Chapter 1, Problem 1.72P

The roof of a car in a parking lot absorbs a solar radiant flux of $800{\text{W/m}}^{\text{2}},$ and the underside is perfectly insulated. The convection coefficient between the roof and the ambient air is $12{\text{W/m}}^{\text{2}}\cdot \text{K}\text{.}$

1. Neglecting radiation exchange with the surroundings, calculate the temperature of the roof under steady-state conditions if the ambient air temperature is $20°\text{C}\text{.}$ For the same ambient air temperature, calculate the temperature of the roof if its surface emissivity is 0.8.
2. The convection coefficient depends on airflow conditions over the roof, increasing with increasing air speed. Compute and plot the roof temperature as a function of h for $2\le h\le 200{\text{W/m}}^{\text{2}}\cdot \text{K}\text{.}$