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.
Highlights
Flow through curved geometry is of general importance due to its enormous application in fluid engineering, biofluid mechanics and haemodynamics
The hydrodynamic behaviour of fluids in curvilinear geometries is a prevalent concept which emanates from stability/instability of the radial pressure gradient, aspect ratio and curvature of the geometry
Unsteady hydrodynamically fully developed flow of viscid incompressible fluid in a curved annulus formed by two infinite concentric cylinders is considered
Summary
Flow through curved geometry is of general importance due to its enormous application in fluid engineering, biofluid mechanics and haemodynamics. This can be ascribed to its practical use in most of the systems in the aforementioned fields of endeavour. In diaphragm pumps and dialysis machines, flow is due to pulsation within the curved tube rather than convective current. It is widely known that the underlying principle of convective-driven flows has its setbacks as heat alters the rheological properties of some fluids. The hydrodynamic behaviour of fluids in curvilinear geometries is a prevalent concept which emanates from stability/instability of the radial pressure gradient, aspect ratio and curvature of the geometry
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