Hydrodynamic effect of slip boundaries and exponentially decaying/growing time-dependent pressure gradient on Dean flow

Abstract

Abstract 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.

Keywords

• Dean flow
• Exponential time-dependent pressure gradient
• Unsteady
• Riemann-sum approximation (RSA)
• Slip flow