Hydrodynamic efect of slip boundaries and exponentially decaying/growing time‑dependent pressure gradient on Dean fow

Document Type : Original Article

Authors

Department of Mathematics, Ahmadu Bello University, Zaria, Nigeria.

https://doi.org/10.1186/s42787-021-00120-z

Abstract

Hydrodynamic behaviour of slip fow 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 diferential 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 efect 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 coefcient. Stability of the
Dean vortices is achieved by suppressing time, wall slippage and inducing an exponentially decaying time-dependent pressure gradient.

Keywords

Journal of the Egyptian Mathematical Society
Volume 29, Issue 1
2021
Pages 1-15

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