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.

(a) If a dryer is designed to operate with an electric power consumption of P_elec = 500 W and to heat air from an ambient temperature of Ti = 20°C to a discharge temperature of To = 45°C, at what volumetric flow rate ∀ 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 mm, what is the discharge velocity V. of the air? The density and specific heat of the air may be approximated as p = 1.10 kg/m³ and c_p = 1007 J/kg. K, respectively.

(b) Consider a dryer duct length of L = 150 mm and a surface emissivity of ɛ =0.8. If the coefficient associated with heat transfer by natural convection from the casing to the ambient air is h = 4 W/m². K and the temperature of the air and the surroundings is T∝ = Tsur = 20°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°C.