić; Dragiša Nikodijević; Branko Obrović; Živojin Stamenković. Universal equations of unsteady two-dimensional MHD boundary layer whose temperature varies with time. Theoretical and applied mechanics, Tome 36 (2009) no. 2, p. 119 . doi: 10.2298/TAM0902119B

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