S. Asghar

PERISTALTIC TRANSPORT OF A THIRD-ORDER FLUID IN A CIRCULAR CYLINDRICAL TUBE

The effect of a third-order fluid on the peristaltic transport is analysed in a circular cylindrical tube, such as some organs in the living body. The third-order flow of an incompressible fluid in a circular cylindrical tube, on which an axisymmetric travelling sinusoidal wave is imposed, is considered. The wavelength of the peristaltic waves is assumed to be large compared to the tube average radius, whereas the amplitude of the wave need not be small compared to the average radius. Both analytic (perturbation) and numerical solutions are given. For the perturbation solution, a systematic approach based on an asymptotic expansion of the solution in terms of a small Deborah number is used and solutions up to the first order are presented in closed forms. The numerical solution, valid for any Deborah number, represents a new approach to peristaltic flows, and its features illuminate the physical behaviour much more than the analytical research on this problem. Comparison is made between the analytic (perturbation) and numerical results. Furthermore, the obtained results could also have applications to a range of peristaltic flows for a variety of non-Newtonian fluids such as aqueous solutions of high-molecular weight polyethylene oxide and polyacrylamide.

Peristaltic transport of an Oldroyd-B fluid in a planar channel

The effects of an Oldroyd-B fluid on the peristaltic mechanism are examined under the long wavelength assumption. Analytical expressions for the stream function, the axial velocity, and the pressure rise per wavelength are obtained up to the second order in the dimensionless wave number. The effects of the various parameters of interest on the flow are shown and discussed.

Some unsteady unidirectional flows of a non-Newtonian fluid

Abstract Exact analytic solutions for a class of unsteady unidirectional flows and the frictional forces of an incompressible second grade fluid are obtained. The periodic Poiseuille flow and frictional force due to an oscillating pressure gradient are examined. The flows and the frictional forces between two parallel boundaries are also studied.

Magnetohydrodynamic flow due to non-coaxial rotations of a porous oscillating disk and a fluid at infinity

Abstract An exact solution of the Navier–Stokes equations is constructed for the case of flow due to non-coaxial rotations of a porous disk and a fluid at infinity. The disk executes oscillations in its own plane and is non-conducting. The viscous fluid is incompressible and electrically conducting. Analytical solution is established by the method of Laplace transform. The velocity fields are obtained for the cases when the angular velocity is greater than, smaller than or equal to the frequency of oscillations. The structure of the steady and the unsteady velocity fields are investigated. The difficulty of the hydrodynamic steady solution associated with the case of resonant frequency is resolved in the present analysis.

Cylindrical wave diffraction by a perfectly conducting strip in a homogeneous bi-isotropic medium

Abstract The diffraction of an electromagnetic wave by a perfectly conducting strip in a bi-isotropic medium is studied. The problem is solved using integral transforms, the Wiener-Hopf technique and asymptotic methods. The diffracted field is found to be the sum of the fields produced by the two edges of the strip and an interaction field.

Homotopy Analysis for Stagnation Slip Flow and Heat Transfer on a Moving Plate

The development of two-dimensional or axisymmetric stagnation flow of an incompressible viscous fluid over a moving plate with partial slip has been investigated. The effects of partial slip on the flow and heat transfer characteristics are considered. The equations of conservation of mass, momentum, and energy, which govern the flow and heat transfer, are solved analytically using homotopy analysis method. The convergence of the series solution is analyzed explicitly. Comparison of the present homotopy results is made with the existing numerical and asymptotic solution (Wang, 2006, “Stagnation Slip Flow and Heat Transfer on a Moving Plate ,” Chem. Eng. Sci., 23, pp. 7668–7672) and an excellent agreement is achieved.

On semi-inverse solutions for the time-dependent flows of a second-grade fluid

This paper deals with analytical solutions for the time-dependent equations arising in a second-grade fluid. The solutions have been developed by assuming certain forms of the stream function. Expressions for velocity components are obtained for flows in plane polar, axisymmetric cylindrical, and axisymmetric spherical polar coordinates. The obtained solutions are compared with existing results.

EXACT SOLUTIONS FOR MAGNETOHYDRODYNAMIC FLOW IN A ROTATING FLUID

An analytical solution is obtained for the flow due to solid-body rotations an oscillating porous disk and of a fluid at infinity. Neglecting the induced magnetic field, the effects of the transversely applied magnetic field on the flow are studied. Further, the flow confined between two disks is also discussed. It is found that an infinite number of solutions exist for the flow confined between two disks.

Stagnation-Point Flow by an Exponentially Stretching Sheet in the Presence of Viscous Dissipation and Thermal Radiation

AbstractThe stagnation-point flow of viscous fluid induced by an exponentially stretching sheet is investigated in the presence of viscous dissipation and thermal radiation. Appropriate transformations reduced the partial differential equation into the ordinary differential equations. The resulting nonlinear problems are computed. Nusselt number values are tabulated. Comparative study between present and previous attempts made in a limiting sense. The flow quantities through pertinent parameters are examined.

Scattering of a Spherical Gaussian Pulse Near an Absorbing Half Plane

Abstract The space–time acoustic wave diffraction due to a spherical Gaussian pulse near an absorbing half plane introducing the Kutta–Joukowski condition (wake condition) is considered. The temporal Fourier transform is used to calculate the diffracted field. It is found that the field produced by the Kutta–Joukowski condition will be substantially in excess of that in its absence when the source is near the edge.