A \(3 \mathrm{~m} \times 3 \mathrm{~m}\) vertical plate is exposed on one side to saturated steam at atmospheric pressure and on the other side to cooling water that maintains a plate temperature of \(50^{\circ} \mathrm{C}\).

(a) What is the rate of heat transfer to the coolant? What is the rate at which steam condenses on the plate?

(b) For plates inclined at an angle \(\theta\) from the vertical, the average convection coefficient for condensation on the upper surface, \(\bar{h}_{L(\text { incl })}\), may be approximated by an expression of the form, \(\bar{h}_{L \text { (incl) }} \approx(\cos \theta)^{1 / 4} \cdot \bar{h}_{L(\text { vert })}\), where \(\bar{h}_{L \text { (vert) }}\) is the average coefficient for the vertical orientation. If the \(3 \mathrm{~m} \times 3 \mathrm{~m}\) plate is inclined \(30^{\circ}\) from the vertical, what are the rates of heat transfer and condensation?