Water at a temperature of 77°C is to be evaporated slowly in a vessel. The water is in a low pressure container surrounded by steam as shown in the sketch below. The steam is condensing at 107°C. The overall heat transfer coefficient between the water and the steam is 1100 W/(m2 K). Calculate the surface area of the container which would be required to evaporate water at a rate of 0.01 kg/s.

Question

GIVEN

• Water evaporated slowly in a low pressure vessel surrounded by steam

• Water temperature (Tw) = 77°C

• Steam condensing temperature (Ts) = 107°C

• Overall transfer coefficient between the water and the steam (U) = 1100 W/(m2 K)

• Evaporation rate m

w= 0.01 kg/s

FIND

• The surface area (A) of the container required

ASSUMPTIONS

• Steady state prevails

• Vessel pressure is held constant at the saturation pressure corresponding to 77°C

SKETCH



PROPERTIES AND CONSTANTS

The heat transfer required to evaporate water at the given rate is q = m

Answer 1

The heat transfer required to evaporate water at the given rate is



For the heat transfer between the steam and the water



Solving this for the transfer area