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.

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 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.

A model-train transformer plugs into 120 V ac, and draws 0.75 A while supplying $15 ~\mathrm{A}$ to the train.

(a) What voltage is present across the tracks? (b) Is the transformer step-up or step-down?

Electric doorbells found in many homes require 10.0 V to operate. To obtain this voltage from the standard 120-V supply, a transformer is used. Is a step-up or a step-down transformer needed, and what is its turns ratio

$$N _ { s } / N _ { p } ?$$

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

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.

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:

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

Hot water flows through a PVC $(k=0.092 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})$ pipe whose inner diameter is $2 \mathrm{~cm}$ and whose outer diameter is $2.5 \mathrm{~cm}$. The temperature of the interior surface of this pipe is $35^{\circ} \mathrm{C}$, and the temperature of the exterior surface is $20^{\circ} \mathrm{C}$. The rate of heat transfer per unit of pipe length is (a) $22.8 \mathrm{~W} / \mathrm{m}$ (b) $38.9 \mathrm{~W} / \mathrm{m}$ $(c)$ $48.7 \mathrm{~W} / \mathrm{m}$ (d) $63.6 \mathrm{~W} / \mathrm{m}$ (e) $72.6 \mathrm{~W} / \mathrm{m}$

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

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?

Why do some appliances have step-down transformers built in?

A model-train transformer plugs into 120-V ac and draws 0.35 A while supplying 7.5 A to the train. Is the transformer step-up or step-down?

A high-intensity desk lamp is rated at $35 \mathrm{~W}$ but requires only $12 \mathrm{~V}$. It contains a transformer that converts $120~\mathrm{V}$ household voltage. Is the transformer step-up or step-down?