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:

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

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.

How would the illustration look if it were showing a step-down transformer?

Combustion gases passing through a $5$-cm-internaldiameter circular tube are used to vaporize wastewater at atmospheric pressure. Hot gases enter the tube at $115\ \mathrm{kPa}$ and $250^{\circ} \mathrm{C}$ at a mean velocity of $5 \mathrm{~m} / \mathrm{s}$ and leave at $150^{\circ} \mathrm{C}$. If the average heat transfer coefficient is $120 \mathrm{~W} / \mathrm{m}^2 \cdot \mathrm{K}$ and the inner surface temperature of the tube is $110^{\circ} \mathrm{C}$, find (a) the tube length and (b) the rate of evaporation of water. Use air properties for the combustion gases.

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.

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

How would the illustration look if it were showing a step-down transformer?

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.

a. What does a transformer do? b. Interpreting Diagrams . What is the difference between a step-up transformer and a step-down transformer? c. Why do some appliances have step-down transformers built into them?

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.

Consider an array of vertical rectangular fins which is to be used to cool an electronic device mounted in quiescent, atmospheric air at $T_{\mathrm{x}}=27^{\circ} \mathrm{C}$. Each fin has $L=20 \mathrm{~mm}$ and $H=150 \mathrm{~mm}$ and operates at an approximately uniform temperature of $T_s=77^{\circ} \mathrm{C}$. Viewing each fin surface as a vertical plate in an infinite, quiescent medium, calculate the rate of heat transfer from a fin by free convection. Comment on the effect of boundary layer formation on specifying the spacing between fins.

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 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 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?