Chapter 13, Problem 13.103P

The spectral absorptivity of a large diffuse surface is ${\alpha }_{\lambda }=0.9$ for $\lambda <1\mu \text{m}$ and ${\alpha }_{\lambda }=0.3$ for $\lambda \ge 1\mu \text{m}$ . The bottom of the surface is well insulated, while the top may be exposed to one of two different conditions.

Case (a)

Case (b)

(a) In case (a) the surface is exposed to the sun, which provides an irradiation of $G_S=1200{\text{W/m}}^2$ , and to an airflow for which $T_{\infty }=300\text{K}$ . If the surface temperature is $T_s=320\text{K}$ , what is the convection coefficient associated with the airflow?
(b) In case (b) the surface is shielded from the sun by a large plate and an airflow is maintained between the plate and the surface. The plate is diffuse and gray with an emissivity of ${\epsilon }_p=0.8$ . If $T_{\infty }=300\text{K}$ and the convection coefficient is equivalent to the result obtained in pan (a), what is the plate temperature T_pthat is needed to maintain the surface at $T_s=320\text{K}$ ?