It's a sunny winter day. In your haste to get to an exam you accidentally lock Rover in the car. The interior dimensions are \(\left(L=2 \mathrm{~m}\right.\), Area \(=2.5 \mathrm{~m}^{2}\), Volume \(\left.=4 \mathrm{~m}^{3}\right)\). Solar radiation provides a heat flux of \(116.5 \mathrm{~W} / \mathrm{m}^{2}\) through the moon roof and windows (Area \(=2.5 \mathrm{~m}^{2}\) ). A breeze \(\left(v_{\infty}=5 \mathrm{~m} / \mathrm{s}, T_{\infty}=25^{\circ} \mathrm{C}\right)\) blows over the car. From your final fluids class project, you know that the friction factor for flow over the car obeys:

\[\frac{\overline{C_{f}}}{2}=0.05 \operatorname{Re}_{L}^{-0.35}\]

Assuming only air inside the car \(\left(v_{\text {air }}=0 ; T(t=0)=25^{\circ} \mathrm{C}\right)\), the fact that Rover can withstand a temperature of \(55^{\circ} \mathrm{C}\), and that all the net energy from the sun gets transferred to the air inside the greenhouse:

a. What is the heat transfer coefficient?

b. How fast does the temperature initially rise or fall in the greenhouse?

c. Will Rover expire before you have finished the exam? Why?