Chapter 12, Problem 12.119P

Radiation from the atmosphere or sky can be estimated as a fraction of the blackbody radiation corresponding to the air temperature near the ground, $T_{air}$ .That is, irradiation from the sky can be expressed as $G_{atm}={\epsilon }_{sky}\sigma T_{air}^4$ and for a clear night sky, the emissivity is correlated by an expression of the form ${\epsilon }_{sky}=0.741\text{ + 0}{\text{.0062T}}_{dp},{\text{ where T}}_{dp}$ is the dew point temperature $\left(c\right)$ Consider a flat plate exposed to the night sky and in ambient air at ${15}^{\circ }C$ c with a relative humidity of 70%. Assume the back side of the plate is insulated, and that the convection coefficient on the front side can be estimated by the correlation $h\left(W/m^2\cdot K\right)=1.25\Delta T^{1/3}$ , where $\Delta T$ is the absolute value of the plate-to-air temperature difference. Will dew form on the plate if the surface is (a) clean and metallic with $\epsilon \text{=0}\text{.23}$ , and (b) painted with $\epsilon \text{=0}\text{.85}$ ?