The convection heat transfer coefficient for a clothed person standing in moving air is expressed as $h=14.8 \mathrm{~V}^{0.69}$ for $0.15<V<1.5 \mathrm{~m} / \mathrm{s}$, where $V$ is the air velocity. For a person with a body surface area of $1.7 \mathrm{~m}^{2}$ and an average surface temperature of $29^{\circ} \mathrm{C}$, Find the rate of heat loss from the person in windy air at $10^{\circ} \mathrm{C}$ by convection for air velocities of $(a) 0.5 \mathrm{~m} / \mathrm{s}$, (b) $1.0 \mathrm{~m} / \mathrm{s}$, and $(c) 1.5 \mathrm{~m} / \mathrm{s}$.

In the boiler of a power plant are tubes through which water flows as it is brought from $0.6\ \mathrm{MPa}, 130^{\circ} \mathrm{C}$ to $200^{\circ} \mathrm{C}$ at essentially constant pressure. Combustion gases with a mass flow rate of $400 \mathrm{~kg} / \mathrm{s}$ pass over the tubes and cool from $827^{\circ} \mathrm{C}$ to $327^{\circ} \mathrm{C}$ at essentially constant pressure. The combustion gases can be modeled as air behaving as an ideal gas. There is no significant heat transfer from the boiler to its surroundings.

A vertical piston–cylinder device initially contains $0.2 \mathrm{m}^{3}$ of air at $20^{\circ} \mathrm{C}.$ The mass of the piston is such that it maintains a constant pressure of 300 kPa inside. Now a valve connected to the cylinder is opened, and air is allowed to escape until the volume inside the cylinder is decreased by one-half. Heat transfer takes place during the process so that the temperature of the air in the cylinder remains constant. Determine (a) the amount of air that has left the cylinder and (b) the amount of heat transfer.

A transistor with a height of $0.4 \mathrm{~cm}$ and a diameter of $0.6 \mathrm{~cm}$ is mounted on a circuit board. The transistor is cooled by air flowing over it with an average heat transfer coefficient of $30 \mathrm{~W} / \mathrm{m}^{2} \cdot{ }^{\circ} \mathrm{C}$. If the air temperature is $55^{\circ} \mathrm{C}$ and the transistor case temperature is not to exceed $70^{\circ} \mathrm{C}$, Find the amount of power this transistor can dissipate safely. Disregard any heat transfer from the transistor base.

Air with a mass flow rate of $5\ \mathrm{lb} / \mathrm{s}$ enters a horizontal nozzle operating at steady state at $800^{\circ} \mathrm{R}, 50\ \mathrm{lbf} / \mathrm{in}^2$ and a velocity of $10\ \mathrm{ft} / \mathrm{s}$. At the exit, the temperature is $570^{\circ} \mathrm{R}$ and the velocity is $1510\ \mathrm{ft} / \mathrm{s}$. Using the ideal gas model for air, determine

(a) the area at the inlet, in $\mathrm{ft}^2$, and

(b) the heat transfer between the nozzle and its surroundings, in Btu per lb of air flowing.

A finned-tube heat exchanger operates with water in the tubes and airflow across the fins. The water inlet temperature is $130^{\circ} \mathrm{F}$ while the incoming air temperature is $75^{\circ} \mathrm{F}$. An overall heat-transfer coefficient of $57 \mathrm{~W} / \mathrm{m}^2 \cdot{ }^{\circ} \mathrm{C}$ is experienced when the water-flow rate is $0.5 \mathrm{~kg} / \mathrm{s}$. The area of the exchanger is $52 \mathrm{~m}^2$ and the airflow is $2.0 \mathrm{~kg} / \mathrm{s}$ for the given conditions. Determine the exit water temperature, expressed in ${ }^{\circ} \mathrm{C}$.

You have just washed your hair and you now blowdry it in a room with 23$^{0} \mathrm{C}$, $\phi$ = 60%, (1). The Dryer, 500 W, heats the air to 49$^{0} \mathrm{C}$, (2), blows it through your hair, where the air becomes saturated(3), and then flows on to hit a window, where it cools to 15$^{\circ} \mathrm{C}$ (4). Find the relative humidity at state 2, the heat transfer per kilogram of dry air in the dryer, the air flow rate, and the amount of water condensed on the window, if any.

