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Arun Kumar Ghosh

Bio: Arun Kumar Ghosh is an academic researcher from Jadavpur University. The author has contributed to research in topics: Magnetic field & Flow velocity. The author has an hindex of 4, co-authored 7 publications receiving 52 citations.

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TL;DR: In this paper, an initial value problem is solved for the motion of an incompressible viscous conducting fluid with embedded small inert spherical particles bounded by an infinite rigid nonconducting plate.
Abstract: An initial value problem is solved for the motion of an incompressible viscous conducting fluid with embedded small inert spherical particles bounded by an infinite rigid non-conducting plate. Both the plate and the fluid are in a state of solid-body rotation with constant angular velocity about an axis normal to the plate. The unsteady flow is generated in the fluid-particle system due to velocity tooth pulses subjected on the plate in presence of a transverse magnetic field. It is assumed that no external electric field is imposed on the system and the magnetic Prandtl number is very small. The operational method is used to derive exact solutions for the fluid and the particle velocities and the shear stress at the wall. Some limiting cases of these solutions including the steady-state results are discussed. The general solutions for the fluid velocity and the wall shear stress are examined numerically and the simultaneous effects of rotation, the magnetic field and the particles on them are determined. Finally, the present result for the fluid velocity has been compared numerically with that generated by an impulsively moved plate in a particular case when time is large.

21 citations

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TL;DR: In this article, the effects of the magnetic field and elasticity on the flow as well as on the skin-friction on the walls were examined quantitatively, and it was shown that the expressions for the fluid velocity obtained by the method of Fourier analysis and by the Laplace transforms coincide to provide the same exact solution of the problem.
Abstract: The unsteady unidirectional motion of an incompressible electrically conducting Oldroyd-B fluid in a channel bounded by two infinite rigid non-conducting parallel plates in presence of an external magnetic field acting in a direction normal to the plates has been discussed in this paper. The flow is supposed to generate impulsively from rest due to rectified sine pulses applied periodically on the upper plate with the lower plate held fixed. There is no external electric field imposed on the system and the magnetic Reynolds number is very small. Exact solution of the problem is obtained both by the methods of Fourier analysis and the Laplace transforms. The enquiries are made about the velocity field and the skin-friction on the walls. The influence of the magnetic field and the elasticity on the flow as well as on the skin-friction are examined quantitatively. Finally, it is shown that the expressions for the fluid velocity obtained by the method of Fourier analysis and by the method of Laplace transforms coincide to provide the same exact solution of the problem.

16 citations

Journal ArticleDOI
TL;DR: In this paper, an initial value investigation is made of the motion of an incompressible, viscoelastic, conducting Oldroyd-B fluid bounded by an infinite rigid nonconducting plate.
Abstract: An initial value investigation is made of the motion of an incompressible, viscoelastic, conducting Oldroyd-B fluid bounded by an infinite rigid non-conducting plate. Both the plate and the fluid are in a state of solid body rotation with a constant angular velocity about an axis normal to the plate. The flow is generated from rest in the rotating viscoelastic system due to harmonic oscillations of a given frequency superimposed on the plate in presence of a transverse magnetic field. The exact solutions for the velocity field and the wall shear stress are obtained. The results are examined quantitatively for a particular case of an impulsively moved plate and the effects of various flow parameters on them are discussed. Many known results are found to emerge as limiting cases of the present analysis.

7 citations

Journal ArticleDOI
TL;DR: In this paper, an initial value problem concerning the motion of an incompressible, electrically conducting, viscoelastic Oldroyd-B fluid bounded by an infinite rigid nonconducting plate is solved.
Abstract: An initial value problem concerning the motion of an incompressible, electrically conducting, viscoelastic Oldroyd-B fluid bounded by an infinite rigid non-conducting plate is solved. The unsteady motion is generated impulsively from rest in the fluid due to half rectified sine pulses subjected on the plate in its own plane in presence of an external magnetic field. It is assumed that no external electric field is acting on the system and the magnetic Reynolds number is very small. The operational method is used to obtain exact solutions for the fluid velocity and the shear stress on the wall. Quantitative analysis of the results is presented with a view to disclose the simultaneous effects of the external magnetic field and the fluid elasticity on the flow and the wall shear stress for different periods of pulsation of the plate. It is also shown that the classical and hydromagnetic Rayleigh solutions appear as the limiting cases of the present analysis.

4 citations


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TL;DR: In this paper, a mathematical model for the two-dimensional boundary layer flow of an Oldroyd-B fluid is presented, where the obtained partial differential equations are reduced to an ordinary differential equation by a suitable transformation.
Abstract: In this paper, the mathematical model for the two-dimensional boundary layer flow of an Oldroyd-B fluid is presented. The developed equations are used to discuss the problem of two-dimensional flow in the region of a stagnation point over a stretching sheet. The obtained partial differential equations are reduced to an ordinary differential equation by a suitable transformation. The obtained equation is then solved using a finite difference method. The influence of the pertinent fluid parameters on the velocity is discussed through graphs. The behaviour of f ″(0) is also investigated with changes in parameter values. It is observed that an increase in the relaxation time constant causes a reduction in the boundary layer thickness. To the best of our knowledge, this type of solution for an Oldroyd-B fluid is presented for the first time in the literature.

77 citations

Journal ArticleDOI
TL;DR: In this paper, a sharp relationship between the squared norm of the second fundamental form and the warping function in terms of the slant angle is established, and the equality case is also considered.
Abstract: Recently, Sahin studied the warped product semi-slant submanifolds of locally product Riemannian manifolds. In this paper, we obtain some geometric properties of such submanifolds with an example. Also, we establish a sharp relationship between the squared norm of the second fundamental form and the warping function in terms of the slant angle. The equality case is also considered.

28 citations

Journal ArticleDOI
06 Jul 2015-PLOS ONE
TL;DR: This paper studies the unsteady magnetohydrodynamics thin film flow of an incompressible Oldroyd-B fluid over an oscillating inclined belt making a certain angle with the horizontal using two efficient techniques namely the Optimal Homotopy Asymptotic Method (OHAM) and HPM.
Abstract: This paper studies the unsteady magnetohydrodynamics (MHD) thin film flow of an incompressible Oldroyd-B fluid over an oscillating inclined belt making a certain angle with the horizontal. The problem is modeled in terms of non-linear partial differential equations with some physical initial and boundary conditions. This problem is solved for the exact analytic solutions using two efficient techniques namely the Optimal Homotopy Asymptotic Method (OHAM) and Homotopy Perturbation Method (HPM). Both of these solutions are presented graphically and compared. This comparison is also shown in tabular form. An excellent agreement is observed. The effects of various physical parameters on velocity have also been studied graphically.

25 citations

Journal ArticleDOI
TL;DR: In this paper, a two-phase unsteady MHD Couette flow between two parallel infinite plates has been studied taking the viscosity effect of the two phases into consideration, and the solution obtained is validated by assenting comparisons with the closed form solutions obtained for the steady states which have been derived separately and also by the implicit finite difference method.

24 citations