Laminar Wall Jet of a Non-Newtonian Fluid Over a Curved Surface

1984 ◽  
Vol 51 (2) ◽  
pp. 440-443 ◽  
Author(s):  
Rama Subba Reddy Gorla
Keyword(s):  
Friction Coefficient ◽  
Velocity Field ◽  
Newtonian Fluid ◽  
Similarity Solution ◽  
Skin Friction Coefficient ◽  
Curved Surface ◽  
Wall Jet ◽  
Two Dimensional ◽  
Special Shape ◽  
Curvature Parameter

An analysis is presented for the flow of a laminar, two-dimensional, incompressible, non-Newtonian fluid jet flowing over a curved surface. A unique similarity solution is obtained for both concave and convex surfaces. The similarity solution requires a special shape of the curved surface which is also determined. Numerical results are presented for the details of the velocity field and skin friction coefficient as a function of the curvature parameter.

Similarity Solution for the Curved Two-Dimensional Jet

1972 ◽  
Vol 39 (4) ◽  
pp. 879-882
Author(s):  
G. K. Fleming ◽  
S. A. Alpay
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Nonlinear Equation ◽  
Similarity Solution ◽  
Separation Bubble ◽  
The Other ◽  
Wall Jet ◽  
Two Dimensional ◽  
Two Parameter ◽  
Outer Half

A similarity solution has been obtained for a fluid jet bounded on one side by a separation bubble and on the other by an unbounded region containing the same fluid. The inner boundary has been approximated by a porous pseudowall. The resulting mathematical model reduces to other cases such as the plane wall jet and the free curved jet. A two-parameter family of solutions to the resulting nonlinear equation for the outer half of the jet correlates well with experimental data.

An Experimental Study of a Turbulent Wall Jet on Smooth and Transitionally Rough Surfaces

2011 ◽  
Vol 133 (11) ◽  
Author(s):  
N. Rostamy ◽  
D. J. Bergstrom ◽  
D. Sumner ◽  
J. D. Bugg
Keyword(s):  
Friction Coefficient ◽  
Skin Friction ◽  
Laser Doppler Anemometry ◽  
Skin Friction Coefficient ◽  
Wall Jet ◽  
Roughness Effects ◽  
Mean Velocity ◽  
Turbulent Wall ◽  
Inner Region ◽  
Effect Of Surface

The effect of surface roughness on the mean velocity and skin friction characteristics of a plane turbulent wall jet was experimentally investigated using laser Doppler anemometry. The Reynolds number based on the slot height and exit velocity of the jet was approximately Re = 7500. A 36-grit sheet was used to create a transitionally rough flow (44 < ks+ < 70). Measurements were carried out at downstream distances from the jet exit ranging from 20 to 80 slot heights. Both conventional and momentum-viscosity scaling were used to analyze the streamwise evolution of the flow on smooth and rough walls. Three different methods were employed to estimate the friction velocity in the fully developed region of the wall jet, which was then used to calculate the skin friction coefficient. This paper provides new experimental data for the case of a plane wall jet on a transitionally rough surface and uses it to quantify the effects of roughness on the momentum field. The present results indicate that the skin friction coefficient for the rough-wall case compared to a smooth wall increases by as much as 140%. Overall, the study suggests that for the transitionally rough regime considered in the present study, roughness effects are significant but mostly confined to the inner region of the wall jet.

On Two-Dimensional Laminar Hydromagnetic Fluid-Particle Flow Over a Surface in the Presence of a Gravity Field

2000 ◽  
Vol 123 (1) ◽  
pp. 43-49 ◽  
Author(s):  
Ali J. Chamkha
Keyword(s):  
Magnetic Field ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Analytical Solutions ◽  
Fluid Phase ◽  
Skin Friction Coefficient ◽  
Two Dimensional ◽  
Particle Phase ◽  
Phase Stresses ◽  
The Magnetic Field

A continuum two-phase fluid-particle model accounting for particle-phase stresses and a body force due to the presence of a magnetic field is developed and applied to the problem of two-dimensional laminar hydromagnetic flow of a particulate suspension over a horizontal surface in the presence of a gravity field. Analytical solutions for the velocity distributions and the skin-friction coefficients of both phases are reported. Two cases of wall hydrodynamic (velocity) conditions corresponding to stationary and oscillatory velocity distributions are considered. Numerical evaluations of the analytical solutions are performed and the results are reported graphically to elucidate special features of the solutions. The effects of the particle-phase stresses and the magnetic field are illustrated through representative results for the horizontal velocity profiles, fluid-phase displacement thickness, and the complete skin-friction coefficient for various combinations of the physical parameters. It is found that the presence of the magnetic field increases the fluid-phase skin-friction coefficient for various particulate volume fraction levels while the presence of the particle-phase viscous stresses reduces it for various particle-to-fluid density ratios.

