Q1: Heat Transfer (Conduction, Radiation, Convection) (5 pts) A cubic box of water, with outer dimensions 80 cm on a side, is surrounded on all sides by air at TAIR 15°C (with a convection coefficient of h = 10 W/m²K), within a much larger room "environment" at TROOM=10°C. The outer surface of the box has a uniform surface temperature of Tour = 100°C and thermal emissivity = 0.9. Each of the six walls of the box is made of 0.5 cm thick plastic, with thermal conductivity k = 1.3 W/mK. Assuming the box is at steady-state conditions, with the inner surface of the box walls at a uniform (but unknown) temperature, calculate... = TROOM -10°C TAIR = 15°C h = 10 W/m²K 80 cm Tour 100°C a) the total rate of energy transfer due to heat, Q, leaving the box of water (in Watts), b) the inner temperature of the wall, TN (in °C). 8=0.9 Hints! There's all three modes of heat transfer going on here. There's radiation between the outer surface of the box and the room, convection between the outer surface of the box and the surrounding air, and conduction of heat between the inner and outer surfaces of the box. Since each side of the box will behave similarly, I recommend you just analyze one plastic wall, and then multiply your result by six. And since the box is at steady-state conditions, you can make an energy (heat) balance, similar to the house example we did in class. Also, don't get hung up on what's going on in the corners of the box-since each plastic wall is so much thinner than the side lengths, just treat each side as a wall with the same area through the entire thickness.