A solar air heater consists of a flat air duct composed on one side of an absorbing sheet backed by insulation and on the other side by a transparent sheet, as shown in Fig 5-26. The absorbing sheet absorbs 500 W/m^2 and delivers all this heat to the air being heated, which loses some to the atmosphere through the transparent sheet. The convection heat transfer coefficient from the transparent sheet to ambient air is 12 W/(m^2 . K) and from the air being heated to the transparent sheet is 45 W/(m^2 . K). The air enters with a temperature that is the same as the ambient, namely 15 C, and the flow rate of air is 0.02 Kg/s per meter width. Develop the equation for the temperature of heated air t as a function of length along the collector x assuming no conduction in the sheet in the direction of air flow.

 

Airflow 0.02 kg/s 15C Cp = 500 W/m absorbed H 1000 J/(kg .K) FIGURE 5-26 Solar air heater in Prob. 5.15. 25. - Ambient 15C Insulation x m 1 m Absorbing sheet Transparent sheet `h = 45 W/(mK) h = 12 W/(mK)