A Numercial Investigation of the Skin Friction Coefficient and Nusselt Number in a Laminar Wall Jet That Evolves From a Parabolic Velocity Profile to its Self-Similar Behavior

2014 ◽  
Author(s):  
Johnny Issa ◽  
Alfonso Ortega
Keyword(s):  
Reynolds Number ◽  
Nusselt Number ◽  
Friction Coefficient ◽  
Velocity Profile ◽  
Prandtl Number ◽  
Boundary Conditions ◽  
Skin Friction Coefficient ◽  
Wall Jet ◽  
Parabolic Velocity Profile ◽  
Self Similar

A finite volume numerical approach is used to study the steady, laminar, plane wall jet that evolves from a parabolic velocity profile with uniform temperature to its self-similar behavior downstream of the jet exit. A variety of Reynolds numbers ranging between 50 and 250 is considered in this numerical investigation. The working fluids are air and water with constant physical properties corresponding to Prandtl number of 0.712 and 7 at ambient conditions. In these types of flows, a developing region over which the flow converges to its self-similar behavior is observed in the vicinity of the jet exit. The location of the dimensionless virtual origin, which is of main importance in determining the flow field in the self-similar region, is carefully studied and correlated as a function of Reynolds number. The local skin friction coefficient is observed to converge to the analytical self-similar solution at downstream locations. Given that an analytical solution for the thermal behavior of this problem doesn’t exist in either the developing or self-similar regions, the thermal solution of this problem is studied for isothermal and uniform heat flux boundary conditions at the wall. The idea of a dimensionless thermal virtual origin is introduced and correlated as a function of Reynolds number. The Nusselt number dependence on Prandtl number, Reynolds number and the downstream location are obtained for both thermal boundary conditions at the wall.

The laminar wall-jet over a curved surface

1968 ◽  
Vol 31 (3) ◽  
pp. 459-465 ◽  
Author(s):  
I. J. Wygnanski ◽  
F. H. Champagne
Keyword(s):  
Laminar Flow ◽  
Velocity Profile ◽  
Skin Friction ◽  
Surface Pressure ◽  
Similarity Solution ◽  
Plane Surface ◽  
Curved Surface ◽  
Radius Of Curvature ◽  
Wall Jet ◽  
The One

The laminar flow of a wall jet over a curved surface is considered. A unique similarity solution is obtained for both concave and convex surfaces when the local radius of curvature is proportional to x3/4. This solution satisfies a similar invariant condition to the one derived by Glauert for the wall jet over a plane surface. The variation of the shape of the velocity profile, the skin friction, and the surface pressure as a function of curvature is given.

Displacement and curvature effects in a wall jet

1971 ◽  
Vol 50 (2) ◽  
pp. 369-392 ◽  
Author(s):  
Ann L. Clark ◽  
E. J. Watson
Keyword(s):  
Boundary Layer ◽  
Conformal Transformation ◽  
Curved Surface ◽  
Dimensional Case ◽  
Wall Jet ◽  
Two Dimensional ◽  
Outer Flow ◽  
General Solutions ◽  
Boundary Layer Equations ◽  
Curvature Effects

This paper presents a solution of the second-order boundary-layer equations for the two-dimensional case of a wall jet on a curved surface. The outer flow is obtained by means of a conformal transformation, and general solutions for the displacement and curvature effects are given both as series and as integrals. These solutions are applied to symmetrical flow over a parabolic surface, the wall jet being either outside or inside.

Dynamic Reversibility in Fluid Flows

1967 ◽  
Vol 89 (1) ◽  
pp. 237-238 ◽  
Author(s):  
Kirit Yajnik
Keyword(s):  
Velocity Field ◽  
Newtonian Fluid ◽  
Fluid Flows ◽  
The Other ◽  
Two Dimensional ◽  
Reversed Flow ◽  
Unidirectional Flow ◽  
Flow Through ◽  
Simple Character ◽  
Dynamic Reversibility

This note points out the relatively simple character of dynamically reversible flows. A flow is said to be dynamically reversible if the reversed flow is possible under the action of suitable forces. The velocity field in the case of such flows of a Newtonian fluid subjected to conservative body forces can be decomposed into two parts, one satisfying Laplace’s equation and the other, the conduction equation. An integral similar to Bernoulli’s integral can also be found. In addition, the vorticity in two-dimensional flows is constant along a streamline. The property of dynamic reversibility is enjoyed by many flows such as irrotational flows, unidirectional flow through pipes, and two-dimensional axisymmetric vortexes.

