The unsteady magnehydrodynamics （MHD） Couette flow of an electrically conducting fluid in a rotating system is investigated by taking the Hall and ion-slip currents into consideration. The derived fundamental equati...The unsteady magnehydrodynamics （MHD） Couette flow of an electrically conducting fluid in a rotating system is investigated by taking the Hall and ion-slip currents into consideration. The derived fundamental equations on the assumption of a small magnetic Reynolds number are solved analytically with the well-known Laplace transform technique. The unified closed-form expressions axe obtained for the velocity and the skin friction in the two different cases of the magnetic field being fixed to either the fluid or the moving plate. The effects of various parameters on the velocity and the skin friction axe discussed by graphs. The results reveal that the primary and secondary velocities increase with the Hall current. An increase in the ion-slip paxameter also leads to an increase in the primary velocity but a decrease in the secondary velocity. It is also shown that the combined effect of the rotation, Hall, and ion-slip parameters determines the contribution of the secondary motion in the fluid flow.展开更多
A numerical study is reported on the fully developed unsteady laminar fluid flow in microchannel parallel-plates partially filled with a uniform porous medium and partially filled with a clear fluid. The flow is induc...A numerical study is reported on the fully developed unsteady laminar fluid flow in microchannel parallel-plates partially filled with a uniform porous medium and partially filled with a clear fluid. The flow is induced by the movement of one of the plates and the pressure gradient. The Brinkman-extended Darcy model is utilized to model the flow in the porous region, while the Stokes equation is used in the clear fluid region. A theoretical analysis is also presented for the fully developed steady flow to find closed- form expressions for the interracial velocity and the velocity and skin frictions at the bounding plates. Numerical computations shows excellent agreement between the closedform solutions for fully developed steady flow and the numerical solution to unsteady flow at large values of time.展开更多
The extended Brinkman Darcy model for momentum equations and an energy equation is used to calculate the unsteady natural convection Couette flow of a viscous incompressible heat generating/absorbing fluid in a vertic...The extended Brinkman Darcy model for momentum equations and an energy equation is used to calculate the unsteady natural convection Couette flow of a viscous incompressible heat generating/absorbing fluid in a vertical channel （formed by two infinite vertical and parallel plates） filled with the fluid-saturated porous medium. The flow is triggered by the asymmetric heating and the accelerated motion of one of the bounding plates. The governing equations are simplified by the reasonable dimensionless parameters and solved analytically by the Laplace transform techniques to obtain the closed form solutions of the velocity and temperature profiles. Then, the skin friction and the rate of heat transfer are consequently derived. It is noticed that, at different sections within the vertical channel, the fluid flow and the temperature profiles increase with time, which are both higher near the moving plate. In particular, increasing the gap between the plates increases the velocity and the temperature of the fluid, however, reduces the skin friction and the rate of heat transfer.展开更多
文摘The unsteady magnehydrodynamics （MHD） Couette flow of an electrically conducting fluid in a rotating system is investigated by taking the Hall and ion-slip currents into consideration. The derived fundamental equations on the assumption of a small magnetic Reynolds number are solved analytically with the well-known Laplace transform technique. The unified closed-form expressions axe obtained for the velocity and the skin friction in the two different cases of the magnetic field being fixed to either the fluid or the moving plate. The effects of various parameters on the velocity and the skin friction axe discussed by graphs. The results reveal that the primary and secondary velocities increase with the Hall current. An increase in the ion-slip paxameter also leads to an increase in the primary velocity but a decrease in the secondary velocity. It is also shown that the combined effect of the rotation, Hall, and ion-slip parameters determines the contribution of the secondary motion in the fluid flow.
文摘A numerical study is reported on the fully developed unsteady laminar fluid flow in microchannel parallel-plates partially filled with a uniform porous medium and partially filled with a clear fluid. The flow is induced by the movement of one of the plates and the pressure gradient. The Brinkman-extended Darcy model is utilized to model the flow in the porous region, while the Stokes equation is used in the clear fluid region. A theoretical analysis is also presented for the fully developed steady flow to find closed- form expressions for the interracial velocity and the velocity and skin frictions at the bounding plates. Numerical computations shows excellent agreement between the closedform solutions for fully developed steady flow and the numerical solution to unsteady flow at large values of time.
文摘The extended Brinkman Darcy model for momentum equations and an energy equation is used to calculate the unsteady natural convection Couette flow of a viscous incompressible heat generating/absorbing fluid in a vertical channel （formed by two infinite vertical and parallel plates） filled with the fluid-saturated porous medium. The flow is triggered by the asymmetric heating and the accelerated motion of one of the bounding plates. The governing equations are simplified by the reasonable dimensionless parameters and solved analytically by the Laplace transform techniques to obtain the closed form solutions of the velocity and temperature profiles. Then, the skin friction and the rate of heat transfer are consequently derived. It is noticed that, at different sections within the vertical channel, the fluid flow and the temperature profiles increase with time, which are both higher near the moving plate. In particular, increasing the gap between the plates increases the velocity and the temperature of the fluid, however, reduces the skin friction and the rate of heat transfer.
