$2$uestion $4$

Consider the combined gravity:Couctte driven four between two incliner, paralles plates, as depteted in the figure. The larer plate is stationary, while the upper plate moves at constant upward velocity $V_{\text{i}\text{n}\text{p}}.$ The plates are very long and wide and they are separated by a small gap of length $h.$ The fluid hise viscosity a and density $.$

Figure $3$ Inclaned gravity and Couctte driven flow.

$($a$)$ What asamptions can be made about this flow scenario?

$($b$)$ Write the coniplete Navjer$-$Stakes equations governing this forw, including known Boundary Canditions.

$($c$)$ Simplify and reduce the governing equations to a second order ordmary differmatial equation $($ODE$).$ Justify yout aseumptions

$($d$)$ Fiad the sobution to this ODE using appropriate Boundary Conditions,