Question

Consider the combined gravity$-$Couette driven flow hetween two inclined, parallel platea, as depicted in the figure. The lower plate is stationary, while the upper plate moves at constant upward melocity $V_{\text{r}\text{e}\text{p}\text{.}}.$ The plates are wery loag and wide and they are sparated by a small gap of jength $h.$ The fluid has viscosity a and density $a$

Figure $3$ Inclined gravity fund Couctte driven flow.

$($a$)$ What assumptions can be made ahout this How scemurio?

$($b$)$ Write the complete Navier Stakes oquations governing this fow, ibetuding known Buundary Conditions.

$($c$)$ Simplify and reduce the governing equations to a secund arder ordinary differential equation $($ODE$).$ Justify your assumptions.

$($d$)$ Find the solution to this ODE using appropriate Boundary Conditions.