New exact solutions for magnetohydrodynamic flows of an Oldroyd-B fluid

Khan, Masood; Mahmood, Sajid; Fetecău, Constantin

doi:10.1007/s00033-008-8029-7

Cited by 5 publications

(3 citation statements)

References 18 publications

(21 reference statements)

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“…Asghar et al [8] presented the solution of a problem concerning Hall effects on unsteady hydromagnetic flows of an Oldroyd-B fluid. Khan et al [9][10][11] found (i) Exact solution for MHD flow of a generalized Oldroyd-B fluid with modified Darcy's law, (ii) Influence of Hall current on the flows of a generalized Oldroyd-B fluid in a porous space and (iii) New exact solutions of magnetohydrodynamic flows of an Oldroyd-B fluid. Fetecau et al [12,13] analyzed the problem of unsteady flow of an Oldroyd-B fluid induced by the impulsive motion of a plate between two side walls perpendicular to the plate in one paper while in the other they described the Rayleigh-Stokes problem for an edge in a generalized Oldroyd-B fluid.…”

Section: Introductionmentioning

confidence: 99%

On Hydromagnetic Flow of an Oldroyd-B Fluid Between Two Oscillating Plates

Ghosh

Datta

Sen

2015

Int. J. Appl. Comput. Math

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An initial value investigation is made of the motion of an incompressible, viscoelastic, electrically conducting Oldroyd-B fluid bounded by two infinite rigid nonconducting plates. The flow is generated impulsively from rest in the fluid due to rectilinear oscillations of given frequencies superimposed on the plates in their own planes in presence of an external magnetic field acting transversely to the plates. The operational method is used to derive exact solutions for the fluid velocity and the shear stress on the walls. The quantitative evaluation of the results is considered when two plates oscillate in phase but with different frequencies. The results are shown graphically for different time periods of oscillations of the plates which represent the cases: (i) the lower plate oscillates with a time period less than the upper, (ii) both the plates oscillate with the same time period and (iii) the lower plate oscillates with a time period grater than the upper. It is seen that the effect of fluid elasticity on the flow depends on the advancing and retarding motion of the plates. On the other hand, the magnetic field damps the fluid motion for all values of the time period of oscillations of the plates. The drag on the plates, for small and large time, are shown graphically when the time period of oscillation of the lower plate is small. For small values of time, the drag on the lower plate is negative with the amplitude decreasing continuously till the oscillations occur from moderately large values of time. Similar phenomenon also occurs for the drag which is positive at the upper plate for small values of time. In all cases, the amount of drag on the plates increases with the increase of the elasticity of the fluid and the magnetic field. Some particular results for the fluid velocity are derived as special cases of the present solution.

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Section: Introductionmentioning

confidence: 99%

On Hydromagnetic Flow of an Oldroyd-B Fluid Between Two Oscillating Plates

Ghosh

Datta

Sen

2015

Int. J. Appl. Comput. Math

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“…This is due to the fact that fluid transient may be expected at the start up time of MHD devices such as, MHD power generators and pumps, MHD accelerators, nuclear reactors and so forth. Therefore, many researchers have discussed the flows of non-Newtonian fluids in different configurations; however, there are at hand few attempts which include the effects of MHD (for instance, see the studies in [21][22][23]).…”

Section: Introductionmentioning

confidence: 99%

Stokes' First Problem for an MHD Burgers Fluid

Khan¹

2013

Commun. Theor. Phys.

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This work is related to the flow of a magnetohydrodynamic Burgers fluid. The flow of an incompressible conducting Burgers fluid in the presence of a uniform transverse magnetic field over a plate that is moved suddenly is considered. By the application of the Laplace and Fourier sine transforms techniques, the exact analytical expressions for the velocity field and associated shear stress are determined in simple forms. They are written as a sum of steady-state and transient solutions. The graphical results are plotted for different values of indispensable parameters and some interesting results are concluded. The corresponding solutions for the hydrodynamic Burgers fluid appear as the limiting cases of the obtained solutions.

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“…International Journal of Mathematics and Mathematical Sciences a porous layer. The literature survey revealed that very few attempts are available in which the flows of electrically conducting Oldroyd-B fluid through a porous medium are studied [21][22][23][24][25][26] . Therefore, the basic objective of the present paper is to study the motion of Oldroyd-B fluid taking into account both magnetic and porosity effects.…”

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confidence: 99%

New Exact Solutions for an Oldroyd‐B Fluid in a Porous Medium

Khan

Imran

Fakhar

2011

International Journal of Mathematics and Mathematical Sciences

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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.

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New exact solutions for magnetohydrodynamic flows of an Oldroyd-B fluid

Cited by 5 publications

References 18 publications

On Hydromagnetic Flow of an Oldroyd-B Fluid Between Two Oscillating Plates

On Hydromagnetic Flow of an Oldroyd-B Fluid Between Two Oscillating Plates

Stokes' First Problem for an MHD Burgers Fluid

New Exact Solutions for an Oldroyd‐B Fluid in a Porous Medium

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