To more accurately model the energy input from the sun, suppose the absorbed flux in Problem 3.23

Question:

To more accurately model the energy input from the sun, suppose the absorbed flux in Problem 3.23 is given by

q_abs (t) = t (375 – 46.875 t)

where t is in hours and q_abs is in W/m². (This time variation of q_abs gives the same total heat input to the wall as in Problem 3.23, i.e., 2000 W hr/m²). Repeat Problem 3.23 with the above equation for q_abs in place of the constant value of 500 W/m². Explain your results.

From Problem 3.23: A Trombe wall is a masonry wall often used in passive solar homes to store solar energy. Suppose such a wall, fabricated from 200 cm thick solid concrete blocks (k = 0.13 W/(mK),α = 0.05 \ 10^–5 m²s) is initially at 15°C in equilibrium with the room in which it is located. It is suddenly exposed to sunlight and absorbs 500 W/m² on the exposed face. The exposed face loses heat by radiation and convection to the outside ambient temperature of – 15°C through a combined heat transfer coefficient of 10 W/(m² K). The other face of the wall is exposed to the room air through a heat transfer coefficient of 10 W/(m² K). Assuming that the room air temperature does not change, determine the maximum temperature in the wall after 4 hours of exposure and the net heat transferred to the room.

GIVEN