A hair dryer may be idealized as a circular duct

Chapter 1, Problem 1.52

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A hair dryer may be idealized as a circular duct throughwhich a small fan draws ambient air and within whichthe air is heated as it flows over a coiled electric resis-tance wire. (a) If a dryer is designed to operate with an electricpower consumption of Pelec?500 W and to heatair from an ambient temperature of Ti?20C to adischarge temperature of To?45C, at what volu-metric flow rate should the fan operate? Heat lossfrom the casing to the ambient air and the surround-ings may be neglected. If the duct has a diameter ofD?70 mm, what is the discharge velocity Voofthe air? The density and specific heat of the air maybe approximated as ??1.10 kg/m3and cp?1007J/kg?K, respectively.(b) Consider a dryer duct length of L?150 mm and asurface emissivity of ??0.8. If the coefficientassociated with heat transfer by natural convectionfrom the casing to the ambient air is h?4 W/m2?K and the temperature of the air and the surroundings is T??Tsur?20C, confirm that the heat loss from the casing is, in fact, negligible.The casing may be assumed to have an average surface temperature of Ts?40C

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