Incompressible micropolar fluid flow over a semi-infinite plate

Micropolar fluid flow over a semi-infinite flat plate has been described by using the parabolic co-ordinates and the method of series truncation in order to study the flow for low to large Reynolds numbers. These co-ordinates permit to study the flow regime at the leading edge. Numerical results have been presented for different Reynolds numbers. Results show a reduction in skin friction.     

Unsteady thermal boundary layer flow of a non-newtonian fluid over a flat plate

The transient thermal response of a power law type non-Newtonian, laminar boundary layer flow past a flat plate is investigated. Consideration is given to the case of a step change in surface temperature. The transient heat flux and details of the temperature field are obtained and have been illustrated graphically. The range of Prandtl numbers investigated was 5–1000 while the viscosity index was allowed to vary 0.1–5.0.     

Heat transfer in micropolar boundary layer flow over a flat plate

Boundary layer solutions are presented to study the steady state heat transfer from a semi-infinite flat plate to a micropolar fluid. The boundary conditions of isothermal wall, constant surface heat flux and insulated wall with viscous dissipation effects have been treated in this paper. Numerical results for the temperature distribution and the missing wall values of the thermal functions have been given. The range of Prandtl numbers investigated was from 10 to 1000 while the dimensionless grouping of the material properties was allowed to vary over a wide range.     

Boundary layer flow due to a moving plate: variable fluid properties

Summary The influence of temperature dependent fluid properties on laminar boundary layer flows over a continuous moving flat surface is examined. The governing equations are changed to ordinary equations by similarity transformations. They are then solved numerically for different values of the parameters involved. These parameters are shown to have a significant effect on the flow and heat transfer characteristics of this problem.     

The Navier-Stokes solution for laminar flow past a semi-infinite flat plate

Summary A numerical solution joining Carrier and Lin's solution near the leading edge to the boundary layer solution at large distance of the leading edge is presented. The solution is valid for any Reynolds number. Results are given for the skin friction, the integrated skin friction, the displacement thickness, the pressure along the plate and the velocity ahead of the plate. The asymptotic value of the integrated skin friction agrees very well with the exact value. The displacement thickness is already different from zero for small distances ahead of the plate.     

Heat transfer effects on dusty gas flow past a semi-infinite inclined plate

Heat transfer effects on dusty gas flow past a semi-infinite isothermal inclined plate are considered here-with. The governing boundary layer equations for the above problem are set up and non-dimensionalised. The non-dimensional governing equations are solved by an implicit finite difference scheme of Crank–Nicolson method, which is fast convergent and unconditionally stable. Gas-velocity, dust particle-velocity, temperature, skin friction and Nusselt numbers are calculated numerically for various parameters occurring into the problem and are shown graphically. It is observed that the velocity of the dusty-gas decreases with decreasing inclination angle ϕ to the horizontal. An increase in the mass concentration of dust also causes a fall in the gas-velocity.     

Boundary layer of a microstructural fluid on a plate

A numerical solution of the self-similar problem of the boundary layer of a micropolar model fluid on a semiinfinite plate is obtained.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 36, No. 1, pp. 121–126, January, 1979.     

Stability of flow of a structurally viscous fluid in the boundary layer on a flat plate

The method of small perturbations has been used to study the hydrodynamical stability of flow of a structurally viscous fluid in the boundary layer on a flat plate.     

Turbulent flow of a polymer solution over a flat plate

Logarithmic drag equations are derived by the Prandtl-Kármán method. Error estimates for certain simplifications are given, and errors occurring in the literature are eliminated. The maximum drag-reduction regime is discussed.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 31, No. 3, pp. 486–492, September, 1976.     

On the hydromagnetic boundary layer flow past a flat plate

Summary The Falkner-Skan transformation has been generalized to study the boundary layer flow of a viscous incompressible conducting fluid past a flat plate in the presence of a uniform transverse magnetic field fixed to the plate. Keeping the convergence aspect in view series solution, different from the conventional, for the velocity boundary layer has been developed. It is found that only few terms in the series expansion are enough to give the skin-friction coefficient to a good degree of accuracy.

