Question: In the production of salt from sea water, the sea water is being run into a large pond 100 ft long, 20 ft wide, and 2 ft deep. There the water is evaporated by exposure to the sun and dry air, leaving solid salt on the bottom of the pond.
At a certain point in this cycle of operations, the brine in the pond is 1 ft deep. On the evening of a clear day a workman finds that the sun has heated the brine to 90°F. During the following 10-hour period of the night, the average air temperature is 70°F, and the average effective blackbody temperature of the sky is -100°F.
Model the properties of the brine as those of water, and model the brine temperature as uniform from top to bottom. The coefficient of heat transfer from the surface of the pond to air by natural convection may be taken as
Neglecting vaporization andor crystallization effects, and assuming negligible heat transfer between the brine and the earth, estimate the temperature of the brine at the end of the 10-hour period.