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

The general form of the Stefan-Maxwell equation for mass transfer of species i in an n-component ideal gas mixture along the z-direction for flux is given by

$$\frac{d y_{i}}{d z}=\sum_{j=1, j \neq i}^{n} \frac{y_{i} y_{j}}{D_{i j}}\left(\nu_{j}-\nu_{i}\right)$$

Show that for a gas-phase binary mixture of species A and B, this relationship is equivalent to Fick's rate equation:

$$N_{A, z}=-c D_{A B} \frac{d y_{A}}{d z}+y_{A}\left(N_{A, z}+N_{B, z}\right)$$

A -395 kg/s of water is to be cooled from $90^{\circ} \mathrm{C}$ to $70^{\circ} \mathrm{C}$ in a shell and tube heat exchanger having four shell passes and eight tube passes. The cooling fluid is also water with a flow rate of $5 \mathrm{~kg} / \mathrm{s}$ that enters at a temperature of $50^{\circ} \mathrm{C}$. The overall heat-transfer coefficient is $800 \mathrm{~W} / \mathrm{m}^2,{ }^{\circ} \mathrm{C}$. Determine the total area of the heat exchanger assuming all four shells are the same size.

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?

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.

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.

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.

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.

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.

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 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?

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.

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.

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