Twice Order Slip on the Flows of Fractionalized MHD Viscoelastic Fluid

Muhammad Jamil, Israr Ahmed

Abstract

The objective of this article is to investigate the effect of twice order slip on the MHD flow of fractionalized Maxwell fluid through a permeable medium produced by oscillatory movement of an infinite bottom plate. The governing equations are developed by fractional calculus approach. The exact analytical results for velocity field and related shear stress are calculated using Laplace transforms and presented in terms of generalized M-function satisfying all imposed initial and boundary conditions. The flow results for fractionalized Maxwell, traditional Maxwell and Newtonian fluid with and without slips, in the presence and absence of magnetic and porous effects are derived as the limiting cases. The impact of fractional parameter, slip coefficients, magnetic force and porosity parameter over the velocity field and shear stress are discussed and analyzed through graphical illustrations. The outcomes demonstrate that the speed comparing to streams with slip condition is lower than that for stream with non-slip conditions, and the speed with second-slip condition is lower than that with first-order slip condition.

Keywords

Twice order slip, MHD Maxwell fluid, fractional derivative, unsteady flow, M-function, velocity field, shear stress, Laplace transforms.

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