Symmetrical Laminar Channel Flow With Wall Suction

1976 ◽  
Vol 98 (3) ◽  
pp. 469-474 ◽  
Author(s):  
B. K. Gupta ◽  
E. K. Levy
Keyword(s):  
Velocity Profile ◽  
Channel Flow ◽  
Similarity Solutions ◽  
Inlet Velocity ◽  
Boundary Layer Equations ◽  
Wide Range ◽  
Laminar Channel Flow ◽  
Dimensional Boundary ◽  
Steady Laminar ◽  
Good Agreement

Entrance region solutions of the two-dimensional boundary layer equations are presented in terms of a convergent power series for steady, laminar, incompressible channel flow with uniform mass suction at the walls. The entrance solutions obtained using both uniform and parabolic velocity profiles at the inlet to the channel are compared to the solutions obtained from the similarity equations for a wide range of non-dimensional suction velocities (0 ≤ Rew ≤ 30). With a parabolic inlet velocity profile, the flow does not become fully developed for Rew > 7, except right at the downstream end of the channel (x = L). The similarity solutions are in good agreement with the entrance solutions over a reasonable length of the channel only for very small values of Rew. With a uniform inlet velocity profile, the flow does not become fully developed in the range 7 < Rew < 13, except right at x = L. In this case, the similarity equations should not be used to predict overall axial pressure variations except for very large values of Rew.

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.

A Fast Approximate Solution of the Laminar Boundary-Layer Equations

1986 ◽  
Vol 108 (2) ◽  
pp. 200-207 ◽  
Author(s):  
Sei-ichi Iida ◽  
Akira Fujimoto
Keyword(s):  
Boundary Layer ◽  
Velocity Profile ◽  
Computational Time ◽  
Computational Techniques ◽  
Boundary Layer Flows ◽  
Boundary Layer Equations ◽  
Laminar Boundary Layers ◽  
Layer Characteristic ◽  
Comparison Of The Results ◽  
Steady Laminar

A new approximate method of calculating steady laminar boundary-layers is presented. This method is based on the mutual relationships between boundary-layer characteristic quantities. The governing equations are efficiently solved without assuming a specific velocity profile. Moreover, a method of estimating the velocity profile using the characteristic quantities is also proposed. Comparison of the results obtained for a wide variety of applications to boundary-layer flows with separations with exact solutions indicates that the present method enables one to obtain solutions with sufficient accuracy and shorter computational time when compared with existing computational techniques.

Heat Transfer in a Laminar Channel Flow Generated by Injection Through Porous Walls

2007 ◽  
Vol 129 (8) ◽  
pp. 1048-1057 ◽  
Author(s):  
Clarisse Fournier ◽  
Marc Michard ◽  
Françoise Bataille
Keyword(s):  
Channel Flow ◽  
Numerical Solutions ◽  
Scaling Law ◽  
Similarity Solutions ◽  
Temperature Profiles ◽  
Governing Equations ◽  
Temperature Boundary ◽  
Laminar Channel Flow ◽  
Porous Walls ◽  
Uniform Fluid

Steady state similarity solutions are computed to determine the temperature profiles in a laminar channel flow driven by uniform fluid injection at one or two porous walls. The temperature boundary conditions are non-symmetric. The numerical solution of the governing equations permit to analyze the influence of the governing parameters, the Reynolds and Péclet numbers. For both geometries, we deduce a scaling law for the boundary layer thickness as a function of the Péclet number. We also compare the numerical solutions with asymptotic expansions in the limit of large Péclet numbers. Finally, for non-symmetric injection, we derive from the computed temperature profile a relationship between the Nusselt and Péclet numbers.

Flow resistance of ice-covered streams

1984 ◽  
Vol 11 (4) ◽  
pp. 815-823 ◽  
Author(s):  
S. P. Chee ◽  
M. R. I. Haggag
Keyword(s):  
Velocity Profile ◽  
Channel Flow ◽  
Flow Resistance ◽  
Ice Cover ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Cross Sectional ◽  
Roughness Elements ◽  
Mixing Length Theory ◽  
Good Agreement

This paper deals with the underlying theory of the hydraulics of channel flow with a buoyant boundary as an ice cover. It commences by developing the velocity distribution in two-dimensional covered channel flow using the Reynolds form of the Navier–Stokes equation in conjunction with the Prandtl – Von Karman mixing length theory. Central to the theory is the division of the channel into two subsections. From the developed velocity profile, the functional relationship for the division surface is obtained. Finally, the composite roughness of the channel is derived.Experimental verification of the developed theory was conducted in laboratory flumes. Seven cross-sectional shapes were utilized. Ice covers were simulated with polyethylene plastic pellets as well as floating plywood boards with roughness elements attached to the underside. Velocity profile and composite roughness measurements made in these flumes were in good agreement with the theoretical equations. The composite roughness relationship derived from the theory is very comprehensive, as it takes into account not only the varying rugosities of the channel and its floating boundary but also the shape of the cross section. Key words: composite roughness, ice cover, flow resistance, velocity profile, buoyant boundary, covered channel.

