scholarly journals Boundary layer of the dissociated gas flow over a porous wall under the conditions of equilibrium dissociation

2005 ◽  
Vol 32 (2) ◽  
pp. 165-190 ◽  
Author(s):  
Branko Obrovic ◽  
Dragisa Nikodijevic ◽  
Slobodan Savic
Keyword(s):  
Boundary Layer ◽  
Gas Flow ◽  
Air Flow ◽  
Porous Wall ◽  
The Body ◽  
Boundary Layer Equations ◽  
Equilibrium Dissociation ◽  
Dissociated Air

This paper studies the ideally dissociated air flow in the boundary layer when the contour of the body within the fluid is porous. By means of adequate transformations, the governing boundary layer equations of the problem are brought to a general form. The obtained equations are numerically solved in a three-parametric localized approximation. Based on the obtained solutions, very important conclusions about behavior of certain boundary layer physical values and characteristics have been drawn.

scholarly journals Ionized gas boundary layer on a porous wall of the body within the electroconductive fluid

2004 ◽  
Vol 31 (1) ◽  
pp. 47-71 ◽  
Author(s):  
Branko Obrovic ◽  
Slobodan Savic
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Gas Flow ◽  
Numerical Solutions ◽  
Porous Wall ◽  
The Body ◽  
Generalized Equations ◽  
Ionized Gas ◽  
Boundary Layer Equations ◽  
Longitudinal Coordinate

This paper investigates the ionized gas flow in the boundary layer, when the contour of the body within the fluid is porous. Ionized gas is exposed to the influence of the outer magnetic field induction Bm = Bm(x), which is perpendicular to the contour of the body within the fluid. It is presumed that the electroconductivity of the ionized gas is a function only of the longitudinal coordinate, i.e. ? = ?(x). By means of adequate transformations, the governing boundary layer equations are brought to a generalized form. The obtained generalized equations are solved in a four-parameter localized approximation. Based on the obtained numerical solutions, diagrams of important physical values and characteristics of the boundary layer have been made. Conclusions have also been drawn.

scholarly journals Investigation of the ionized gas flow adjacent to porous wall in the case when electroconductivity is a function of the longitudinal velocity gradient

2010 ◽  
Vol 14 (1) ◽  
pp. 89-102
Author(s):  
Slobodan Savic ◽  
Branko Obrovic ◽  
Dusan Gordic ◽  
Sasa Jovanovic
Keyword(s):  
Boundary Layer ◽  
Electric Fields ◽  
Velocity Gradient ◽  
Gas Flow ◽  
Numerical Solutions ◽  
Longitudinal Velocity ◽  
Porous Wall ◽  
The Body ◽  
Ionized Gas ◽  
Boundary Layer Equations

This paper studies the laminar boundary layer on a body of an arbitrary shape when the ionized gas flow is planar and steady and the wall of the body within the fluid porous. The outer magnetic field is perpendicular to the fluid flow. The inner magnetic and outer electric fields are neglected. The ionized gas electroconductivity is assumed to be a function of the longitudinal velocity gradient. Using transformations, the governing boundary layer equations are brought to a general mathematical model. Based on the obtained numerical solutions in the tabular forms, the behavior of important non-dimensional quantities and characteristics of the boundary layer is graphically presented. General conclusions about the influence of certain parameters on distribution of the physical quantities in the boundary layer are drawn.

scholarly journals The influence of the magnetic field on the ionized gas flow adjacent to the porous wall

2010 ◽  
Vol 14 (suppl.) ◽  
pp. 183-196
Author(s):  
Slobodan Savic ◽  
Branko Obrovic ◽  
Milan Despotovic ◽  
Dusan Gordic
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Gas Flow ◽  
Great Influence ◽  
Porous Wall ◽  
Boundary Layer Separation ◽  
The Body ◽  
Ionized Gas ◽  
Friction Function ◽  
The Magnetic Field