Series solution of hydromagnetic flow and heat transfer with Hall effect in a second grade fluid over a stretching sheet

Open Physics ◽  
2010 ◽  
Vol 8 (1) ◽  
Author(s):  
Muhammad Ayub ◽  
Haider Zaman ◽  
Masud Ahmad
Keyword(s):  
Heat Transfer ◽  
Friction Coefficient ◽  
Velocity Field ◽  
Stretching Sheet ◽  
Skin Friction Coefficient ◽  
Second Grade ◽  
Hydromagnetic Flow ◽  
Second Grade Fluid ◽  
Flow And Heat Transfer ◽  
Grade Fluid

AbstractWe examine the problem of flow and heat transfer in a second grade fluid over a stretching sheet [K. Vajravelu, T. Roper, Int. J. Nonlinear Mech. 34, 1031 (1999)]. The equations considered by Vajravelu and Roper [K. Vajravelu, T. Roper, Int. J. Nonlinear Mech. 34, 1031 (1999)], are found to be incorrect in the literature. In this paper, we not only corrected the equation but found a useful analytic solution to this important problem. We also extended the problem for hydromagnetic flow and heat transfer with Hall effect. The explicit analytic homotopy solution for the velocity field and heat transfer are presented. Graphs for the velocity field, skin friction coefficient, and rate of heat transfer are presented. Tables for the skin friction coefficient and rate of heat transfer are also presented. The convergence of the solution is also properly checked and discussed.

scholarly journals Energy budget in internal wave attractor experiments

2019 ◽  
Vol 880 ◽  
pp. 743-763 ◽  
Author(s):  
Géraldine Davis ◽  
Thierry Dauxois ◽  
Timothée Jamin ◽  
Sylvain Joubaud
Keyword(s):  
Velocity Field ◽  
Internal Wave ◽  
Boundary Layers ◽  
Energy Budget ◽  
Dissipation Rate ◽  
Theoretical Expression ◽  
Two Dimensional ◽  
Energy Sink ◽  
Set Up ◽  
Different Sources

The current paper presents an experimental study of the energy budget of a two-dimensional internal wave attractor in a trapezoidal domain filled with uniformly stratified fluid. The injected energy flux and the dissipation rate are simultaneously measured from a two-dimensional, two-component, experimental velocity field. The pressure perturbation field needed to quantify the injected energy is determined from the linear inviscid theory. The dissipation rate in the bulk of the domain is directly computed from the measurements, while the energy sink occurring in the boundary layers is estimated using the theoretical expression for the velocity field in the boundary layers, derived recently by Beckebanze et al. (J. Fluid Mech., vol. 841, 2018, pp. 614–635). In the linear regime, we show that the energy budget is closed, in the steady state and also in the transient regime, by taking into account the bulk dissipation and, more importantly, the dissipation in the boundary layers, without any adjustable parameters. The dependence of the different sources on the thickness of the experimental set-up is also discussed. In the nonlinear regime, the analysis is extended by estimating the dissipation due to the secondary waves generated by triadic resonant instabilities, showing the importance of the energy transfer from large scales to small scales. The method tested here on internal wave attractors can be generalized straightforwardly to any quasi-two-dimensional stratified flow.

Impact of viscosity variation on oblique flow of Cu–H2O nanofluid

2017 ◽  
Vol 232 (5) ◽  
pp. 622-631 ◽  
Author(s):  
R Tabassum ◽  
Rashid Mehmood ◽  
O Pourmehran ◽  
NS Akbar ◽  
M Gorji-Bandpy
Keyword(s):  
Heat Flux ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Volume Fraction ◽  
Variable Viscosity ◽  
Solid Volume Fraction ◽  
Local Heat ◽  
Skin Friction Coefficient ◽  
Viscosity Parameter ◽  
Local Heat Flux

The dynamic properties of nanofluids have made them an area of intense research during the past few decades. In this article, flow of nonaligned stagnation point nanofluid is investigated. Copper–water based nanofluid in the presence of temperature-dependent viscosity is taken into account. The governing nonlinear coupled ordinary differential equations transformed by partial differential equations are solved numerically by using fourth-order Runge–Kutta–Fehlberg integration technique. Effects of variable viscosity parameter on velocity and temperature profiles of pure fluid and copper–water nanofluid are analyzed, discussed, and presented graphically. Streamlines, skin friction coefficients, and local heat flux of nanofluid under the impact of variable viscosity parameter, stretching ratio, and solid volume fraction of nanoparticles are also displayed and discussed. It is observed that an increase in solid volume fraction of nanoparticles enhances the magnitude of normal skin friction coefficient, tangential skin friction coefficient, and local heat flux. Viscosity parameter is found to have decreasing effect on normal and tangential skin friction coefficients whereas it has a positive influence on local heat flux.

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