Background
Navier-Stokes and continuity equations are utilized to simulate fully developed laminar Dean flow with an oscillating time-dependent pressure gradient. These equations are solved analytically with the appropriate boundary and initial conditions in terms of Laplace domain and inverted to time domain using a numerical inversion technique known as Riemann-Sum Approximation (RSA). The flow is assumed to be triggered by the applied circumferential pressure gradient (azimuthal pressure gradient) and the oscillating time-dependent pressure gradient. The influence of the various flow parameters on the flow formation are depicted graphically. Comparisons with previously established result has been made as a limit case when the frequency of the oscillation is taken as 0 (ω = 0).
Results
It was revealed that maintaining the frequency of oscillation, the velocity and skin frictions can be made increasing functions of time. An increasing frequency of the oscillating time-dependent pressure gradient and relatively a small amount of time is desirable for a decreasing velocity and skin frictions. The fluid vorticity decreases with further distance towards the outer cylinder as time passes.
Conclusion
Findings confirm that increasing the frequency of oscillation weakens the fluid velocity and the drag on both walls of the cylinders.
Hydrodynamic behaviour of slip flow and radially applied exponential time-dependent pressure gradient in a curvilinear concentric cylinder is examined. A two-step method of solution has been utilized in resolving the governing momentum equation. Accordingly, the exact solution of the time-dependent partial differential equation is derived in terms of the Laplace parameter. Afterwards, the Laplace domain solution is then inverted to time domain using a numerical-based inverting scheme known as Riemann-sum approximation. The effect of various dimensionless parameters involved in the problem on the Dean velocity, shear stresses and Dean vortices is discussed with the aid of graphs. It is found that maximum Dean velocity is due to an exponentially growing time-dependent pressure gradient and slip wall coefficient. Stability of the Dean vortices is achieved by suppressing time, wall slippage and inducing an exponentially decaying time-dependent pressure gradient.
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