This paper studies the influence of the magnetic field on the planar laminar steady flow of the ionized gas in the boundary layer. The present outer magnetic field is homogenous and perpendicular to the body within the fluid. The gas of the same physical characteristics as the gas in the main flow is injected (ejected) through the contour of the body. The governing boundary layer equations for different forms of the electroconductivity variation law are transformed, brought to a generalized form and solved numerically in a four-parametric approximation. It has been determined that the magnetic field, through the magnetic parameter, has a great influence on certain quantities and characteristics of the boundary layer. It has also been shown that this parameter has an especially significant influence on the non-dimensional friction function, and hence the boundary layer separation point.

scholarly journals Analysis of the axisymmetrical ionized gas boundary layer adjacent to porous contour of the body of revolution

2016 ◽  
Vol 20 (2) ◽  
pp. 529-540
Author(s):  
Slobodan Savic ◽  
Branko Obrovic ◽  
Nebojsa Hristov
Keyword(s):  
Boundary Layer ◽  
Gas Flow ◽  
Mhd Flow ◽  
The Body ◽  
Generalized Solutions ◽  
Body Of Revolution ◽  
Ionized Gas ◽  
Bodies Of Revolution ◽  
Boundary Layer Equations ◽  
Longitudinal Coordinate

The ionized gas flow in the boundary layer on bodies of revolution with porous contour is studied in this paper. The gas electroconductivity is assumed to be a function of the longitudinal coordinate x. The problem is solved using Saljnikov's version of the general similarity method. This paper is an extension of Saljnikov?s generalized solutions and their application to a particular case of magnetohydrodynamic (MHD) flow. Generalized boundary layer equations have been numerically solved in a four-parametric localized approximation and characteristics of some physical quantities in the boundary layer has been studied.

scholarly journals The influence of variation of electroconductivity on ionized gas flow in the boundary layer along a porous wall

2006 ◽  
Vol 33 (2) ◽  
pp. 149-179 ◽  
Author(s):  
Slobodan Savic ◽  
Branko Obrovic
Keyword(s):  
Boundary Layer ◽  
Gas Flow ◽  
Longitudinal Velocity ◽  
Porous Wall ◽  
Outer Edge ◽  
Ionized Gas ◽  
Boundary Layer Equations ◽  
Characteristic Boundary ◽  
Longitudinal Variable ◽  
Similarity Method

This paper investigates ionized gas flow in the boundary layer when its electroconductivity is varied. The flow is planar and the contour is porous. At first, it is assumed that the ionized gas electroconductivity ? depends only on the longitudinal variable. Then we adopt that it is a function of the ratio of the longitudinal velocity and the velocity at the outer edge of the boundary layer. For both electroconductivity variation laws, by application of the general similarity method, the governing boundary layer equations are brought to a generalized form and numerically solved in a four-parametric three times localized approximation. Based on many tabular solutions, we have shown diagrams of the most important nondimensional values and characteristic boundary layer functions for both of the assumed laws. Finally, some conclusions about influence of certain physical values on ionized gas flow in the boundary layer have been drawn. .

Second-order effects in free convection

1974 ◽  
Vol 62 (4) ◽  
pp. 793-809 ◽  
Author(s):  
I. C. Walton
Keyword(s):  
Boundary Layer ◽  
Free Convection ◽  
Equations Of State ◽  
Asymptotic Series ◽  
Inviscid Flow ◽  
Second Order ◽  
The Body ◽  
Order Effects ◽  
Boundary Layer Equations ◽  
Second Order Effects

The equations of conservation of momentum, energy and mass together with the equations of state are examined for free convection from a vertical paraboloid. A transformation due to Saville & Churchill is applied to the first- and second-order boundary-layer equations, which are then solved using series about the stagnation point, using asymptotic series far up the body and in between by a method due to Merk. The second-order outer inviscid flow is given in terms of infinite integrals as a solution of Laplace's equation in paraboloidal co-ordinates.Eight second-order effects are distinguished, depending on longitudinal and transverse curvatures, the displacement flow, heat flux into the boundary layer and the variation of density, viscosity, thermometric conductivity and the coefficient of expansion with temperature. Expressions for the skin friction, heat-transfer coefficient and various flux thicknesses are obtained and a comparison of the second-order effects is made.

