Three-dimensional Couette Flow Research Articles

Three-Dimensional Couette Flow of a Second-Grade Fluid Along Periodic Injection/Suction

This work explores the three-dimensional laminar flow of an incompressible second-grade fluid between two parallel infinite plates. The assumed suction velocity comprises a basic steady dispersal with a superimposed weak transversally fluctuating distribution. Because of variation of suction velocity in transverse direction on the wall, the problem turns out to be three-dimensional. Analytic solutions for velocity field, pressure and skin friction are presented and effects of dimensionless parameters emerging in the model are discussed. It is observed that the non-Newtonian parameter plays dynamic part to rheostat the velocity component along main flow direction.

Magnetohydrodynamic Three-Dimensional Couette Flow of a Second-Grade Fluid with Sinusoidal Injection/Suction

A mathematical model for magnetohydrodynamic (MHD) three-dimensional Couette flow of an incompressible second-grade fluid is developed and analyzed theoretically. The application of normal sinusoidal injection at the lower fixed plate and its equivalent deduction by suction through the uniformlymoving upper plate leads to three-dimensional flow.Approximate solutions for components of velocity, pressure and skin friction are obtained. The effects of flow parameters such as Hartmann number, Reynolds number, suction/injection parameter, non-Newtonian parameter on velocity components, skin friction factors along main flow direction and transverse direction, and pressure through parallel porous plates are discussed graphically. It is noted that Hartmann number provides a mechanism to stable the skin friction component along the main flow direction.

Half-range lattice Boltzmann models for the simulation of Couette flow using the Shakhov collision term

The three-dimensional Couette flow between parallel plates is addressed using mixed lattice Boltzmann models which implement the half-range and the full-range Gauss-Hermite quadratures on the Cartesian axes perpendicular and parallel to the walls, respectively. The ability of our models to simulate rarefied flows are validated through comparison against previously reported results obtained using the linearized Boltzmann-BGK equation for values of the Knudsen number (Kn) up to $100$. We find that recovering the non-linear part of the velocity profile (i.e., its deviation from a linear function) at ${\rm Kn} \gtrsim 1$ requires high quadrature orders. We then employ the Shakhov model for the collision term to obtain macroscopic profiles for Maxwell molecules using the standard $\mu \sim T^\omega$ law, as well as for monatomic Helium and Argon gases, modeled through ab-initio potentials, where the viscosity is recovered using the Sutherland model. We validate our implementation by comparison with DSMC results and find excellent match for all macroscopic quantities for ${\rm Kn} \lesssim 0.1$. At ${\rm Kn} \gtrsim 0.1$, small deviations can be seen in the profiles of the diagonal components of the pressure tensor, the heat flux parallel to the plates, and the velocity profile, as well as in the values of the velocity gradient at the channel center. We attribute these deviations to the limited applicability of the Shakhov collision model for highly out of equilibrium flows.

Three-dimensional couette flow of dusty fluid with heat transfer in the presence of magnetic field

This paper is focused on the mathematical modelling of three-dimensional couette flow and heat transfer of a dusty fluid between two infinite horizontal parallel porous flat plates in the presence of an induced magnetic field. The problem is formulated using a continuum two-phase model and the resulting equations are solved analytically. The lower plate is stationary while the upper plate is undergoing uniform motion in its plane. These plates are, respectively subjected to transverse exponential injection and its corresponding removal by constant suction. Due to this type of injection velocity, the flow becomes three dimensional. The closed-form expressions for velocity and temperature fields of both the fluid and dust phase are obtained by solving the governing partial differentiation equations using the perturbation method. A selective set of graphical results is presented and discussed to show interesting features of the problem. It is found that the velocity profiles of both fluid and dust particles decrease due to the increase of (magnetic parameter) Hartmann number.

Three-dimensional Couette flow of a Jeffrey fluid along periodic injection/suction

Three-dimensional Couette flow of an incompressible Jeffrey fluid is formulated and discussed analytically and graphically. The suction is applied over uniformly moving upper plate and its equivalent deduction by injection at the lower stationary plate. Because of this type of suction/injection, this flow turns into three-dimensional. An analytical method is applied to get main flow velocity, secondary flows velocities and pressure components. Also skin friction components along the main and secondary flow directions have been calculated. The effects of different physical parameters, for example, the Deborah number, suction/injection parameter, the ratio of relaxation time to the retardation time and Reynolds number have been discussed graphically. It is witnessed that the Deborah number plays vital role to control the main flow velocity.

