Assume the following for the properties of water for this problem.

Liquid heat capacity: 4197 J kg^-1 K^-1

Liquid density: 971 kg/m³

Consider the model 03014 shell and tube heat exchanger in the UO lab. This model has 52 tubes. The tubes are made of 24 BWG 316 stainless steel. Each is 14 inches long with an outer diameter of 0.25 inches. Recall that water flows on the tube side and steam condenses on the shell side. The following conditions are set on the unit.

Flowrate of water: 45 gal/min = 0.002839 m³/s

Saturated Steam Pressure: 25 psig = 172.4 kPa

Ambient Pressure: 87 kPa

The unit is then turned on, and the system is allowed to reach steady state.

What is the overall heat transfer coefficient (UA) if the inlet water temperature for these conditions is 77 C and the outlet water temperature is 85 C? Report four significant digits.