Similar solutions of the boundary layer equations for a slender body of revolution in the presence of a positive pressure gradient

1972 ◽  
Vol 5 (1) ◽  
pp. 161-163
Author(s):  
L. M. Kolesnikova ◽  
L. G. Frolov ◽  
V. N. Shmanenkov
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Slender Body ◽  
Positive Pressure ◽  
Body Of Revolution ◽  
Boundary Layer Equations ◽  
Similar Solutions ◽  
Slender Body Of Revolution

scholarly journals Similarity Solutions of the MHD Boundary Layer Flow Past a Constant Wedge within Porous Media

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Ramesh B. Kudenatti ◽  
Shreenivas R. Kirsur ◽  
Achala L. Nargund ◽  
N. M. Bujurke
Keyword(s):  
Boundary Layer ◽  
Porous Medium ◽  
Pressure Gradient ◽  
Adverse Pressure Gradient ◽  
Velocity Profiles ◽  
Similarity Solutions ◽  
Positive Pressure ◽  
Boundary Layer Equations ◽  
Similarity Transformations ◽  
Wide Range

The two-dimensional magnetohydrodynamic flow of a viscous fluid over a constant wedge immersed in a porous medium is studied. The flow is induced by suction/injection and also by the mainstream flow that is assumed to vary in a power-law manner with coordinate distance along the boundary. The governing nonlinear boundary layer equations have been transformed into a third-order nonlinear Falkner-Skan equation through similarity transformations. This equation has been solved analytically for a wide range of parameters involved in the study. Various results for the dimensionless velocity profiles and skin frictions are discussed for the pressure gradient parameter, Hartmann number, permeability parameter, and suction/injection. A far-field asymptotic solution is also obtained which has revealed oscillatory velocity profiles when the flow has an adverse pressure gradient. The results show that, for the positive pressure gradient and mass transfer parameters, the thickness of the boundary layer becomes thin and the flow is directed entirely towards the wedge surface whereas for negative values the solutions have very different characters. Also it is found that MHD effects on the boundary layer are exactly the same as the porous medium in which both reduce the boundary layer thickness.

The behaviour of similar solutions in a compressible boundary layer

1968 ◽  
Vol 34 (2) ◽  
pp. 337-342 ◽  
Author(s):  
J. B. Mcleod ◽  
J. Serrin
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Compressible Boundary Layer ◽  
Rigorous Proof ◽  
Velocity Overshoot ◽  
Boundary Layer Equations ◽  
Mathematical Properties ◽  
Model Fluid ◽  
Similar Solutions

This paper discusses the mathematical properties of similar solutions of the boundary-layer equations in a compressible model fluid, under assumptions first introduced by Stewartson and by Li & Nagamatsu. Assuming a favourable pressure gradient and that backflow is not present, our results include (among other things) a rigorous proof that velocity overshoot occurs in the boundary layer if the wall is heated, and that this is true whether or not suction, blowing or slipping occurs at the wall; while, conversely, velocity overshoot does not occur when the wall is cooled and the amount of slipping at the wall is suitably restricted.

Further Solution of the Corner Boundary-Layer Equations

1973 ◽  
Vol 24 (3) ◽  
pp. 219-226 ◽  
Author(s):  
M Zamir
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Existence And Uniqueness ◽  
Boundary Layer Equation ◽  
Critical Value ◽  
Numerical Accuracy ◽  
Boundary Layer Equations ◽  
The Past ◽  
Similar Solutions ◽  
High Degree

SummarySimilar solutions of an equation governing the flow in the plane of symmetry of a corner boundary layer with favourable pressure gradient are extended to a “critical” value of the pressure gradient for which no solution could be found previously. It is shown that the failure to achieve this result in the past was due to the “singular” nature of this solution rather than to its non-existence as one was tempted to suspect. The existence and uniqueness of this crucial solution are demonstrated and the solution itself is obtained to a high degree of numerical accuracy. Criticism of the theory on which this corner boundary-layer equation is based is discussed in an Appendix.

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