Chapter 1, Problem 1.52P

A hair dryer may be idealized as a circular duct through which a small fan draws ambient air and within which the air is heated as it flows over a coiled electric resistance wire.

1. If a dryer is designed to operate with an electric power consumption of $P_{\text{elec}}=500\text{W}$ and to heat air from an ambient temperature of $T_i=20°\text{C}$ to a discharge temperature of $T_o=45°\text{C,}$ at what volumetric flow rate $\stackrel{.}{\forall }$ should the fan operate? Heat loss from the casing to the ambient air and the surroundings may be neglected. If the duct has a diameter of $D=70\text{mm,}$ what is the discharge velocity $V_o$ of the air? The density and specific heat of the air may be approximated as $\rho =1.10{\text{kg/m}}^{\text{3}}$ and $c_p=1007\text{J/kg}\cdot \text{K,}$ respectively.
2. Consider a dryer duct length of $L=150\text{mm}$ and a surface emissivity of $\epsilon =\mathrm{0.8.}$ If the coefficient associated with heat transfer by natural convection from the casing to the ambient air is $h=4{\text{W/m}}^{\text{2}}\cdot \text{K}$ and the temperature of the air and the surroundings is $T_{\infty }=T_{\text{sur}}=20°\text{C,}$ confirm that the heat loss from the casing is, in fact, negligible. The casing may be assumed to have an average surface temperature of $T_s=40°\text{C}\text{.}$