Chapter 12, Problem 12.124P

A circular metal disk having a diameter of 0.4 m is placed firmly against the ground in a barren horizontal region where the earth is at a temperature of 280 K. The effective sky temperature is also 280 K. The disk is exposed to quiescent ambient air at 300 K and direct solar irradiation of $745{\text{ W/m}}^2$ . The surface of the disk is diffuse with ${\epsilon }_{\lambda }=0.9\text{ for 0<}\lambda \text{<1}\mu \text{m and }{\epsilon }_{\lambda }=0.2\text{ for 0>1}\mu \text{m}$ . After some time has elapsed, the disk achieves a uniform, steady-state temperature. The thermal conductivity of the soil is $\text{0}\text{.52 W/m}\cdot \text{K}$ .

(a) Determine the fraction of the incident solar irradiation that is absorbed.

(b) What is the emissivity of the disk surface?

(c) For a steady-state disk temperature of 340K, employ a suitable correlation to determine the average free convection heat transfer coefficient at the upper surface of the disk.

(d) Show that a disk temperature of 340K does indeed yield a steady-state condition for the disk