A system consisting of 3 lb of water vapor in a piston–cylinder assembly, initially at $350^{\circ} \mathrm{F}$ and a volume of 71.7 $\mathrm{ft}^{3}$, is expanded in a constant-pressure process to a volume of 85.38 $\mathrm{ft}^{3}$. The system then is compressed isothermally to a final volume of 28.2 $\mathrm{ft}^{3}$. During the isothermal compression, energy transfer by work into the system is 72 Btu. Kinetic and potential energy effects are negligible. Determine the heat transfer, in Btu, for each process.

Air is compressed in an axial-flow compressor operating at steady state from $27^{\circ} \mathrm{C},$ 1 bar to a pressure of 2.1 bar. The work required is 94.6 kJ per kg of air flowing. Heat transfer from the compressor occurs at an average surface temperature of $40^{\circ} \mathrm{C}$ at the rate of 14 kJ per kg of air flowing. The effects of motion and gravity can be ignored. Let $T_{0}=20^{\circ} \mathrm{C}, p_{0}=1$ bar. Assuming ideal gas behavior, (a) determine the temperature of the air at the exit, in $^\circ C,$ (b) determine the rate of exergy destruction within the compressor, in kJ per kg of air flowing, and (c) perform a full exergy accounting, in kJ per kg of air flowing, based on work input.

Water $(c_p = 4180 J/kg \cdot K)$ enters the 2.5-cm-internal-diameter tube of a double-pipe counter-flow heat exchanger at $17^\circ C$ at a rate of 1.8 kg/s. Water is heated by steam condensing at $120^\circ C (h_{fg} = 2203 kJ/kg)$ in the shell. If the overall heat transfer coefficient of the heat exchanger is $700 W/m^2 \cdot K,$ determine the length of the tube required in order to heat the water to $80^\circ C$ using (a) the LMTD method and (b) the $\varepsilon — NTU$ method.

A spherical vessel, with 30.0-cm outside diameter, is used as a reactor for a slow endothermic reaction. The vessel is completely submerged in a large water-filled tank, held at a constant temperature of $30^\circ C.$ The outside surface temperature of the vessel is $20^\circ C.$ Calculate the rate of heat transfer in steady operation for the following cases: (a) the water in the tank is still, (b) the water in the tank is still (as in a part a), however, the buoyancy force caused by the difference in water density is assumed to be negligible, and (c) the water in the tank is circulated at an average velocity of 20 cm/s.

Water is the working fluid in an ideal Rankine cycle. Superheated vapor enters the turbine at $10\ \mathrm{MPa}, 480^{\circ} \mathrm{C}$, and the condenser pressure is $6\ \mathrm{kPa}$. Determine for the cycle (a) the heat transfer to the working fluid passing through the steam generator, in $\mathrm{kJ}$ per $\mathrm{kg}$ of steam flowing. (b) the thermal efficiency. (c) the heat transfer from the working fluid passing through the condenser to the cooling water, in $\mathrm{kJ}$ per $\mathrm{kg}$ of steam flowing.

A steam turbine operating at steady state develops 9750 hp. The turbine receives 100,000 pounds of steam per hour at $400 \text { lbf/in. }^{2}$ and $600^{\circ} \mathrm{F}.$ At a point in the turbine where the pressure is $60 \mathrm{lbf} / \mathrm{in} .^{2}$ and the temperature is $300^{\circ} \mathrm{F},$ steam is bled off at the rate of 25,000 lb/h. The remaining steam continues to expand through the turbine, exiting at $2 \mathrm{lbf} / \mathrm{in}^{2}$ and 90% quality. a. Determine the rate of heat transfer between the turbine and its surroundings, in Btu/h. b. Devise and evaluate an exergetic efficiency for the turbine. Kinetic and potential energy effects can be ignored. Let $T_{0}=77^{\circ} \mathrm{F}, p_{0}=1 \mathrm{atm}.$

Oil in an engine is being cooled by air in a cross- flow heat exchanger, where both fluids are unmixed. Oil $\left(c_{p h}=2047 \mathrm{J} / \mathrm{kg} \cdot \mathrm{K}\right)$ flowing with a flow rate of 0.026 kg/s enters the tube side at $75^{\circ} \mathrm{C},$ while air $\left(c_{p c}=1007 \mathrm{J} / \mathrm{kg} \cdot \mathrm{K}\right)$ enters the shell side at $30^{\circ} \mathrm{C}$ with a flow rate of 0.21 kg/s. The overall heat transfer coefficient of the heat exchanger is $53 \mathrm{W} / \mathrm{m}^{2} \cdot \mathrm{K}$ and the total surface area is $1 m^2.$ If the correction factor is F = 0.96, determine the outlet temperatures of the oil and air.