Pulsatile flow between two coaxial porous cylinders with slip on inner cylinder

A fully developed, axisymmetric, pulsatile motion of an incompressible Newtonian fluid,under the action of an oscillatory pressure gradient, has been considered in this work. The fl ow is assumed to take place in the annular space between two coaxial circular cylinders, the outer one a porous cylinder of uniform permeability and the inner one a naturally permeable tube. There arises a coupled flow, which has been analysed by solving the Navier-Stokes equations in the free fluid region and the Darcy's equation in the porous region, together with the Beavers-Joseph slip condition at the free fl uid-porous medium interface. Using an appropriate set of similarity variables, the governing partial differential equations have been transformed to a system of nonlinear ordinary differential equations. The solution of the resulting system, together with appropriate boundary conditions, has been obtained, for a special case, by a perturbation approach. It has been assumed that the frequency of pulsation and the suction parameter are small (<< 1). The variation of velocity pro les, pressure drop and skin friction has been illustrated in a number of cases of interest. The analytical results have been compared with numerical solution for small values of suction parameter

Pulsatile flow between two coaxial porous cylinders with slip on inner cylinder for large frequency of pulsation

The unsteady component of axial flow of an incompressible fluid in the region lying between the annular spaces of two coaxial cylinders has been investigated. The outer cylinder is assumed to possess uniform permeability and the inner one is a naturally permeable tube obeying Darcy's Law. The flow is maintained by a periodic pressure gradient across the annulus. Making use of an appropriate set of similarity variables, the governing partial differential equations have been transformed to a set of a system of nonlinear ordinary differential equations. The solution of the resulting equations subject to appropriate boundary conditions has been obtained using a singular perturbation technique. The frequency of pulsation has been considered to be large. The effect of the flow parameters on the unsteady component of axial flow has been discussed. The analytical results have been compared with numerical solutions

Home bias in officiating: Evidence from international cricket

We use data on leg before wicket decisions from 1000 test cricket matches to quantify the systematic bias by officials (umpires) to favour home teams. We exploit recent changes in the regulation of test cricket as a series of natural experiments to help to identify whether social pressure from crowds has a causal effect on home bias. Using negative binomial regressions, we find that home umpires favour home teams and that this effect is more pronounced in the later stages of matches