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 whichthe air is heated as it flows over a coiled electric resistance wire.

(a) If a dryer is designed to operate with an electricpower consumption of $P_{elec}=500\text{W}$ and to heatair from an ambient temperature of $T_i=20°\text{C}$ to adischarge temperature of $T_o=45°\text{C}$ , at what volumetric flow rate $\stackrel{\dot{}}{\forall }$ 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 $D=700\text{mm}$ , what is the discharge velocity $V_0$ , ofthe air? The density and specific heat of the air maybe approximated as $\rho =1.10{\text{kg/m}}^{\text{3}}$ and $c_p=1007\text{J/kg}\cdot \text{K}$ . respectively.
(b) Consider a dryer duct length of $L=150\text{mm}$ and a surface emissivity of $\in =0.8$ . Ii 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 $T_{\infty }=T_{sur}=20\text{°C}$ , confirm that the heat loss from the casing is. in fact, negligible. The casing may be assumed to have an average surface temperature of $T_s=40\text{°C}$ .