Hydromagnetic flow of viscous incompressible fluid past a wedge with permeable surface

Abstract

Flow of a viscous, electrically conducting fluid past a wedge having permeable surface is analyzed. A constant transpiration through the wedge surface is assumed. The equations governing the flow and the magnetic field being reduced to local non-similarity equations are solved numerically. The implicit finite difference method, as well as the local non-similarity method is being used in finding the solutions of the reduced equations against the transpiration parameter, ξ. Perturbation solutions for small and large ξ values are also obtained. Effect of the physical parameters, such as, the magnetic force parameter, S, the magnetic Prandtl number, Pm and free stream velocity gradient, n, on the local skin-friction coefficient, f (0, ξ), and the local current density coefficient, g (0, ξ), are shown graphically. It is found that the perturbation solutions agreed excellently with other solutions at the two extreme ranges of ξ values. From the present investigation we further observe that, incase of withdrawal of fluid both the momentum and magnetic boundary layers decrease with the increase of ξ. On the other hand these layers increase with ξ value when fluid is being injected trough the surface. Further we notice that there is an onset of reverse flow in the down-stream region in case of blowing of fluid and the starting point of this flow, approximately, is ξ = −0.6. 175Later, Davies [3] investigated the boundary layer flow of viscous, electrically conducting liquid in the neighborhood of a semi infinite flat plate, considering the fact that the flow is opposed by magnetodynamic pressure gradient. Further assumptions were considered as the flat plate was non-magnetic and magnetic field well away from the plate was parallel to the surface. This is an extension of Falkner and Skan problem for electrically conducting fluid. In this analysis the adverse magnetodynamic pressure was taken of the form Cx n . Considering this fact an investigation has been made of viscous stress at the surface and also critical value of C and n, when this viscous stress vanishes. The Falkner-Skan problem to magnetohydrodynamic flow past a nonconducting body by imposing a magnetic field whose lines of force are parallel to the undisturbed streamlines had been studied by Gribben [4]. Later, Hildyard [5] found that the magnetic-field boundary condition used by Gribben was inappropriate. After doing the necessary correction he obtained the asymptotic series solutions for large and small values of the magnetic Prandtl number.An initial attempt to consider heat transfer problem for such flows has been made by Ramamoorthy [6]. A more thorough study of the above problem, which takes into account both viscous and Ohmic heating is attempted by Tan et al. [7]. The same problem was then extended by Tan [8] including the mass transfer across the surface. Later, Chawla [9] studied the effect of free stream fluctuations on the flow over a semi-infinite plate, with an aligned magnetic field, using von Kármán-Pohlhausen technique.Since the boundary layer ...

MHD boundary layer radiative, heat generating and chemical reacting flow past a wedge moving in a nanofluid

“…The solutions remain valid and correct and the reviewer is referred to the following references corroborating this approach- Khan and Gorla [44] and Mahmood et al . [45]. In this context, M is a local magnetic body force number (Mahmood et al .…”

“…In this context, M is a local magnetic body force number (Mahmood et al . [45]) and λ T is therefore a function of local thermal Grashof number and λ m is a function of local species Grashof number (Khan and Gorla [44]).…”

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