Effect of Velocity-Slip Boundary Conditions on Jeffery–Hamel Flow Solutions

2010 ◽  
Vol 77 (4) ◽  
Author(s):  
M. A. Al-Nimr ◽  
Vladimir A. Hammoudeh ◽  
M. A. Hamdan
Keyword(s):  
Friction Coefficient ◽  
Skin Friction ◽  
Flow Direction ◽  
Velocity Slip ◽  
Skin Friction Coefficient ◽  
Second Order ◽  
Slip Model ◽  
Wall Angle ◽  
First Order ◽  
Slip Boundary

In the present work, the Jeffery–Hamel flow problem has been studied using both first- and second-order velocity-slip models, and then compared with the no-slip model. The objectives are to observe the behavior of the flow predicted by the two slip models and to establish criteria for using the two velocity-slip models. The study concentrates on examining the effect of the change in the Knudsen number (Kn) on the velocity profiles, magnitude of slip at the wall, and skin friction coefficient. Assuming that a difference between the two slip models of the order of 10% or less justifies the use of the simple first-order model, the transitional Kn numbers have been found. These Kn numbers depend on the flow direction, being either inflow or outflow. Also, there are three distinct regions that specify where to use each of the no-slip, first-order, and second-order slip models. Further, the reversal of the flow has been investigated as a function of the Kn number and for different Re⋅α, where Re is Reynolds number and α is the wall angle. Using the second-order slip models, it is found that as the Kn number increases, reversal occurs at Re⋅α smaller than the 10.31 value at which flow reversal happens in the no-slip model, and increasing the Kn number leads to a reduction in the skin friction coefficient in all cases except when reversal occurs.

scholarly journals Effects of Nanolayer and Second Order Slip on Unsteady Nanofluid Flow Past a Wedge

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1043 ◽  
Author(s):  
Zhu ◽  
Cao
Keyword(s):  
Friction Coefficient ◽  
Skin Friction ◽  
Velocity Slip ◽  
Skin Friction Coefficient ◽  
Second Order ◽  
Analysis Method ◽  
Similarity Transformations ◽  
Flow And Heat Transfer ◽  
Homotopy Analysis ◽  
Fundamental Equations

This paper presents the study of unsteady nanofluids flow and heat transfer past a wedge with second order velocity slip and temperature jump. The model is modified by considering the existence of a nanolayer together with the effects of thermophoresis and Brownian motion. The fundamental equations were transformed into ordinary differential equations by a new set of similarity transformations and solved by using the homotopy analysis method (HAM). We determined that the error reached 10-6 and the effectiveness of HAM was attained. The influence of second-order slip on the fluid skin-friction coefficient was analyzed and we determined that the Nusselt number decreases and skin friction coefficient rises with an increase in the thickness of the nanolayer.

scholarly journals MHD Flow of Nanofluid with Homogeneous-Heterogeneous Reactions in a Porous Medium under the Influence of Second-Order Velocity Slip

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 220 ◽  
Author(s):  
Fahd Almutairi ◽  
S.M. Khaled ◽  
Abdelhalim Ebaid
Keyword(s):  
Porous Medium ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Volume Fraction ◽  
Heterogeneous Reaction ◽  
Mhd Flow ◽  
Velocity Slip ◽  
Skin Friction Coefficient ◽  
Second Order ◽  
Heterogeneous Reactions

