A form of MHD universal equations of unsteady incompressible fluid flow with variable elctroconductivity on heated moving plate

Boricic, Zoran; Nikodijević, Dragiša; Milenković, Dragica; Stamenković, Živojin

doi:10.2298/tam0501065b

Cited by 5 publications

(5 citation statements)

References 7 publications

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“…For further studying of the problem in this paper, the ideas of generalized similarity method have been used [8][9][10] which is extended in papers [11,12]. This method leads to the so-called universal equation of the described problem, and its universal solution enable drawing general conclusions on the development of the boundary layer, and can be also used for calculations concerning particular cases of the boundary layer.…”

Section: Generalized Similarity Methodsmentioning

confidence: 99%

Unsteady plane MHD boundary layer flow of a fluid of variable electrical conductivity

Boricic¹,

Nikodijević²,

Milenkovic³

et al. 2010

THERM SCI

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This paper is devoted to the analysis of unsteady plane laminar magnetohydrodynamic boundary layer flow of incompressible and variable electrical conductivity fluid. The present magnetic field is homogeneous and perpendicular to the body surface. Outer electric filed is neglected and magnetic Reynolds number is significantly lower then one i. e. considered problem is in inductionless approximation. Free stream velocity is an arbitrary differentiable function. Fluid electrical conductivity is decreasing function of velocity ratio. In order to solve the described problem multi-parametric (generalized similarity) method is used and so-called universal equations are obtained. Obtained universal equations are solved numerically in appropriate approximation and a part of obtained results is given in the form of figures and corresponding conclusions.past an arbitrary shape surface has attracted the interest of many researchers in view of its important applications in many engineering problems.Recently the problem of magneto-hydrodynamic (MHD) flow over surfaces has become more important due to the possibility of applications in areas like nuclear fusion, chemical engineering, medicine, and high-speed, noiseless printing. Problem of MHD flow in the vicinity of plate has been studied intensively by a number of investigators [3][4][5][6][7]. Most of previous investigations were concerned with studies of the steady flow of fluid whose electrical conductivity is constant.The subject of the present research is to give an analytic investigation to the problem of unsteady laminar MHD boundary layer flow of a viscous incompressible fluid. The external magnetic field is homogeneous and perpendicular to the body. The fluid which forms the boundary layer is incompressible and its electrical conductivity is variable and can be assumed in the following form:

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Section: Generalized Similarity Methodsmentioning

confidence: 99%

Unsteady plane MHD boundary layer flow of a fluid of variable electrical conductivity

Boricic¹,

Nikodijević²,

Milenkovic³

et al. 2010

THERM SCI

Self Cite

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show abstract

“…Obtained partial differential equations can be solved for every particular case using modern numerical methods and computer. In this paper, quite different approach is used based on ideas in papers (Skadov, 1963;Loicijanski, 1965;Saljnikov, 1978;Busmarin et al, 1974), which is extended in papers (Boricic et al, 2005;Obrovic et al, 2005;Nikodijevic et al, 2009). Essence of this approach is in introducing adequate transformations and sets of parameters in starting equations, which transform the equations system and corresponding boundary conditions into form unique for all particular problems and this form is considered as universal.…”

Section: Universal Equationsmentioning

confidence: 99%

Generalized similarity method in unsteady two-dimensional MHD boundary layer on the body which temperature varies with time

Nikodijević¹,

Boricic²,

Milenković³

et al. 2010

Int. J. Eng. Sci. Tech

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In this paper, the multiparametric method known as generalized similarity method is used to solve the problem of unsteady temperature two-dimensional MHD laminar boundary layer of incompressible fluid. It is assumed that outer magnetic field induction is function only from longitudinal coordinate. Magnetic field acts perpendicular to the body on which boundary layer forms. Body temperature varies with time. Further, electric field is neglected and value of magnetic Reynolds number is significantly less then one i.e. problem is considered in induction-less approximation. According to temperature differences under 50 o C physical properties of fluid are constant. 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. In this paper, quite different approach is used. In the first place new variables are introduced and then similarity parameters which enable transformation of equations into universal form. Obtained universal equations and corresponding boundary conditions do not contain explicit characteristics of particular problems. Based on obtained universal equations, approximated universal differential equations of described MHD boundary layer flow problem are derived. Aproximated universal equations do not depend on the particular problems.

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“…Equation ( 9) does not depend from equation (10) and it can be solved independently. Solution of equation ( 9) is used for solving of equation (10).…”

Section: Mathematical Modelmentioning

confidence: 99%

“…Obtained partial differential equations ( 1), ( 2), (3) can be solved for every particular case using modern numerical methods and computer. In this paper, quite different approach is used based on ideas in papers [6,7,8] which is extended in papers [9,10,11]. Essence of this approach is in introducing adequate transformations and sets of parameters in starting equations of laminar two-dimensional unsteady temperature MHD boundary layer of incompressible fluid, which transform the equations system and corresponding boundary conditions into form unique for all particular problems and this form is considered as universal.…”

Section: Universal Equationsmentioning

confidence: 99%

Universal equations of unsteady two-dimensional MHD boundary layer whose temperature varies with time

Boricic

Nikodijević

Obrović

et al. 2009

Theor appl mech (Belgr)

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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 filed is neglected and magnetic Reynolds number is significantly lower then one i.e. considered problem is in inductionless 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

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A form of MHD universal equations of unsteady incompressible fluid flow with variable elctroconductivity on heated moving plate

Cited by 5 publications

References 7 publications

Unsteady plane MHD boundary layer flow of a fluid of variable electrical conductivity

Unsteady plane MHD boundary layer flow of a fluid of variable electrical conductivity

Generalized similarity method in unsteady two-dimensional MHD boundary layer on the body which temperature varies with time

Universal equations of unsteady two-dimensional MHD boundary layer whose temperature varies with time

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