A problem of a micropolar magnetohydrodynamic boundary-layer flow

2000 ◽  
Vol 77 (10) ◽  
pp. 813-827 ◽  
Author(s):  
M A Ezzat ◽  
M I Othman ◽  
K A Helmy
Keyword(s):  
Boundary Layer ◽  
Laplace Transform ◽  
Boundary Layer Flow ◽  
Plane Surface ◽  
Broad Class ◽  
Vertical Plane ◽  
Transverse Magnetic ◽  
Infinite Plane ◽  
Parallel Plates ◽  
Layer Flow

The matrix exponential method, which constitutes the basis of the state space approach of modern control theory, is applied to the nondimensional equations of unsteady boundary layer flow past an infinite plane surface with a pressure gradient. Laplace-transform techniques are used. The results obtained can be used to generate solutions in the Laplace-transform domain to a broad class of problems in magneto-hydrodynamic boundary layer flow. The technique is applied to the problem of an electrically conducting micropolar fluid flowing past a vertical plane surface in the presence of a transverse magnetic field and to the problem of flow between two parallel plates. A numerical method is employed for the inversion of the Laplace-transforms. Numerical results are given and illustrated graphically for both problems.PACS No.: 47.65+a

Boundary-layer flow of a micropolar fluid on a continuous moving or fixed surface

2006 ◽  
Vol 84 (5) ◽  
pp. 399-410 ◽  
Author(s):  
Anuar Ishak ◽  
Roslinda Nazar ◽  
Ioan Pop
Keyword(s):  
Boundary Layer ◽  
Skin Friction ◽  
Boundary Layer Flow ◽  
Micropolar Fluid ◽  
Plane Surface ◽  
Velocity Ratio ◽  
Skin Friction Coefficient ◽  
Keller Box Method ◽  
Moving Plane ◽  
Layer Flow

The present paper deals with the analysis of boundary-layer flow of a micropolar fluid on a fixed or continuous moving plane surface. Both parallel and reverse moving surfaces to the free stream are considered. The resulting system of nonlinear ordinary differential equations is solved numerically using the Keller-box method. Numerical results are obtained for skin friction coefficient, local Nusselt number, velocity, angular velocity, and temperature profiles. The results indicate that the effect of the material parameter on skin friction and heat transfer depends on the velocity ratio of the plate and the fluid.PACS No.: 47.15.Cb

The boundary layer due to rectilinear vortex

1978 ◽  
Vol 359 (1697) ◽  
pp. 167-188 ◽  
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Inviscid Flow ◽  
Plane Wall ◽  
Infinite Plane ◽  
Unsteady Boundary Layer ◽  
Short Period ◽  
Time Dependent Problem ◽  
Layer Flow ◽  
Layer Solution

The boundary layer created by the motion of a single rectilinear vortex filament above an infinite plane wall is considered. In a frame of reference which moves uniformly with the vortex the inviscid motion is steady; however, the possibility of a corresponding steady boundary-layer solution can be ruled out and it is concluded that the boundary-layer flow is inherently unsteady for all time. To investigate the nature of the unsteady boundary-layer flow, a time-dependent problem, corresponding to the sudden insertion of the plane wall at time t = 0, is considered; separation in the boundary layer is found to take place in a short period of time and the solution shows possibly explosive features as t increases. It is conjectured that an eventual eruption of the boundary-layer flow is to be expected along with a major modification of the inviscid flow. The theory compares favourably with experiments on the flow induced near the ground by trailing aircraft vortices.

A Note on Oscillatory Couette Flow in a Rotating System

1994 ◽  
Vol 61 (1) ◽  
pp. 208-209 ◽  
Author(s):  
R. Ganapathy
Keyword(s):  
Boundary Layer ◽  
Couette Flow ◽  
Relative Motion ◽  
Boundary Layer Flow ◽  
Alternative Solution ◽  
Parallel Plates ◽  
Rotating System ◽  
Rotating Systems ◽  
Ekman Boundary Layer ◽  
Layer Flow

An alternative solution is proposed for the oscillatory Ekman boundary layer flow bounded by two parallel plates in relative motion (Muzumder, 1991). The solution brings out among other things, the phenomenon of resonance which is of importance in rotating systems.

Effect of Magnetic Field on the Unsteady Boundary Layer Flows Induced by an Impulsive Motion of a Plane Surface

2020 ◽  
Vol 75 (4) ◽  
pp. 343-355
Author(s):  
S. Dholey
Keyword(s):  
Magnetic Field ◽  
Differential Equation ◽  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Plane Surface ◽  
Stokes Problem ◽  
Physical Parameters ◽  
Boundary Layer Flows ◽  
New Type ◽  
Layer Flow

AbstractThe unsteady laminar boundary layer flow of an electrically conducting viscous fluid near an impulsively started flat plate of infinite extent is considered, with a view to examine the influence of transverse magnetic field fixed to the fluid. A new type of similarity transformation is proposed, which renews the governing partial differential equation into a linear ordinary differential equation with four physical parameters, viz. unsteadiness parameter β, magnetic parameter M, and the velocity indices (p, q). The analytic solution of this equation has been found in terms of a first kind confluent hypergeometric function for some specific parameter regimes. This solution shows the structure of a new type of boundary layer flow that includes the solution of the first Stokes problem as a special case. For non-zero values of (p, q), there is a definite range of p (either −∞ < p < 2q or 2q < p < ∞ according to β < or > 0) for which this flow problem will be valid. This analysis reveals an important relation $(p\beta+{M^{2}}=q\beta)$ at which separation appears inside the layer and has been detected as the separation threshold of the problem. Indeed, this relation gives us the critical value of one when the others are known. Flow separation inside the layer is delayed with an increasing value of q but cannot be completely removed whatever is the value of q (>0). The present analysis ensures that the reverse flow can be suppressed by the use of a proper amount of magnetic field M depending upon the values of p, q, and β. The obtained result provides insight into the stability of the boundary layer flows.

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