The influence of second-order velocity slip on the MHD flow of nanofluid in a porous medium under the effects of homogeneous-heterogeneous reactions has been analyzed. The governing flow equation is exactly solved and compared with those in the literature for the skin friction coefficient in the absence of the second slip, where great differences have been observed. In addition, the effects of the permanent parameters on the skin friction coefficient, the velocity, and the concentration have been discussed in the presence of the second slip. As an important result, the behavior of the skin friction coefficient at various values of the porosity and volume fraction is changed from increasing (in the absence of the second slip) to decreasing (in the presence of the second slip), which confirms the importance of the second slip in modeling the boundary layer flow of nanofluids. In addition, five kinds of nanofluids have been investigated for the velocity profiles and it is found that the Ag-water nanofluid is the lowest. For only the heterogeneous reaction, the concentration equation has been exactly solved, while the numerical solution is applied in the general case. Accordingly, a reduction in the concentration occurs with the strengthening of the heterogenous reaction and also with the increase in the Schmidt parameter. Moreover, the Ag-water nanofluid is of lower concentration than the Cu-water nanofluid. This is also true for the general case, when both of the homogenous and heterogenous reactions take place.

Investigation Into the Similarity Solution for Boundary Layer Flows in Microsystems

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
Suhil Kiwan ◽  
M. A. Al-Nimr
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Temperature Jump ◽  
Velocity Slip ◽  
Skin Friction Coefficient ◽  
Heat Transfer Characteristics ◽  
Boundary Layer Flows ◽  
Flow And Heat Transfer

An investigation toward the existence of a complete similarity solution for boundary layer flows under the velocity slip and temperature jump conditions is carried out. The study is limited to the boundary layer flows resulting from an arbitrary freestream velocity U(x)=Uoxm and wall temperature given by Tw−T∞=Cxn. It is found that a similar solution exists only for m=1 and n=0, which represents stagnation flow on isothermal surface. This case has been thoroughly investigated. The analysis showed that three parameters control the flow and heat transfer characteristics of the problem. These parameters are the velocity slip parameter K1, the temperature jump parameter K2, and Prandtl number. The effect of these parameters on the flow and heat transfer of the problem has been studied and presented. It is found that the slip velocity parameter affects both the flow and heat transfer characteristics of the problem. It is found that the skin friction coefficient decreases with increasing K1 and most of changes in the skin friction takes place in the range 0<K1<1. The skin friction coefficient is found to be related to K1 and Rex according to the relation: Cf=3.38Rex−0.5(K1+1.279)−0.8 for 0<K1<5 with an error of ±4%. On the other hand, the correlation between Nu, K1, K2, and Pr has been found by the equation Nu=[(0.449+1.142K11.06)∕(0.515+K11.06)](K2+1.489Pr−0.44)−1, for 0<K1, K2<5, 0.7≤Pr≤5 within a maximum error of ±3%.

Passive control of nanoparticle of micropolar fluid past a stretching sheet with nanoparticles, convective boundary condition and second-order slip

2016 ◽  
Vol 231 (4) ◽  
pp. 704-719 ◽  
Author(s):  
Wubshet Ibrahim
Keyword(s):  
Nusselt Number ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Local Nusselt Number ◽  
Micropolar Fluid ◽  
Passive Control ◽  
Stretching Sheet ◽  
Skin Friction Coefficient ◽  
Second Order ◽  
Non Linear

This article deals with a second-order slip flow and magnetic field on boundary layer flow of micropolar fluid past a stretching sheet. Situation of nil normal flux of nanoparticles at the wall for the stretching flow is taken into account. By employing appropriate similarity transformation and non-dimensional variables, the governing non-linear boundary-value problems were reduced into coupled higher order non-linear ordinary differential equation. Then, numerical solution for velocity, angular velocity (microrotation), temperature, and concentration has been established. The equations were numerically solved using the function bvp4c from the matlab software for different values of governing parameters. Numerical results have been obtained and discussed for non-dimensional velocity, temperature, microrotation, the skin friction coefficient, and local Nusselt number using some fixed values of the governing parameters. The results indicate that the skin friction coefficient Cf increases as the values of slip parameter γ increase. However, the local Nusselt number − [Formula: see text] increases as thermophoresis parameter Nt, microrotation parameter β, and convective parameter Bi increase. The wall couple stress coefficient decreases as the values of governing parameters such as magnetic parameter M, material parameter β, and for both slip parameters γ and δ increase. A comparison with earlier investigations available in the literature has been done and an excellent agreement is achieved.

