Imran Siddique - Academia.edu (original) (raw)

Papers by Imran Siddique

International Journal of Applied Mechanics, 2010

ABSTRACT The velocity field, the longitudinal and the normal tensions corresponding to the axial ... more ABSTRACT The velocity field, the longitudinal and the normal tensions corresponding to the axial flow of an Oldroyd-B fluid due to an infinite circular cylinder subject to a longitudinal time-dependent stress are determined by means of the Laplace and finite Hankel transforms. The similar solutions for Maxwell, second grade or Newtonian fluids have been obtained as particular cases of the solutions for Oldroyd-B fluids. Finally, by using dimensionless variables, some characteristics of the motion as well as the influence of the material parameters on the behavior of fluid are shown by graphical illustrations.

Communications in Nonlinear Science and Numerical Simulation, 2011

In this note the velocity field and the associated tangential stress corresponding to the rotatio... more In this note the velocity field and the associated tangential stress corresponding to the rotational flow of a generalized second grade fluid within an infinite circular cylinder are determined by means of the Laplace and Hankel transforms. At time t = 0 the fluid is at rest and the motion is produced by the rotation of the cylinder, around its axis, with the angular velocity Ωt. The velocity field and the adequate shear stress are presented under integral and series forms in terms of the generalized G-functions. Furthermore, they are presented as a sum between the Newtonian solutions and the adequate non-Newtonian contributions. The corresponding solutions for the ordinary second grade fluid and Newtonian fluid are obtained as particular cases of our solutions for β = 1, respectively α = 0 and β = 1.

International Journal of Non-linear Mechanics, 2009

New exact solutions corresponding to the second problem of Stokes for Maxwell fluids have been es... more New exact solutions corresponding to the second problem of Stokes for Maxwell fluids have been established by means of Laplace transforms. For large times, these solutions reduce to the well-known steady-state solutions which are periodic in time and independent of the initial conditions. Furthermore, the transient solutions are in accordance with the previous solutions obtained using the Fourier sine transform. The required time to get the steady-state is determined by graphical illustrations. This time decreases if the frequency of the velocity increases. The effects of the material parameters on the decay of the transients in time are also investigated by graphs.

Acta Mechanica Sinica, 2009

This paper deals with the rotational flow of a generalized second grade fluid, within a circular ... more This paper deals with the rotational flow of a generalized second grade fluid, within a circular cylinder, due to a torsional shear stress. The fractional calculus approach in the constitutive relationship model of a second grade fluid is introduced. The velocity field and the resulting shear stress are determined by means of the Laplace and finite Hankel transforms to satisfy all imposed initial and boundary conditions. The solutions corresponding to second grade fluids as well as those for Newtonian fluids are obtained as limiting cases of our general solutions. The influence of the fractional coefficient on the velocity of the fluid is also analyzed by graphical illustrations.

Computers & Mathematics With Applications, 2011

The steady flow of a non-Newtonian fluid when slippage between the plate and the fluid occurs is ... more The steady flow of a non-Newtonian fluid when slippage between the plate and the fluid occurs is considered. The constitutive equations of the fluid are modeled for a fourth-grade non-Newtonian fluid with partial slip; they give rise to nonlinear boundary value problems. Analytical solutions are obtained using powerful analytic techniques for solving nonlinear problems, homotopy perturbation and optimal homotopy asymptotic methods. The results obtained are compared with the numerical results and it is shown that solutions exist for all values of the non-Newtonian parameters. The solutions valid for the no-slip condition for all values of the non-Newtonian parameters can be derived as special cases of the present analysis. Finally the solutions are discussed using a graphical approach.

Computers & Mathematics With Applications, 2008

Exact and approximative expressions for dissipation, the power due to the shear stress at the wal... more Exact and approximative expressions for dissipation, the power due to the shear stress at the wall and the boundary layer thickness corresponding to the unsteady motion of a second-grade fluid, induced by an infinite plate subject to a shear stress, are established. For α 1 −→ 0, similar results for Newtonian fluids performing the same motion are obtained. The results that have been obtained here are different to those corresponding to the Rayleigh-Stokes problem. A series solution for the velocity field is also determined. Its form, as was to be expected, is identical to that resulting from the general solution using asymptotic approximations.

$Research paper thumbnail of Helical flows of an Oldroyd-B fluid with fractional derivatives in an annular pipe$

Communications in Nonlinear Science and Numerical Simulation

$Research paper thumbnail of A note on the unsteady torsional sinusoidal flow of fractional viscoelastic fluid in an annular cylinder$

Journal of King Saud University - Science, 2011

In this note, the velocity field and the associated shear stress corresponding to the torsional o... more In this note, the velocity field and the associated shear stress corresponding to the torsional oscillatory flow of a generalized second grade fluid, between two infinite coaxial circular cylinders, are determined by means of Laplace and Hankel transforms. Initially both cylinders and fluid are at rest and then the two cylinders suddenly start torsional oscillations around their common axis with simple harmonic motions having angular frequencies x 1 and x 2 . The solutions that have been obtained are presented under integral and series forms in terms of the generalized G and R functions and satisfy the governing differential equation and all imposed initial and boundary conditions. The respective solutions for the motion between the cylinders, when one of them is at rest, can be obtained from our general solutions. Furthermore, the corresponding solutions for the similar flow of ordinary second grade fluid and Newtonian fluid are also obtained as limiting cases of our general solutions. At the end, flows corresponding to the Newtonian, second grade and generalized second grade fluids are shown graphically by plotting velocity profiles.

Nonlinear Analysis-real World Applications

In this paper, we have determined the exact starting solutions of velocity field and associated s... more In this paper, we have determined the exact starting solutions of velocity field and associated shear and normal stresses corresponding to the unsteady flow of a Maxwell fluid, due to torsional oscillations of two infinite coaxial circular cylinders by means of Laplace and Hankel transforms. The fluid is situated at rest in an annular region between the cylinders. Suddenly both

Physical Review B, 2007

On the basis of the Kadanoff-Baym (KB) varient of the time dependent Green's function method a ne... more On the basis of the Kadanoff-Baym (KB) varient of the time dependent Green's function method a new ansatz for the approximation of a spectral function is offered. The ansatz possesses all the advantages of quasiparticle (QP) and extended quasiparticle (EQP) approximations and satisfies the KB equation for a spectral function in the case of slightly nonequilibrium system when disturbances in space and time are taken into consideration in the gradient approximation. This feature opens new opportunities for the microscopic derivation of the Landau kinetic equation for the quasiparticle distribution function of the normal fermi liquid and provides the widening of these equation's temperature rang of validity.

We give a number new examples analytically and numerically to confirm the Kohler conjecture. It t... more We give a number new examples analytically and numerically to confirm the Kohler conjecture. It turned out that for a rather large class of nonnegative functions the equality (A) hold.

Mathematical Biosciences, 2010

Richardson's phenomenological mathematical model of the thrombi growth in microvessels is extende... more Richardson's phenomenological mathematical model of the thrombi growth in microvessels is extended to describe the realistic features of the phenomenon. The main directions of the generalization of Richardson's model are: (1) the dependence of platelet activation time on the distance from the injured vessel wall; (2) the non-homogeneity of the platelet distribution in blood flow in the vicinity of the vessel wall;