A simple solar heater consists of a flat plate of glass below which is located a shallow pan filled with water, so that the water is in contact with the glass plate above it. Solar radiation is passing through the glass at the rate of 490 W/m2. The water is at 92°C and the surrounding air is 27°C. If the heat transfer coefficients between the water and the glass and the glass and the air are 28 W/(m2 K), and 7 W/(m2 K), respectively, determine the time required to transfer 1.1 MJ/m2 of surface to the water in the pan. The lower surface of the pan may be assumed to be insulated.

Question

GIVEN

• A simple solar heater: shallow pan of water below glass, the water touches the glass

• Solar radiation passing through glass (qr/A) = 490 W/m2

• Water temperature (Tw) = 92°C

• Surrounding air temperature (T?) = 27°C

• Heat transfer coefficients

? Between water and glass ( cw h ) = 28 W/(m2 K)

? Between glass and air ( ca h ) = 7 W/(m2 K)

FIND

• The time (t) required to transfer 1.1 MJ/m2 to the water

ASSUMPTIONS

• One dimensional, steady state heat transfer prevails

• The heat loss from the bottom of the pan is negligible

• The radiative loss from the top of the glass is negligible

• The thermal resistance of the glass is negligible

SKETCH

Answer 1

The total thermal resistance between the water and the surrounding air is the sum of the two

convective thermal resistances



The net rate of heat transfer to the water is



At this rate, the time required to transfer 100 Btu/ft 2 to the water is