A New Theoretical Approach of Wall Transpiration in the Cavity Flow of the Ferrofluids

Abstract

An idea of permeable (suction/injection) chamber is proposed in the current work to control the secondary vortices appearing in the well-known lid-driven cavity flow by means of the water based ferrofluids. The Rosensweig model is conveniently adopted for the mathematical analysis of the physical problem. The governing equation of model is first transformed into the vorticity transport equation. A special finite difference method in association with the successive over-relaxation method (SOR) is then employed to numerically simulate the flow behavior. The effects of intensity of magnetic source (controlled by the Stuart number), aspect ratio of the cavity, rate of permeability (i.e., α p = V 0 U ), ratio of speed of suction/injection V 0 to the sliding-speed U of the upper wall of a cavity, and Reynolds number on the ferrofluid in the cavity are fully examined. It is found that the secondary vortices residing on the lower wall of the cavity are dissolved by the implementation of the suction/injection chamber. Their character is dependent on the rate of permeability. The intensity of magnetic source affects the system in such a way to alter the flow and to transport the fluid away from the magnetic source location. It also reduces the loading effects on the walls of the cavity. If the depth of cavity (or the aspect ratio) is increased, the secondary vortices join together to form a single secondary vortex. The number of secondary vortices is shown to increase if the Reynolds number is increased for both the clear fluid as well as the ferrofluids. The suction and injection create resistance in settlement of solid ferroparticles on the bottom. The results obtained are validated with the existing data in the literature and satisfactory agreement is observed. The presented problem may find applications in biomedical, pharmaceutical, and engineering industries.

Thermal Transport in Radiative Nanofluids by Considering the Influence of Convective Heat Condition

“…In this regard, a study is reported in [29] by considering the flow inside the cavity filled with nanoliquid. The authors treated the model numerically and authenticate their results with previously published work.…”

Radiative unsteady hydromagnetic 3D flow model for Jeffrey nanofluid configured by an accelerated surface with chemical reaction

“…The resulting dimensionless equations (12) to (15), together with boundary constraints (16), are highly nonlinear, which commences a challenge to recommend the numerical or analytical solution. The homotopy analysis method is the best analytic technique to attain a series solution of such nonlinear partial differential expressions with excellent accuracy.…”

“…8 The interesting shape of nanoparticles influenced by Hall current, exponential heat source, and mixed convection features due to rotating frame was numerically examined by Mahanthesh et al 9 The rheological outcomes for Eyring-Powell nanomaterial with activation energy and slip impact were assessed by Alwatban et al 10 Khan et al 11 focused on the rheological features of magnetized couple stress nanofluid in which numerical simulations were performed with the implementation of shooting algorithm with convincing accuracy. Siddiqui and Turkyilmazoglu 12 considered the consequences of ferrofluids in a lid-driven cavity flow subjected to the suction/injection characteristics. The significance of chemical reaction and activation energy in the flow of magnetized Sisko nanofluid was analyzed by Ahmad et al 13 Tlili et al 14 formulated the Oldroyd-B nanofluid model with activation energy over a stretched cylinder.…”

Numerical Study on the Static Cooling of Waxy Crude Oil in the Vault Tank

“…However, Turkyilmazoglu [26], [27] proposed an implicit numerical scheme for solving transient flows based on the spectral Chebyshev collocation technique in the direction normal to the disk and forward marching in time, which can better solve the magnetohydrodynamic time-dependent of von Karman flow. And Abid and Turkyilmazoglu [28] employ a special finite dierence method in association with the successive over-relaxation method (SOR) to numerically simulate the flow behavior. These researches definitely provide inspirations for the numerical simulation in this paper.…”