We have formulated and solved the boundary-value problem of steady, symmetric and onedimensional electro-osmotic flow of a micropolar fluid in a uniform rectangular microchannel, under the action of a uniform applied electric field. The Helmholtz-Smoluchowski equation and velocity for micropolar fluids have also been formulated. Numerical solutions turn out to be virtually identical to the analytic solutions obtained after using the Debye-Hückel approximation, when the microchannel height exceeds the Debye length, provided that the zeta potential is sufficiently small in magnitude. For a fixed Debye length, the mid-channel fluid speed is linearly proportional to the microchannel height when the fluid is micropolar, but not when the fluid is simple Newtonian. The stress and the microrotation are dominant at and in the vicinity of the microchannel walls, regardless of the microchannel height. The midchannel couple stress decreases, but the couple stress at the walls intensifies, as the microchannel height increases and the flow tends towards turbulence.
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.
In this work, we investigate the the problem of an unsteady tank drainage while considering an isothermal and incompressible Ellis fluid. Exact solution is gotten for a resulting non-linear PDE (partial differential equation)subject to proper boundary conditions-. The special cases such as Newtonian, Power law, and as well as Bingham solution are retrieved from this suggested model of Ellis fluid. Expressions for velocity profile, shear stress on the pipe, volume flux, average velocity, and the relationship between the time vary with the depth of a tank and the time required for complete drainage are obtained. Impacts of different developing parameters on velocity profile vz and depth H(t) are illustrated graphically. The analogy of the Ellis, power law, Newtonian, and Bingham Plastic fluids for the relation of depth with respect to time, unfold that the tank can be empty faster for Ellis fluid as compared to its special cases.
In this study, the lubrication approximation theory is used to provide numerical results in roll coating over a moving flat porous web. The rate of injection at the roll surface is assumed equal to the rate of suction on the web. The second-grade fluid is used, which reduces with appropriate modifications to the Newtonian fluid model. Results are obtained in such quantities as coating thickness, split location, pressure distribution, stresses, forces, the power input to the roll, and adiabatic temperature rise between the coating roll and the coated web. Some of these results are shown graphically. It is found that material parameters and Reynolds number are the parameters to control flow rate, coating thickness separation points, separation force, power input, and pressure.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.