Resonance instabilities in the boundary-layer flow over a rotating-disk under the influence of a uniform magnetic field

Abstract

Instabilities due to resonating waves in the three-dimensional incompressible viscous/inviscid rotating-disk boundary-layer flow are investigated numerically. The influence of a normal magnetic field on the resonances leading, respectively, to the direct spatial instability, the direct temporal instability and the absolute instability are worked out, in an attempt to determine the physically most significant one. It is found that the magnetic field has a stabilizing influence on all the resonance mechanisms outlined. However, the direct spatial-resonance-instability mechanism persists for low Reynolds numbers, when the flow is still in the laminar regime. Thus, attention should be directed to this specific instability mechanism, which offers a strong route to transition to turbulence by means of triggering the nonlinearity.

Effect of Hall current on the MHD Fluid Flow and Heat Transfer due to a rotating disk with uniform radial electric field

“…In many boundary layer problems different methods have been applied to solve the system of the equations. For example, Sahoo [17], Attia [2], Jasmine & Gajjar [12] and Turkyilmazoglu [22], [25] reached their results using finite-difference method, a special technique, and also Chebyshev collocation method respectively.…”

“…Following this, we believe that, it would be interesting to study the effect of the electric field and also Hall parameter on instability mechanisms over rotating disk. For similar works, we refer to Jasmine &Gajjar [12] and Turkyilmazoglu [25]…”

“…The study has been continued by Attia & Aboul-Hassan in [4] and by Siddiqui, Rana & Naseer in [19]. The case without the Hall effect on a rotating infinite disk has been investigated in [1], [6], [8], [9], [12], [14], [15], [16], [19], [20], [21], [22], [23], [24], and [25].…”

“…Cochran [7] and Benton [5] have considered by Kármán [13], they investigated the steady motion of an incompressible viscous fluid. The effect of uniform magnetic field on the flow over a rotating infinite disk has been studied by many researchers [8], [12], [19], [20], [22], [23], [24], [25]. Hall effect has been taken into consideration in some of the works in the literature.…”

Hall impact on the MHD fluid flow and heat transfer with uniform radial electric field due to a stretching rotating disk

“…Sparrow & Cess [30], Riley [27], Kumar, Thacker & Watson [22] studied the effects of magnetic field to the heat transfer over a infinite rotating disk. Many researchers followed them in [9], [20], [29], [30], [33], [34], [35], [36], [37], [38] and [39]. Ultimately, effects of the uniform radial electric field have been considered in some works in the literature [33], [38] and [39].…”