$[30$pt$]$ A ME student is installing a solar panel that is $1$ meters long and $0\mathrm{.}8$ meters wide on a rooftop. The wind flow over the rooftop is $u_{}=5\frac{m}{s}$ at $T_{}=20C.$ In order to operate the solar panel efficiently, it should be positioned in the area with the greatest cooling effect. The $x-$coordinate is measured along the rooftop from the gutters $($leading edge$),$ and the rooftop is $5$ meters long. For simplicity, assume the entire surface of the rooftop and the solar panel is maintained at $T_s=50C$ due to direct sunlight.

For air,

$k=0\mathrm{.}025\frac{W}{m}*K$

$u=1\mathrm{.}5{10}^{-5}\frac{m^2}{s}$

$Pr=0\mathrm{.}71$

a$.$ At which location, $x_1,$ will you install the solar panel? Please briefly explain your reasoning in terms of laminar and turbulent flow.

b$.$ Determine the rate of heat loss from the solar panel $($located at $x_1$ calculated above$)$ due to convection under steady$-$state operating conditions. Choose one of the following approaches.

i$.$ Approach $1$: The convection coefficient at the center of the solar panel can be approximated as the average convection coefficient over the panel surface.

ii$.$ Approach $2$: $q_{\text{p}\text{a}\text{n}\text{e}\text{l}}=q_{0x_2}-q_{0x_1}.$ The heat loss from the panel is equal to the difference in surface heat loss up to $x_2$ and $x_1.$