Question

P2 (50 pts.) Assume the roof of a room in a typical house is 12 cm thick concrete slab with a thermal conductivity k = 1.50 W/m•°C. The roof of the room is 4 m wide and 4 m long. Assume convection heat transfer coefficients on the inner and outer surfaces of the roof are hi=6 and ho=10 W/m2°C, respectively. At noon, when the sun is "hotter" the solar irradiation is estimated to be color = 750 W/m- and the solar absorptivity of the roof surface is a=0.85 (this means that the slab absorbs 85% of the solar irradiation). The ambient air outside is reported to be T.,o=30°C (due to the high humidity, you can neglect radiation to the sky). The room of the house has an air conditioner system that removes heat at a rate of 3300 Watts (-11300 BTU/h). If you neglect gains from the walls of the room and consider only gains from the roof of the room, which is going to be the inner temperature of the room, T.;?

Answer 1

Assuming Steady State V solar = 750 w/we Tolal q (solar) e 750 x 4x4 Since 0.85 of Total V (gelar) is o. 9 0.85 x 750 x 4x4 absorbed = 10200 w Ti – 30 10200 - thicknen - + - + 0.12 4X4x1.5 6x4x4 10xyxy l Aren I Aren Aren K Ti - 30 → 10200 - - 0.02 1666 & 221 - Ti - 30 & Ti - 251°c