Magnetohydrodynamic Three-Dimensional Couette Flow of a Maxwell Fluid with Periodic Injection/Suction

A mathematical model for magnetohydrodynamic (MHD) three-dimensional Couette flow of an incompressible Maxwell fluid is developed and analyzed theoretically. The application of transverse sinusoidal injection at the lower stationary plate and its equivalent removal by suction through the uniformly moving upper plate lead to three-dimensional flow. Approximate solutions for velocity field, pressure, and skin friction are obtained. The effects of flow parameters such as Hartmann number, Reynolds number, suction/injection parameter, and the Deborah number on velocity components, skin friction factors along main flow direction and transverse direction, and pressure through parallel porous plates are discussed graphically. It is noted that Hartmann number provides a mechanism to control the skin friction component along the main flow direction.

Slip behavior of liquid flow in rough nanochannels

The molecular dynamics simulation is applied to investigate the liquid flow in rough nanochannels with a focus on interfacial velocity slip via three-dimensional Couette flow system. The typical liquid spatial distribution, velocity profile and slip length for liquid flow in rough nanochannels are evaluated and compared with smooth nanochannel. The effects of liquid–solid interaction, surface roughness and shear flow orientation on slip behavior of liquid flow in rough nanochannels are all investigated and discussed. The results indicate that, regardless of whether the liquid flow in transverse or longitudinal flow configuration, the rough surface induces extra energy losses and contributes to the reduction of interfacial velocity in nanochannel when compared with smooth surface. A larger roughness size introduces a more irregular near-wall flow, which results in a smaller interfacial velocity slip. In addition, irrespective of surface condition, increases in liquid–solid interaction strength lead to small interfacial velocity slip and expand the extent of velocity nonlinearity in wall-neighboring region. In particular, the slip behavior of liquid flow in rough nanochannels is also influenced by the shear flow orientation. Interestingly, we find that interfacial velocity slip at the rough solid surface in transverse flow configuration is smaller than that in longitudinal flow configuration.

Three-dimensional Couette flow of a dusty fluid with heat transfer

This work is focused on the mathematical modeling of three-dimensional Couette flow and heat transfer of a dusty fluid between two infinite horizontal parallel porous flat plates. The problem is formulated using a continuum two-phase model and the resulting equations are solved analytically. The lower plate is stationary while the upper plate is undergoing uniform motion in its plane. These plates are, respectively, subjected to transverse exponential injection and its corresponding removal by constant suction. Due to this type of injection velocity, the flow becomes three dimensional. The closed-form expressions for velocity and temperature fields of both the fluid and dust phases are obtained by solving the governing partial differential equations using the perturbation method. A selective set of graphical results is presented and discussed to show interesting features of the problem.

Heat transfer effects in a Couette flow through a composite channel partly filled by a porous medium with a transverse sinusoidal injection velocity and heat source

This study theoretically analyzes the heat transfer effects in a three dimensional Couette flow through a composite parallel porous plate channel partly filled by a porous medium. The flow is three dimensional in the channel because of the application of a transverse sinusoidal injection velocity of a particular form at the lower stationary plate. The governing equations are solved using a perturbation series expansion method. The effects of various flow parameters such as, Prandtl number (Pr), suction/injection parameter (?), permeability of the porous medium (K), heat source parameter (S), and viscosity ratio parameter (?1), are investigated on temperature distribution in the composite channel and rate of heat transfer at the upper moving plate and at the fluid-porous medium interface, and discussed graphically.

Radiation effect on temperature distribution in three-dimensional Couette flow with suction or injection

A theoretical analysis of three-dimensional Couette flow with radiation effect on temperature distribution has been analysed, when the injection of the fluid at the lower stationary plate is a transverse sinusoidal one and its corresponding removal by constant suction through the upper porous plate is in uniform motion. Due to this type of injection velocity, the flow becomes three-dimensional. The effect of Prandtl number, radiation parameter and injection parameter on rate of heat transfer has been examined by the help of graphs. The Prandtl number has a much greater effect on the temperature distribution than the injection or radiation parameter.

Rotational and orientational behaviour of three-dimensional spheroidal particles in Couette flows

This paper reports the results of lattice Boltzmann simulations of the rotation behaviour of neutrally buoyant spheroidal particles in a three-dimensional Couette flow. We find several distinctive states depending on the Reynolds number range and particle shape. As the Reynolds number increases, rotation may change from one state to another. For a prolate spheroid, two rotation transitions are found. In the low Reynolds number range , the oblate spheroid still spins with a constant rate around its minor axis but there is a finite inclination angle between the minor axis and the vorticity vector. This angle increases as the Reynolds number increases.

MHD Three-Dimensional Couette Flow with Transpiration Cooling

An analysis of the Couette flow between two horizontal parallel porous flat plates of an electrically conducting, viscous, incompressible fluid is presented. The stationary plate is subjected to a transverse sinusoidal injection of the fluid and its corresponding removal by constant suction through the other plate in uniform motion. The flow becomes three-dimensional due to such an injection velocity. A magnetic field of uniform strength is also applied normal to the planes of the plates. The effects of the injection/suction velocity and the magnetic field on the flow field, skin friction, and heat transfer are reported.