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.

Ambient air at 100 kPa and 300 K is compressed isentropically in a steady-flow device to 0.8 MPa. Determine (a) the work input to the compressor, (b) the exergy of the air at the compressor exit, and (c) the exergy of compressed air after it is cooled to 300 K at 0.8 MPa pressure.

A preheater involves the use of condensing steam at $100^{\circ} \mathrm{C}$ on the inside of a bank of tubes to heat air that enters at 1 atm and $25^{\circ} \mathrm{C}$. The air moves at 5 m/s in cross flow over the tubes. Each tube is 1 m long and has an outside diameter of 10 mm. The bank consists of 196 tubes in a square, aligned array for which $S_{T}=S_{L}=15 \mathrm{mm}$. What is the total rate of heat transfer to the air? What is the pressure drop associated with the airflow?

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 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 $(c) 1.5 \mathrm{~m} / \mathrm{s}$.

Water is the working fluid in an ideal Rankine cycle. Superheated vapor enters the turbine at 10 MPa, $480^\circ C,$ and the condenser pressure is 6 kPa. Isentropic efficiencies of the turbine and pump are 84% and 73%, respectively. Determine for the cycle a. the heat transfer to the working fluid passing through the steam generator, in kJ per 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 kJ per kg of steam flowing.

Obtain a relation for the fin efficiency for a fin of constant cross-sectional area $A_c,$ perimeter p, length L, and thermal conductivity k exposed to convection to a medium at $T_{\infty}$ with a heat transfer coefficient h, Assume the fins are sufficiently long so that the temperature of the fin at the tip is nearly $T_{\infty}.$ Take the temperature of the fin at the base to be $T_b$ and neglect heat transfer from the fin tips. Simplify the relation for (a) a circular fin of diameter D and (b) rectangular fins of thickness t.

Nitrogen $(N_2)$ initially at $40^{\circ} \mathrm{F} \text { and } 14.7 \mathrm{lbf} / \mathrm{in}^{2}$ fills a closed, rigid, $6.5-ft^3$ tank fitted with a paddle wheel. During a process, the paddle wheel provides 5 Btu of energy transfer by work to the gas. The gas temperature reaches $80^\circ F$ at the end of the process. Assuming ideal gas behavior, determine the mass of nitrogen, in lb, and the heat transfer, in Btu. Kinetic and potential energy effects can be ignored.

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) $31.7^\circ C$

Heat is to be transferred from water to air through an aluminum wall. It is proposed to add rectangular fins 0.05-in. thick and 3/4-in. long spaced 0.08 in. apart to the aluminium surface to aid in transferring heat. The heat-transfer coefficients on the air and water sides are 3 and 25 Btu/h ft2 $^{\circ} \mathrm{F}$, respectively. Evaluate the percent increase in heat transfer if these fins are added to (a) the air side, (b) the water side, (c) and both sides. What conclusions may be reached regarding this result?

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?

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 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) $1393 W/m^2 \cdot K$

An ASTM B335 nickel alloy rod, with a diameter of $5 \mathrm{~mm}$ and a length of $10 \mathrm{~cm}$, is used to boil water at $1 \mathrm{~atm}$. The rod is immersed in the water horizontally, and it has an emissivity of $0.3$. The maximum use temperature for ASTM B335 nickel alloy rod is $427^{\circ} \mathrm{C}$ (ASME Code for Process Piping, ASME B31.3-2014). Find the highest rate of heat transfer that can be supplied from the ASTM B335 rod to boil the water without heating the rod surface above the maximum use temperature.