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Assumptions and Model Purpose

The water at the top of the glass has a radius of 5.64 centimeters (cm), a circumference of 35.4 cm and an exposed surface area of 100 square centimeters. The glass is a perfect cylinder, so the exposed surface area will remain constant at 100 square centimeters as the water evaporates. Initially, the water stands 10 cm high. Water density is 1 gram/cc, so the initial mass is 1,000 grams. The glass is 0.5 cm thick, and it sits on a well insulated table in a room with a constant air temperature of 20 degrees and a relatively low humidity. Evaporation takes place at the rate of 2 feet/year. The latent heat of evaporation (the heat needed to evaporate the water) is 585 calories per gram.

If we are to study changes in the energy stored in the water, we might consider simulating four heat flows:

evaporation
(top surface) The heat loss due to evaporation depends on the latent heat of evaporation and the rate at which water evaporates. This flow will be included in the model.

conduction
(side wall) Heat may flow into the water from conduction across the side surface where the water touches the glass. Initially, this surface area is 354 square centimeters. But this surface area will shrink over time as evaporation removes water from the glass. This flow will be included in the model.

conduction
(bottom surface) Heat may flow out of the water through conduction through the bottom of the glass. Let's ignore this flow since the table is well insulated.

convection
(top surface) Heat may flow into the water by convective forces through the surface area exposed to the air. Let's ignore the convective flow because it would probably amount to only about 1% of the conductive flows across the side surface of the glass.

So, our purpose is to simulate the heat flows from evaporation at the top surface and conduction across the side wall. The model may then be used to address the question raised at the outset -- what will happen to the temperature of the water over time?

evaporation (top surface)		The heat loss due to evaporation depends on the latent heat of evaporation and the rate at which water evaporates. This flow will be included in the model.
conduction (side wall)		Heat may flow into the water from conduction across the side surface where the water touches the glass. Initially, this surface area is 354 square centimeters. But this surface area will shrink over time as evaporation removes water from the glass. This flow will be included in the model.
conduction (bottom surface)		Heat may flow out of the water through conduction through the bottom of the glass. Let's ignore this flow since the table is well insulated.
convection (top surface)		Heat may flow into the water by convective forces through the surface area exposed to the air. Let's ignore the convective flow because it would probably amount to only about 1% of the conductive flows across the side surface of the glass.