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Homotopy simulation of non-Newtonian Spriggs fluid flow over a flat plate with oscillating motion

Ray A. K., Vasu B., Gorla R. S. R.

International Journal of Applied Mechanics and Engineering

2019

Vol. 24, no. 2

359--385

An incompressible flow of a non-Newtonian Spriggs fluid over an unsteady oscillating plate is investigated using the Homotopy Analysis Method (HAM). An analytic solution of sine and cosine oscillations of the plate has been obtained. The similarity transformation is introduced to reduce the governing partial differentia equations into a single non-linear dimensionless partial differential equation. The effects of the power index of Spriggs fluid and convergence control parameter of HAM for the flow are studied extensively. The range of the convergence control parameter for convergence of series solution for different values of the power index of Spriggs fluid is obtained. The solution for a Spriggs fluid is noticeably different from the solution obtained for a Newtonian fluid. The influences of the shear thinning and shear thickening fluid on the velocity profile are shown graphically. The transient flow effect is higher for non-Newtonian Spriggs fluid than that of a Newtonian fluid. It is also observed that the interval to reach the steady state for the cosine case is less than the sine case. The applications of Stokes’ second problem have been widely found in the variety of fields of biomedical, medical, chemical, micro and nanotechnology.

Oscillating magnetohydrodynamic flow past a rigid plane wall

Poria S., Mazumdar H. P.

Journal of Technical Physics

2002

Vol. 43, no 3

343-350

In this paper, the effects of a magnetic field acting perpendicularly to the direction of an oscillatory, viscous, conducting, incompressible fluid stream past a fixed plane wall is investigated. The problem is first converted to the Stokes second problem by introducing a new coordinate system and prescribing the appropriate forms for the pressure gradient corresponding to two sets of boundary and initial conditions. Solutions to the problem are then obtained by invoking an invariance principle, and computed numerically for different values of a magnetic parameter. The effects of the transversal magnetic field on the velocity profiles are finally discussed.