Consider a house whose south wall consists of a 30-cm-thick Trombe wall whose thermal cond...

Consider a house whose south wall consists of a 30-cm-thick Trombe wall whose thermal conductivity is k= 0.70 W/m·K and whose thermal diffusivity is α = 0.44 X 10-6 m2/s. The variations of the ambient temperature Tout and the solar heat flux  incident on a south-facing vertical surface throughout the day for a typical day in February are given in the table in 3-h intervals. The Trombe wall has single glazing with an absorptivity-transmissivity product of K=0.76 (that is, 76 percent of the solar energy incident is absorbed by the exposed surface of the Trombe wall) , and the average combined heat transfer coefficient for heat loss from the Trombe wall to the ambient is determined to be hout = 3.4 W/m2·K. The interior of the house is maintained at Tin = 20°Cat all times, and the heat transfer coefficient at the interior surface of the Trombe wall is hin = 9.1 W/m2∙K. Also. the vents on the Trombe wall are kept closed. and thus the only heat transfer between the air in the house and the Trombe wall' is through the interior surface of the wall. Assuming the temperature of the Trombe wall to vary linearly between 20°C at the interior surface and 0°C at the exterior surface at 7 AM 'and using the explicit finite difference method with a uniform nodal spacing of dx = 5 cm. determine the temperature distribution along the thickness of the Trombe wall after 6, 12, 18, 24, 30, 36,42, and 48 hours and plot the results. Also, determine the net amount of heat transfer red to the house from the Trombe wall during the first day if the wall is 2.8 m high and 7 m long.

FIGURE P5-102

TABLE P5-102

The hourly variations of the monthly average ambient ' temperature and solar heat flux incident on a vertical surface