Water at $0^{\circ} \mathrm{C}$ releases $333.7 \mathrm{~kJ} / \mathrm{kg}$ of heat as it freezes to ice $\left(\rho=920 \mathrm{~kg} / \mathrm{m}^{3}\right)$ at $0^{\circ} \mathrm{C}$. An aircraft flying under icing conditions maintains a heat transfer coefficient of $150 \mathrm{~W} / \mathrm{m}^{2}$. ${ }^{\circ} \mathrm{C}$ between the air and wing surfaces. What temperature must the wings be maintained at to prevent ice from forming on them during icing conditions at a rate of $1 \mathrm{~mm} / \mathrm{min}$ or less?

Consider a very long rectangular fin attached to a flat surface such that the temperature at the end of the fin is essentially that of the surrounding air, i.e. $20^{\circ} \mathrm{C}$. Its width is $5.0 \mathrm{~cm}$; thickness is $1.0 \mathrm{~mm}$; thermal conductivity is $200 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}$; and base temperature is $40^{\circ} \mathrm{C}$. The heat transfer coefficient is $20 \mathrm{~W} / \mathrm{m}^{2}$. $K$. Estimate the fin temperature at a distance of $5.0 \mathrm{~cm}$ from the base and the rate of heat loss from the entire fin.

The heat transfer coefficient of a copper tube $(1.9-\mathrm{cm}$ ID and $2.3-\mathrm{cm} \mathrm{OD}$ ) is $500 \mathrm{~W} / \mathrm{m}^2 \mathrm{~K}$ on the inside and $120 \mathrm{~W} / \mathrm{m}^2 \mathrm{~K}$ on the outside, but a deposit with a fouling factor of $0.009 \mathrm{~m}^2 \mathrm{~K} / \mathrm{W}$ (based on the tube outside diameter) has built up over time. Estimate the percentage increase in the overall heat transfer coefficient if the deposit were removed.

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 $300 \mathrm{~kPa}$ 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. Find (a) the amount of air that has left the cylinder and (b) the amount of heat transfer.

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 $T_{0}=77^{\circ} \mathrm{F}, p_{0}=1 \mathrm{atm}.$

Water is boiled at $150^\circ C$ in a boiler by hot exhaust gases $(c_p = 1.05 kJ/kg \cdot ^\circ C)$ that enter the boiler at $400^\circ C$ at a rate of 0.4 kg/s and leaves at $200^\circ C.$ The surface area of the heat exchanger is $0.64 m^2.$ The overall heat transfer coefficient of this heat exchanger is (a) $940 W/m^2 \cdot K$ (b) $1056 W/m^2 \cdot K$ (c) $1145 W/m^2 \cdot K$ (d) $1230 W/m^2 \cdot K$ (e) $1393 W/m^2 \cdot K$

Consider the velocity and temperature profiles for airflow in a tube with diameter of 8cm can be expressed as

$$\begin{array}{l}{u(r)=0.2\left[\left(1-(r / R)^{2}\right]\right.} \\ {T(r)=250+200(r / R)^{3}}\end{array}$$

with units in m/s and K, respectively. If the convection heat transfer coefficient is $100 \mathrm{W} / \mathrm{m}^{2} \cdot \mathrm{K},$ determine the mass flow rate and surface heat flux using the given velocity and temperature profiles. Evaluate the air properties at $20^\circ C$ and 1 atm.

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.

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 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.

A cross-flow heat exchanger consists of a bundle of 32 tubes in a $0.6-\mathrm{m}^{2}$ duct. Hot water at $150^{\circ} \mathrm{C}$ and a mean velocity of 0.5 m/s enters the tubes having inner and outer diameters of 10.2 and 12.5 mm. Atmospheric air at $10^{\circ} \mathrm{C}$ enters the exchanger with a volumetric flow rate of $1.0 \mathrm{m}^{3} / \mathrm{s}$. The convection heat transfer coefficient on the tube outer surfaces is $400 \mathrm{W} / \mathrm{m}^{2} \cdot \mathrm{K}$. Estimate the fluid outlet temperatures.

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 ${ }^{\circ} \mathrm{C}$.

Water at $0^{\circ} \mathrm{C}$ releases $333.7 \mathrm{~kJ} / \mathrm{kg}$ of heat as it freezes to ice $\left(\rho=920 \mathrm{~kg} / \mathrm{m}^3\right)$ at $0^{\circ} \mathrm{C}$. An aircraft flying under icing conditions carries a heat transfer coefficient of $150 \mathrm{~W} / \mathrm{m}^2 \cdot \mathrm{K}$ between the air and wing surfaces. What temperature must the wings be kept at to prevent ice from forming on them during icing conditions at a rate of $1 \mathrm{~mm} / \mathrm{min}$ or less?

An air-cooled condenser is used to condense isobutane in a binary geothermal power plant. The isobutane is condensed at $85^\circ C$ by air $(c_p = 1.0 kJ/kg \cdot K)$ that enters at $22^\circ C$ at a rate of 18 kg/s. The overall heat transfer coefficient and the surface area for this heat exchanger are $2.4 kW/m^2 \cdot K$ and $1.25 m^2,$ respectively. The outlet temperature of air is (a) $45.4^\circ C$(b) $40.9^\circ C$ (c) $37.5^\circ C$ (d) $34.2^\circ C$ (e) $31.7^\circ C$