In beauty salons and in homes, a ubiquitous device is a hair dryer. The front end of the typical hair dryer is idealized as a thin walled cylindrical duct with a 6-cm diameter with a fan at the inlet that blows air over an electric heating coil as schematically shown in the figure. The design of the appliance requires two power settings, with which the air blown over the electric heating coil is heated from the ambient temperature of 220C to an outlet temperature of 440C and with exit air velocities of 1.0 m/s and 1.5 m/s. Estimate the electric power required for the heating coil to meet these conditions, assuming that the heat loss from the outside of the dryer duct is neglected.
GIVEN
- Dryer idealized as cylindrical duct of d= 6 cm =0.06 m with 2 power settings
- Air blown over coil is heated from T?=220C to outlet temp Tf=440C with exit air velocities (a) 1.0
m/s and (b) 1.5 m/s.
FIND
- Electric power required for heating coil to meet these condition.
ASSUMPTIONS
- Steady state conditions prevail
- Heat loss from outside of dryer duct is neglected.
PROPERTIES AND CONSTANTS
The air properties at 300 K are
Density of air (?)=1.177 kg/m3
Specific heat capacity(Cp)= 1.0049 kJ/kgK
Mass flow rate of air in each case is given by
Power required for heating the air is given by formula
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