The dryer section of a paper mill consists of 30 hot, 1.5-m-diameter cylindrical rollers of length \(3 \mathrm{~m}\). A \(225^{\circ}\) arc of each roller is in contact with the moist paper sheet, while the remaining roller surface is covered with a water film that is directly exposed to high-velocity air at a temperature of \(T_{\infty}=35^{\circ} \mathrm{C}\) and relative humidity of \(95 \%\). Determine the area-averaged mass transfer coefficient associated with the exposed roller surfaces if the water temperature is \(90^{\circ} \mathrm{C}\) and the total evaporation rate from the exposed surfaces is \(80 \mathrm{~kg} / \mathrm{s}\).