Electromagnetohydrodynamic (EMHD) Flow Of The Jeffrey Fluid Through Two Parallel Microchannels

The electronmagnetohydrodynamic (EMHD) flow of an electrically conducting and incompressible linear viscoelastic fluid is studied between two microparallel plates. The constitutive relationship of the linear viscoelastic fluid is described by the Jeffrey fluid model. Under the no-slip and slip conditions, the method of separation of variables is employed to give analytic solution of velocity. The solution involves the linearized unsteady Cauchy momentum equation and the Jeffrey fluid constitutive equation. By numerical computations of MATLAB, the influences of Reynolds number Re, Hartmann number Ha, the dimensionless relaxation time λ1ω and retardation time λ2ω on the EMHD flow velocity amplitude are analyzed graphically. Results show that the dimensionless slip length a tends to increase the flow velocity; therefore, if there is partial slip at the boundary/boundaries the velocity is higher than that of the no-slip case. The magnitude of the velocity amplitude grows at small Ha and diminishes with larger Ha. With the increasing of relaxation time λ1ω, the velocity becomes larger. However, increases in the Reynolds number Re and retardation time λ2ω diminish the fluid velocities on the contrary.