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.

中文翻译：

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滑动边界和指数衰减/随时间变化的压力梯度对迪安流动的流体力学影响

在曲线同心圆柱体中研究了滑流的流体动力学行为和径向施加的指数随时间变化的压力梯度。在解决控制动量方程时，采用了两步法求解。因此，根据拉普拉斯参数得出了与时间有关的偏微分方程的精确解。之后，然后使用称为Riemann-sum逼近的基于数字的反演方案将Laplace领域解决方案反演为时域。借助图形讨论了问题中涉及的各种无量纲参数对Dean速度，剪切应力和Dean涡旋的影响。发现最大迪安速度是由于与时间有关的压力梯度和滑移壁系数呈指数增长。