$3)$ Cold air is blown over the top surface of a heated compartment, which is composed of two equal$-$sized portions, one very rough and one very smooth. The rough surface causes an instant transition from laminar to turbulent flow.

a$)$ For the two configurations illustrated, which configuration would you expect to lead to a higher average convection heat transfer rate $($rough plate first or smooth plate first$)?$ You may assume that Re reaches the critical $\backslash (\backslash$operatorname$\{$Re$\}\backslash )$ at $\backslash ($ x$=$L $/3\backslash ),$ where $\backslash ($ L $\backslash )$ is the total length of the compartment. Be sure to explain your reasoning.$(3$ pts $)$ b$)$ Using the grids below, plot h as a function of x for the two configurations.

$(7$ pts$)$