On the nature of unsteady three-dimensional laminar boundary-layer separation

1978 ◽  
Vol 88 (2) ◽  
pp. 241-258 ◽  
Author(s):  
James C. Williams
Keyword(s):  
Boundary Layer ◽  
Laminar Boundary Layer ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Boundary Layer Separation ◽  
The Body ◽  
Two Dimensional ◽  
Boundary Layer Equations ◽  
Unsteady Separation ◽  
Similar Solutions

Solutions have been obtained for a family of unsteady three-dimensional boundary-layer flows which approach separation as a result of the imposed pressure gradient. These solutions have been obtained in a co-ordinate system which is moving with a constant velocity relative to the body-fixed co-ordinate system. The flows studied are those which are steady in the moving co-ordinate system. The boundary-layer solutions have been obtained in the moving co-ordinate system using the technique of semi-similar solutions. The behaviour of the solutions as separation is approached has been used to infer the physical characteristics of unsteady three-dimensional separation.In the numerical solutions of the three-dimensional unsteady laminar boundary-layer equations, subject to an imposed pressure distribution, the approach to separation is characterized by a rapid increase in the number of iterations required to obtain converged solutions at each station and a corresponding rapid increase in the component of velocity normal to the body surface. The solutions obtained indicate that separation is best observed in a co-ordinate system moving with separation where streamlines turn to form an envelope which is the separation line, as in steady three-dimensional flow, and that this process occurs within the boundary layer (away from the wall) as in the unsteady two-dimensional case. This description of three-dimensional unsteady separation is a generalization of the two-dimensional (Moore-Rott-Sears) model for unsteady separation.

Influence of Favourable Pressure Gradient on the Heat Transfer in Boundary Layer

2010 ◽  
Author(s):  
Alexey Yu. Sakhnov ◽  
Eduard P. Volchkov ◽  
Maxem S. Makarov
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Pressure Gradient ◽  
Cross Flow ◽  
Porous Wall ◽  
Skin Friction Coefficient ◽  
Outer Edge ◽  
Boundary Layer Equations ◽  
Accelerated Flow ◽  
Asymptotic Suction

In the present paper, we analyze, both numerically and analytically, the influence a favourable pressure gradient has on the characteristics of dynamic boundary layer. It is shown that at a certain value of the pressure gradient asymptotic conditions can be reached in laminar boundary layer, with the skin-friction coefficient value being independent of the Reynolds number, like in the case of asymptotic suction of boundary layer through the porous wall. Some analogy between the two types of flow can be traced: in both cases, namely, at porous suction and in the boundary layer of an accelerated flow, a cross flow is generated, directed from the outer edge of the boundary layer toward the wall. For the conditions of the two types, an approximate analytical solution to the boundary-layer equations has been obtained. It is shown that in problems with first- and second-kind boundary conditions the favourable pressure gradient exerts an influence on the heat-transfer characteristics.

scholarly journals Statistical theory of turbulence V-Effect of turbulence on boundary layer theoretical discussion of relationship between scale of turbulence and critical resistance of spheres

1936 ◽  
Vol 156 (888) ◽  
pp. 307-317 ◽  
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Statistical Theory ◽  
Laminar Boundary Layer ◽  
External Disturbance ◽  
The Body ◽  
Theoretical Discussion ◽  
Boundary Layer Equations ◽  
Critical Resistance ◽  
Statistical Theory Of Turbulence

The breakdown of the laminar boundary layer at the surface of a solid body owing to turbulence in the fluid through which the body is moving has not yet been subjected to any theoretical analysis. The boundary layer equations seem to be incapable, at any rate in the form in which they have hitherto been used, of giving a definite value of Reynolds number at which the laminar boundary layer may be expected to become turbulent. When the solid surface is simply a flat plate placed edgewise in the wind the Reynolds number corresponding with the position where the change from laminar to turbulent boundary layer takes place depends on the amount of turbulence present. The boundary layer takes place depends on the amount of turbulence present. The boundary layer equations give a perfectly regular solution (the Blasius rehime) which indicates that in the absence of any external disturbance the regime will continue for an infinite distance down the plate.

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