A New Approach for the Derivation of the Similarity Equation of the 2-D Unsteady Boundary Layer Equations

2012 ◽  
Author(s):  
Md. Abdus Sattar
Keyword(s):  
Boundary Layer ◽  
Numerical Solutions ◽  
Similarity Solutions ◽  
Length Scale ◽  
Local Similarity ◽  
Unsteady Boundary Layer ◽  
Similarity Equation ◽  
Boundary Layer Equations ◽  
Dimensional Boundary ◽  
The One

A local similarity equation for the hydrodynamic 2-D unsteady boundary layer equations has been derived based on a time dependent length scale initially introduced by the author in solving several unsteady one-dimensional boundary layer problems. Similarity conditions for the potential flow velocity distribution are also derived. This derivation shows that local similarity solutions exist only when the potential velocity is inversely proportional to a power of the length scale mentioned above and is directly proportional to a power of the length measured along the boundary. For a particular case of a flat plate the derived similarity equation exactly corresponds to the one obtained by Ma and Hui[1]. Numerical solutions to the above similarity equation are also obtained and displayed graphically.

Laminar Flow in a Porous Tube With Suction

1975 ◽  
Vol 97 (1) ◽  
pp. 66-71 ◽  
Author(s):  
J. P. Quaile ◽  
E. K. Levy
Keyword(s):  
Experimental Investigation ◽  
Laminar Flow ◽  
Velocity Profile ◽  
Circular Tube ◽  
Wall Suction ◽  
Porous Tube ◽  
Inlet Velocity ◽  
Uniform Wall ◽  
Steady Laminar

A theoretical and experimental investigation of the flow in a porous tube with wall suction is described. The flow is steady, laminar, and incompressible with the fluid entering at one end of the circular tube and flowing out through the porous circumferential surface. The study is limited to an inlet velocity profile parabolic in shape and to the case of uniform wall suction.

Stability of turbulent channel flow, with application to Malkus's theory

1967 ◽  
Vol 27 (2) ◽  
pp. 253-272 ◽  
Author(s):  
W. C. Reynolds ◽  
W. G. Tiederman
Keyword(s):  
Velocity Profile ◽  
Channel Flow ◽  
Stability Problem ◽  
Turbulent Channel Flow ◽  
Velocity Profiles ◽  
Neutral Stability ◽  
Mean Velocity ◽  
The Mean ◽  
Two Parameter ◽  
Good Agreement

The Orr-Sommerfeld stability problem has been studied for velocity profiles appropriate to turbulent channel flow. The intent was to provide an evaluation of Malkus's theory that the flow assumes a state of maximum dissipation, subject to certain constraints, one of which is that the mean velocity profile is marginally stable. Dissipation rates and neutral stability curves were obtained for a representative two-parameter family of velocity profiles. Those in agreement with experimental profiles were found to be stable; the marginally stable profile of greatest dissipation was not in good agreement with experiments. An explanation for the apparent success of Malkus's theory is offered.

Temperature Effects in a Laminar Compressible-Fluid Boundary Layer Along a Flat Plate

1941 ◽  
Vol 8 (3) ◽  
pp. A105-A110
Author(s):  
H. W. Emmons ◽  
J. G. Brainerd
Keyword(s):  
Boundary Layer ◽  
Equilibrium Temperature ◽  
Perfect Gas ◽  
Boundary Layer Problem ◽  
Wide Range ◽  
Dimensional Boundary ◽  
Fluid Boundary ◽  
New Phenomena ◽  
Steady Laminar ◽  
Layer Problem

Abstract In this paper the two-dimensional boundary-layer problem of the steady laminar flow of a perfect gas along a thin flat insulated plate has been solved for a wide range of gas velocities and properties. It is found that compressibility and Prandtl number do not introduce any new phenomena, but do alter the drag on the plate, the equilibrium temperature of the plate, and the velocity and temperature distribution through the boundary layer. The drag coefficient for the plate is given by Equation [24] together with Fig. 2. The temperature of the plate is given by Equation [27 a or b], and approximately by Equation [26] or by Figs. 3 or 4. Typical velocity and temperature distributions are given in Figs. 5 to 10, inclusive.

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