Abstract
An analysis is carried out to study the heat transfer in unsteady two-dimensional boundary layer flow of a magnetohydrodynamics (MHD) second grade fluid over a porous oscillating stretching surface embedded in porous medium. The flow is induced due to infinite elastic sheet which is stretched periodically. With the help of dimensionless variables, the governing flow equations are reduced to a system of non-linear partial differential equations. This system has been solved numerically using the finite difference scheme, in which a coordinate transformation is used to transform the semi-infinite physical space to a bounded computational domain. The influence of the involved parameters on the flow, the temperature distribution, the skin-friction coefficient and the local Nusselt number is shown and discussed in detail. The study reveals that an oscillatory sheet embedded in a fluid-saturated porous medium generates oscillatory motion in the fluid. The amplitude and phase of oscillations depends on the rheology of the fluid as well as on the other parameters coming through imposed boundary conditions, inclusion of body force term and permeability of the porous medium. It is found that amplitude of flow velocity increases with increasing viscoelastic and mass suction/injection parameters. However, it decreases with increasing the strength of the applied magnetic field. Moreover, the temperature of fluid is a decreasing function of viscoelastic parameter, mass suction/injection parameter and Prandtl number.
Highlights
Many fluids in industry and technology do not obey the Newton's law of viscosity and are usually classified as a non-Newtonian fluids
The boundary layer flow and heat transfer analysis of these fluids on a continuously moving surface has wide range of applications in engineering and industrial processes, for example, manufacturing of plastic sheets, artificial fibers and polymeric sheets, plastic foam processing, extrusion of polymer sheet from a die, heat materials travelling between a feed roll and many others
For analytical treatment homotopy analysis method was applied while numerical solution was based on finite difference technique
Summary
Many fluids in industry and technology do not obey the Newton's law of viscosity and are usually classified as a non-Newtonian fluids. The boundary conditions (4) and (5) take the following form fyð0; tÞ 1⁄4 sin t; f ð0; tÞ 1⁄4 g; yð0; tÞ 1⁄4 1; ð9Þ fyð; tÞ 1⁄4 0; fyyð; tÞ 1⁄4 0; yð; tÞ 1⁄4 0: ð10Þ pffiffiffiffi In above equations g 1⁄4 vw= nb is the dimensionless mass suction/injection parameter, K = bk0 / νρ in the non-dimensional viscoelastic parameter, S ω / b is the ratio of the oscillation frequency of the sheet to its stretching rate, Pr = μcp / k is the Prandtl number and b 1⁄4 sB20=rb þ u=kb is a combined parameter due to magnetic field and the permeability of the porous medium. We construct a semi-infinite time difference for f and θ, respectively, and make sure that only linear equations for the new time step (n + 1) need to be solved:
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