O An hair dryer is basically a duct with a fan that draws cool air from...

  

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O An hair dryer is basically a duct with a fan that draws cool air from the atmosphere at one end, forces it on an electrical resistor (where the air is heated up) and discharges it at the other end. The system is shown in the figures below. 4 Resistor 3 2 Fan P = Patm = 105 Pa, T = 20C A A3 A4 = 13 cm A > A + CONF HOMIC PARENTS You may Air can be treated as an ideal gas with R=287 J/kg K and c-716 J/kg K. You may assume that the flow is steady and frictionless. The fan is also frictionless. The dryer duct is adiabatic. Note that the pressure at exit 4 is equal to the atmospheric pressure. a) (10 points) First consider the situation in which the resistor is off, while the fan is on. Calculate the temperature T4 at the discharge. Note that flow is frictionless (i.e. no entropy generation) b) (15 points) The resistor is still off. If the discharge velocity of the air is v4-20 m/s, calculate the mass flow rate of air and power of the fan. c) (10 points) For the air mass flow rate calculated in Part (b), find the electrical work rate required by the resistor to heat up the air to 50C (you may assume that the discharge velocity and fan power are the same as in part (b)). d) (15 points) Taking the whole dryer (i.e. the resistor + the fan + the air in the dryer) as your control volume, calculate the entropy generation rate of the dryer, when both the fan and resistor are operating steadily per Part (c) above. O An hair dryer is basically a duct with a fan that draws cool air from the atmosphere at one end, forces it on an electrical resistor (where the air is heated up) and discharges it at the other end. The system is shown in the figures below. 4 Resistor 3 2 Fan P = Patm = 105 Pa, T = 20C A A3 A4 = 13 cm A > A + CONF HOMIC PARENTS You may Air can be treated as an ideal gas with R=287 J/kg K and c-716 J/kg K. You may assume that the flow is steady and frictionless. The fan is also frictionless. The dryer duct is adiabatic. Note that the pressure at exit 4 is equal to the atmospheric pressure. a) (10 points) First consider the situation in which the resistor is off, while the fan is on. Calculate the temperature T4 at the discharge. Note that flow is frictionless (i.e. no entropy generation) b) (15 points) The resistor is still off. If the discharge velocity of the air is v4-20 m/s, calculate the mass flow rate of air and power of the fan. c) (10 points) For the air mass flow rate calculated in Part (b), find the electrical work rate required by the resistor to heat up the air to 50C (you may assume that the discharge velocity and fan power are the same as in part (b)). d) (15 points) Taking the whole dryer (i.e. the resistor + the fan + the air in the dryer) as your control volume, calculate the entropy generation rate of the dryer, when both the fan and resistor are operating steadily per Part (c) above.