Chapter 7, Problem 7.139P

Cylindrical dry-bulb and wet-bulb thermometers are installed in a large-diameter duct to obtain the temperature $T_{\infty }$ and the relative humidity ${\varphi }_{\infty }$ of moist air flowing through the duct at a velocity V. The dry-bulb thermometer has a bare glass surface of diameter $D_{\text{db}}$ and emissivity ${\epsilon }_g.$ The wet-bulb thermometer is covered with a thin wick that is saturated with water flowing continuously by capillary action from a bottom reservoir. Its diameter and emissivity are designated as $D_{\text{wb}}$ and ${\epsilon }_w.$ The duct inside surface is at a known temperature $T_s,$ which is less than $T_{\infty }.$ Develop expressions that may be used to obtain $T_{\infty }$ and ${\varphi }_{\infty }$ from knowledge of the dry-bulb and wet-bulb temperatures $T_{\text{db}}$ and $T_{\text{wb}}$ and the foregoing parameters. Determine $T_{\infty }$ and ${\varphi }_{\infty }$ when $T_{\text{db}}=45°\text{C,}{T}_{\text{wb}}=25°\text{C,}{T}_s=35°\text{C,}p=1\text{atm,}V=5\text{m/s,}{D}_{\text{db}}=3\text{mm,}{D}_{\text{wb}}=4\text{mm,}$ and ${\epsilon }_g={\epsilon }_w=\mathrm{0.95.}$ As a first approximation, evaluate the dry- and wet-bulb air properties at 45 and 25°C, respectively.