The effect of fluctuating Lorentz force on the Ac magnetohydrodynamic micropump is studied. A twodimensional transient fully developed laminar flow and temperature distribution are modeled. The governing Navier-Stokes and energy equations are solved numerically by a finite-difference (ADI) method. The effect of different parameters on the transient and steady flow velocity and temperature, such as aspect ratio, Hartman number, Prandtl number, and Eckert number is studied. The results obtained showed that controlling the flow and the temperature can be achieved by controlling the potential difference, the magnetic flux, and by a good choice of the electrical conductivity. The effect of Stanton number and phase angle is also included, and it is found that at high frequency, the pulsed volume is small which yield a continuous flow instead of pulsating flow, and the magnitude and direction of the flow can be controlled by the phase shift between the electrical and magnetic fields.
List of symbolsB magnetic flux density (T) C p specific heat (kJ/kg K) E electric field intensity (V/m) Ec Eckert number, Ec ¼ u 2 0 C p T w h height of micro-channel (m) Ha Hartman number, Ha ¼ wB ffiffiffiffiffiffiffiffi r=l p J electric current density (Amper/m 2 ) K thermal conductivity (W/m K)
Numerical analysis and analytical solution were performed to study the free convection in transient Couette flow of an electrically conducting fluid confined between two vertical parallel plates. Constant heat flux on the wall with uniform vertical motion in its own plane and periodic temperature on the stationary wall were applied. The dimensionless governing momentum and energy equations are solved numerically using a fully implicit finite difference method. An analytical solution using eigenfunction expansion method is carried out for temperature profile in case of constant plate temperature. Analytical and numerical results converge at a satisfactory degree. The effect of different physical parameters on the transient velocity and temperature, such as Grashof’s number (Gr), magnetic parameter (M), Prandtl number (Pr) and temperature frequency are also studied. It is found that the velocity increases with an increase in Gr and temperature frequency, while it decreases with an increase in Pr and M.
An analysis is carried out in order to examine the effects of non-uniform heat source and thermal radiation on the transient free convective MHD flow past a vertical plate. In this model, an inclined magnetic field with periodic heat flux along the wall is included. The governing equations (in non-dimensional shape) are solved numerically by a fully implicit finite difference scheme. A parametric study is performed in order to illustrate the influences of the model dimensionless parameters, namely, the magnetic parameter, the heat source term, the Grashof number, the Prandtl number, and the radiation parameter. The velocity field and the temperature field are evaluated for several amounts of these parameters. The obtained numerical results are compared with the analytical solution in case of constant heat flux with no heat source, and a full agreement was found.
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