Stokes' Second Problem for Magnetohydrodynamics Flow in a Burgers' Fluid: The Cases γ = λ2/4 and γ>λ2/4

Abstract

The present work is concerned with exact solutions of Stokes second problem for magnetohydrodynamics (MHD) flow of a Burgers' fluid. The fluid over a flat plate is assumed to be electrically conducting in the presence of a uniform magnetic field applied in outward transverse direction to the flow. The equations governing the flow are modeled and then solved using the Laplace transform technique. The expressions of velocity field and tangential stress are developed when the relaxation time satisfies the condition γ = λ2/4 or γ>λ2/4. The obtained closed form solutions are presented in the form of simple or multiple integrals in terms of Bessel functions and terms with only Bessel functions. The numerical integration is performed and the graphical results are displayed for the involved flow parameters. It is found that the velocity decreases whereas the shear stress increases when the Hartmann number is increased. The solutions corresponding to the Stokes' first problem for hydrodynamic Burgers' fluids are obtained as limiting cases of the present solutions. Similar solutions for Stokes' second problem of hydrodynamic Burgers' fluids and those for Newtonian and Oldroyd-B fluids can also be obtained as limiting cases of these solutions.

Flows with Slip of Oldroyd-B Fluids over a Moving Plate

“…Also, if in our results we consider ( ) = sin( ) or ( ) = cos( ), (32)-(34) become equivalent to the results of Khaled and Vafai (see [22], Eqs. (8), (9), (10), (16)) and to the results obtained by Hayat et al (see [23], Eqs. (13), (14), with = 0 and → ∞).…”

“…Furthermore we suppose that the Laplace transform of the function exists. In the case of parallel flow along the -axis, the velocity vector iŝ = ( ( , ), 0, 0) whereas [15][16][17] lead us to the following governing equation:…”

Flow of an Erying-Powell fluid over a stretching sheet in presence of chemical reaction

“…The numerical solution for eqs. (7)- (9) for different values of non-Newtonian fluid parameters K and , Γ Schimidt number, and chemical reaction parameter subject to the boundary conditions (9) is obtained by the most efficient numerical shooting technique with Runge-Kutta-Fehlberg integration scheme. In this method the coupled non-linear two point boundary value problem is transformed into initial value problem which is a first order system and is obtained by defining new variables.…”

“…Mathematical systems for non-Newtonian fluids are of higher order and complicated in comparison to the Newtonian fluids. Despite of all these difficulties and complexities, several researchers in the field are involved in making valuable contributions to the studies of non-Newtonian fluid dynamics [1][2][3][4][5][6][7][8][9][10]. The non-Newtonian fluid models vary in their complexity and ability to capture different physical phenomena.…”

Unsteady Flows of a Generalized Fractional Burgers’ Fluid between Two Side Walls Perpendicular to a Plate

“…So it is expected that the Burgers' model can better capture the complex rheological characteristics of many real fluids than other models. Until now, the Burgers' model has been successfully applied in many studies [10][11][12][13][14][15].…”