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Über die hydromagnetische Grenzschichtströmung an der ebenen Platte

Zusammenfassung Die Falkner-Skan-Transformation wird verallgemeinert für den Fall der Grenzschichtströmung eines leitenden, zähen, inkompressiblen Mediums längs einer ebenen Platte in einem konstanten Magnetfeld senkrecht zur Platte. Es wird eine neue Reihenentwicklung mit guten Konvergenzeigenschaften für die Geschwindigkeit in der Grenzschicht hergeleitet. Hier reichen wenige Terme der Reihenentwicklung aus, um den Koeffizienten der Oberflächenreibung in guter Genauigkeit zu bestimmen.

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With 1 Figure     

Effect of pressure gradient on MHD boundary layer over a flat plate

Summary The magnetohydrodynamic (MHD) boundary layer flow over a flat plate is examined here for two cases, viz. a uniform free-stream velocity and a uniform hydrostatic pressure. The nonlinear boundary layer equations are solved using a reliable finite-difference method. The boundary layer physical parameters such as skin-friction coefficient, displacement, momentum and energy thicknesses of the boundary layer are determined. It is found that the normal surface velocity gradient decreases with the local magnetic interaction parameter for the cases of a uniform hydrostatic pressure, whereas in the case of a uniform free-stream volocity it increases with the interaction parameter.     

Linear instability of flow over a semi-infinite plate in a stream with uniform shear

Summary The linear stability of a boundary layer flow with uniform free stream shear has been studied. The free stream shear is found to stabilize the flow.     

Magnetohydrodynamic flow past a semi-infinite moving plate

Summary The nonlinear boundary layer equations of the title problem are solved numerically for obtaining the coefficient of skin-friction. It is found that the magnitude of the normal surface velocity gradient increases with the magnetic interaction parameter.     

Thermal boundary layer of a micropolar fluid jet impinging normally on a flat plate

Summary The heat transfer is studied in the boundary layer formed on a flat plate by the impingement of an incompressible micropolar fluid jet. The thermal boundary layer equations are obtained after writing the governing equations for the steady two-dimensional flow of an incompressible micropolar fluid in cartesian co-ordinate system. The solution for the energy equation inside the boundary layer is obtained as a polynomial in terms of the distance from the stagnation point. The temperature of the plate and the temperature outside the boundary layer are assumed to be constant. The temperature distribution and the dimensionless heat transfer coefficient are presented graphically for various values of the material parameters which arise due to the micropolar property of the fluid. These results have been compared with the corresponding results for a Newtonian fluid.

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Thermische Grenzschicht eines mikropolaren Flüssigkeitsstrahles, der senkrecht auf eine ebene Platte auftrifft

Zusammenfassung Der Wärmeübergang in der Grenzschicht einer ebenen Platte, zufolge des Auftreffens eines inkompressiblen, mikropolaren Flüssigkeitsstrahles wird untersucht. Die thermischen Grenzschichtgleichungen werden aus den Grundgleichungen für die stationäre zweidimensionale Strömung einer inkompressiblen, mikropolaren Flüssigkeit in kartesischen Koordinaten erhalten. Die Lösung der Energiegleichung innerhalb der Grenzschicht wird als Polynom in Termen des Abstandes zum Staupunkt angegeben. Die Temperatur der Platte, sowie die Temperatur außerhalb der Grenzschicht werden als konstant vorausgesetzt. Die Temperaturverteilung und der dimensionslose Wärmeübergangskoeffizient sind graphisch für verschiedene Werte der Materialparameter, zufolge der mikropolaren Eigenschaften der Flüssigkeit, dargestellt. Diese Ergebnisse wurden mit den entsprechenden Ergebnissen für Newtonsche Flüssigkeiten verglichen.

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With 6 Figures     

The low Rossby number flow of a rotating fluid past a flat plate

Summary In a rotating fluid, the flow between two infinite plates, perpendicular to the rotation axis, is examined when a uniform stream is aligned with a finite flat plate, parallel to the rotation axis. Since the flow in this configuration is depth-independent the motion is analogous to that considered by Blasius in a non-rotating fluid. When the Rossby number Ro is much smaller than E^3/4, where E is the Ekman number, the equations are linear and the flow has been examined by Hocking [5]. However, when RoE^3/4 inertial effects are important in the E^1/4-layer and the boundary-layer equations are non-linear. For Ro of order E^1/2 the boundary-layer flow is calculated numerically and very close to both the leading and trailing edges of the plate the flow is identical to that in the non-rotating case. Goldstein expansions are calculated at both points and the singularity at the trailing edge is examined using triple-deck theory. This demonstrates that for Ro of order E^1/2 the E^1/4-layer exhibits behaviour similar to that of a classical boundary layer.