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.

Low-Reynolds-Number Turbulent Boundary Layers in Zero and Favorable Pressure Gradients

1983 ◽  
Vol 27 (03) ◽  
pp. 147-157 ◽  
Author(s):  
A. J. Smits ◽  
N. Matheson ◽  
P. N. Joubert
Keyword(s):  
Friction Coefficient ◽  
Skin Friction ◽  
Boundary Layers ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Skin Friction Coefficient ◽  
Turbulent Boundary Layers ◽  
Pressure Gradients ◽  
Mean Flow ◽  
Low Reynolds

This paper reports the results of an extensive experimental investigation into the mean flow properties of turbulent boundary layers with momentum-thickness Reynolds numbers less than 3000. Zero pressure gradient and favorable pressure gradients were studied. The velocity profiles displayed a logarithmic region even at very low Reynolds numbers (as low as Rθ = 261). The results were independent of the leading-edge shape, and the pin-type turbulent stimulators performed well. It was found that the shape and Clauser parameters were a little higher than the correlation proposed by Coles [10], and the skin friction coefficient was a little lower. The skin friction coefficient behavior could be fitted well by a simple power-law relationship in both zero and favorable pressure gradients.

Nanofluid flow past an impulsively started vertical plate with variable surface temperature

2016 ◽  
Vol 26 (1) ◽  
pp. 328-347 ◽  
Author(s):  
Rajesh Vemula ◽  
A J Chamkha ◽  
Mallesh M. P.
Keyword(s):  
Nusselt Number ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Vertical Plate ◽  
Aluminium Oxide ◽  
Skin Friction Coefficient ◽  
Viscous Drag ◽  
Content Type ◽  
Variable Surface ◽  
Variable Surface Temperature

Purpose – The purpose of this paper is to focus on the numerical modelling of transient natural convection flow of an incompressible viscous nanofluid past an impulsively started semi-infinite vertical plate with variable surface temperature. Design/methodology/approach – The problem is governed by the coupled non-linear partial differential equations with appropriate boundary conditions. A robust, well-tested, Crank-Nicolson type of implicit finite-difference method, which is unconditionally stable and convergent, is used to solve the governing non-linear set of partial differential equations. Findings – The local and average values of the skin-friction coefficient (viscous drag) and the average Nusselt number (the rate of heat transfer) decreased, while the local Nusselt number increased for all nanofluids, namely, aluminium oxide-water, copper-water, titanium oxide-water and silver-water with an increase in the temperature exponent m. Selecting aluminium oxide as the dispersing nanoparticles leads to the maximum average Nusselt number (the rate of heat transfer), while choosing silver as the dispersing nanoparticles leads to the minimum local Nusselt number compared to the other nanofluids for all values of the temperature exponent m. Also, choosing silver as the dispersing nanoparticles leads to the minimum skin-friction coefficient (viscous drag), while selecting aluminium oxide as the dispersing nanoparticles leads to the maximum skin-friction coefficient (viscous drag) for all values of the temperature exponent m. Research limitations/implications – The Brinkman model for dynamic viscosity and Maxwell-Garnett model for thermal conductivity are employed. The governing boundary layer equations are written according to The Tiwari-Das nanofluid model. A range of nanofluids containing nanoparticles of aluminium oxide, copper, titanium oxide and silver with nanoparticle volume fraction range less than or equal to 0.04 are considered. Practical implications – The present simulations are relevant to nanomaterials thermal flow processing in the chemical engineering and metallurgy industries. This study also provides an important benchmark for further simulations of nanofluid dynamic transport phenomena of relevance to materials processing, with alternative computational algorithms (e.g. finite element methods). Originality/value – This paper is relatively original and illustrates the influence of variable surface temperature on transient natural convection flow of a viscous incompressible nanofluid and heat transfer from an impulsively started semi-infinite vertical plate.

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