A. M. Siddiqui

Thin Film Flow of a Third Grade Fluid on a Moving Belt by He's Homotopy Perturbation Method

The present paper analyses a flow problem where a third grade fluid forms a thin film on a vertically moving belt. The velocity field is solved from the nonlinear governing equation by both the traditional perturbation technique and the homotopy perturbation method proposed by Ji-Huan He. Comparison of the obtained results shows that the homotopy perturbation method can completely overcome the limitations arising in traditional perturbation methods. The expressions for velocity distribution, volume flux and average velocity are also obtained.

Some simple flows of an Oldroyd-B fluid

Exact solutions for the following five problems of an Oldroyd-B fluid are obtained. (i) Stokes problem (ii) modified Stokes problem (iii) the time-periodic Poiseuille flow due to an oscillating pressure gradient (iv) the non-periodic flows between two boundaries, and (v) symmetric flow with an arbitrary initial velocity. Some interesting flows caused by certain special oscillations are also obtained. The physical interpretation of the results is presented.

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.

Couette and Poiseuille Flows for Non-Newtonian Fluids

This paper investigates the Couette flow, plug flow, Poiseuille flow, generalized Couette flow of a fourth grade fluid, and a Sisko fluid. The homotopy perturbation method is applied to solve the resulting non-linear differential equations. Results obtained for Sisko fluid are compared with those obtained for a fourth grade fluid and it shows that the results for a fourth grade fluid are included in the results for a Sisko fluid as a special case.

Application of Homotopy Perturbation Method to Squeezing Flow of a Newtonian Fluid

Axisymmetric viscous flow, generated by two large parallel plates slowly approaching each other, is studied where the effects of fluid inertia are taken into account. The problem is analyzed using the traditional perturbation method and Hes homotopy perturbation method. The results obtained are compared, showing that the homotopy perturbation method appears to be more effective and easy to implement.

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.

Peristaltic motion of a Johnson-Segalman fluid in a planar channel

This paper is devoted to the study of the two-dimensional flow of a Johnson-Segalman fluid in a planar channel having walls that are transversely displaced by an infinite, harmonic travelling wave of large wavelength. Both analytical and numerical solutions are presented. The analysis for the analytical solution is carried out for small Weissenberg numbers. (A Weissenberg number is the ratio of the relaxation time of the fluid to a characteristic time associated with the flow.) Analytical solutions have been obtained for the stream function from which the relations of the velocity and the longitudinal pressure gradient have been derived. The expression of the pressure rise over a wavelength has also been determined. Numerical computations are performed and compared to the perturbation analysis. Several limiting situations with their implications can be examined from the presented analysis.

Periodic unsteady flows of a non-Newtonian fluid

SummaryExact analytic solutions for the flow of non-Newtonian fluid generated by periodic oscillations of a rigid plate are discussed. Some interesting flows caused by certain special oscillations are also obtained.

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.

Exact peristaltic flow in tubes with an endoscope

Peristaltic flow of a Jeffrey fluid through the gap between concentric uniform tubes has been investigated with particular reference to an endoscope effects. The velocity components and axial pressure gradient are obtained analytically. Numerical integration is performed in order to analyze the pressure rise and frictional forces on the inner and outer tubes. The obtained results are compared with the earlier studies existing in the literature.