On Exact Solutions for Oscillatory Flows in a Generalized Burgers Fluid with Slip Condition

2010 ◽  
Vol 65 (5) ◽  
pp. 381-391 ◽  
Author(s):  
Tasawar Hayat ◽  
Saher Najam ◽  
Muhammad Sajid ◽  
Muhammad Ayub ◽  
Said Mesloub
Keyword(s):  
Resonant Frequency ◽  
Exact Solutions ◽  
Slip Condition ◽  
Darcy Law ◽  
Porous Space ◽  
Oscillatory Flows ◽  
Flow Modelling ◽  
Slip Effects ◽  
Burgers Fluid

An analysis is performed for the slip effects on the exact solutions of flows in a generalized Burgers fluid. The flow modelling is based upon the magnetohydrodynamic (MHD) nature of the fluid and modified Darcy law in a porous space. Two illustrative examples of oscillatory flows are considered. The results obtained are compared with several limiting cases. It has been shown here that the derived results hold for all values of frequencies including the resonant frequency.

ROTATING FLOWOF A GENERALIZED BURGERS' FLUID WITH SLIP CONDITION

2010 ◽  
Vol 13 (9) ◽  
pp. 839-845 ◽  
Author(s):  
Tasawar Hayat ◽  
S. Najam ◽  
S. Asghar
Keyword(s):  
Slip Condition ◽  
Burgers Fluid

Lubricating motion of a sphere towards a thin porous slab with Saffman slip condition

2019 ◽  
Vol 867 ◽  
pp. 949-968 ◽  
Author(s):  
Sondes Khabthani ◽  
Antoine Sellier ◽  
François Feuillebois
Keyword(s):  
Slip Length ◽  
Solid Sphere ◽  
Slip Condition ◽  
Darcy Law ◽  
Slab Thickness ◽  
Wide Range ◽  
Sphere Radius ◽  
Permeability Parameter ◽  
Interface Slip ◽  
Range Of Values

Near-contact hydrodynamic interactions between a solid sphere and a plane porous slab are investigated in the framework of lubrication theory. The size of pores in the slab is small compared with the slab thickness so that the Darcy law holds there. The slab is thin: that is, its thickness is small compared with the sphere radius. The considered problem involves a sphere translating above the slab together with a permeation flow across the slab and a uniform pressure below. The pressure is continuous across both slab interfaces and the Saffman slip condition applies on its upper interface. An extended Reynolds-like equation is derived for the pressure in the gap between the sphere and the slab. This equation is solved numerically and the drag force on the sphere is calculated therefrom for a wide range of values of the slab interface slip length and of the permeability parameter $\unicode[STIX]{x1D6FD}=24k^{\ast }R/(e\unicode[STIX]{x1D6FF}^{2})$, where $k^{\ast }$ is the permeability, $e$ is the porous slab thickness, $R$ is the sphere radius and $\unicode[STIX]{x1D6FF}$ is the gap. Moreover, asymptotics expansions for the pressure and drag are derived for high and low $\unicode[STIX]{x1D6FD}$. These expansions, which agree with the numerics, are also handy formulae for practical use. All results match with those of other authors in particular cases. The settling trajectory of a sphere towards a porous slab in a fluid at rest is calculated from these results and, as expected, the time for reaching the slab decays for increasing slab permeability and upper interface slip length.

Oscillatory flows of second grade fluid in a porous space

2010 ◽  
Vol 11 (4) ◽  
pp. 2403-2414 ◽  
Author(s):  
M. Hussain ◽  
T. Hayat ◽  
S. Asghar ◽  
C. Fetecau
Keyword(s):  
Second Grade ◽  
Porous Space ◽  
Second Grade Fluid ◽  
Oscillatory Flows ◽  
Grade Fluid

scholarly journals New Exact Solutions for an Oldroyd-B Fluid in a Porous Medium

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
I. Khan ◽  
M. Imran ◽  
K. Fakhar
Keyword(s):  
Porous Medium ◽  
Shear Stress ◽  
Exact Solutions ◽  
Strong Influence ◽  
Stress Fields ◽  
Porous Space ◽  
New Exact Solutions ◽  
Laplace Transform Technique ◽  
Similar Solutions ◽  
Analytical Expressions

New exact solutions for unsteady magnetohydrodynamic (MHD) flows of an Oldroyd-B fluid have been derived. The Oldroyd-B fluid saturates the porous space. Two different flow cases have been considered. The analytical expressions for velocity and shear stress fields have been obtained by using Laplace transform technique. The corresponding solutions for hydrodynamic Oldroyd-B fluid in a nonporous space appeared as the limiting cases of the obtained solutions. Similar solutions for MHD Newtonian fluid passing through a porous space are also recovered. Graphs are sketched for the pertinent parameters. It is found that the MHD and porosity parameters have strong influence on velocity and shear stress fields.

scholarly journals The Influence of Magnetohydrodynamic Flow and Slip Condition on Generalized Burgers’ Fluid with Fractional Derivative

2020 ◽  
Vol 17 (1) ◽  
pp. 0150
Author(s):  
Nassief Et al.
Keyword(s):  
Shear Stress ◽  
Fractional Calculus ◽  
Fractional Derivative ◽  
Velocity Distribution ◽  
Constant Pressure ◽  
Fluid Model ◽  
Magnetohydrodynamic Flow ◽  
Slip Condition ◽  
Constitutive Relationship ◽  
Burgers Fluid

This paper investigates the effect of magnetohydrodynamic (MHD) of an incompressible generalized burgers’ fluid including a gradient constant pressure and an exponentially accelerate plate where no slip hypothesis between the burgers’ fluid and an exponential plate is no longer valid. The constitutive relationship can establish of the fluid model process by fractional calculus, by using Laplace and Finite Fourier sine transforms. We obtain a solution for shear stress and velocity distribution. Furthermore, 3D figures are drawn to exhibit the effect of magneto hydrodynamic and different parameters for the velocity distribution.

Exact solutions for generalized Burgers’ fluid in an annular pipe

Meccanica ◽  
2008 ◽  
Vol 44 (4) ◽  
pp. 427-431 ◽  
Author(s):  
Dengke Tong ◽  
Liantao Shan
Keyword(s):  
Exact Solutions ◽  
Burgers Fluid ◽  
Annular Pipe
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