Past exam of the mathematics course of the University of Cambridge / 2020 / ib / Paper 2 / 6C / Solution

Let the upper plate in flow A move at speed $U$, with the lower plate fixed. The Couette flow profile isso its mid-plane speed is $U/2$ and its total viscous dissipation per unit plate area is

Write $G=-dp/dx>0$ for the constant pressure-gradient magnitude in flow B. The plane Poiseuille flow profile isEquality of the mid-plane speeds givesSince $u_B^{\prime }(y)=G(h-2y)/(2\mu )$,Hence