Past exam of the mathematics course of the University of Cambridge / 2008 / ii / Paper 1 / 36A / a / Solution

The signed tangential stress component is ${\sigma }_{xy}=\mu u^{\prime }=C-Gy$. ThusWhen ${\mu }_{+}/{\mu }_{-}\to 1$, these approach $+Ga$ and $-Ga$, the usual symmetric plane Poiseuille flow stresses. When ${\mu }_{+}/{\mu }_{-}\to \infty$, they approach $+Ga/2$ and $-3Ga/2$. The upper fluid's velocity tends to zero, but its viscosity times velocity gradient has a finite limit. These are tensor components; traction on a chosen wall normal includes that normal's sign.