On a cool day in April a scantily clothed runner is known to lose heat at a rate of \(450 \mathrm{~W}\) when running on a level surface because of convection to the surrounding air at \(T_{\infty}=15^{\circ} \mathrm{C}\). The runner's skin remains dry and at a temperature of \(T_{s}=30^{\circ} \mathrm{C}\). Three months later, the runner is running uphill at the same speed, but the day is warm and humid with a temperature of \(T_{\infty}=33^{\circ} \mathrm{C}\) and a relative humidity of \(\phi_{\infty}=60 \%\). The runner is now drenched in sweat and has a uniform surface temperature of \(35^{\circ} \mathrm{C}\). Under both conditions constant air properties may be assumed with \(v=1.6 \times 10^{-5} \mathrm{~m}^{2} / \mathrm{s}, k=\) \(0.026 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}, \operatorname{Pr}=0.70\), and \(D_{\mathrm{AB}}\) (water vapor-air) \(=\) \(2.3 \times 10^{-5} \mathrm{~m}^{2} / \mathrm{s}\).

(a) What is the rate of water loss due to evaporation on the summer day?

(b) What is the total rate of convective heat loss on the summer day?