A feedwater heater that supplies a boiler consists of a shell-and-tube heat exchanger with one shell pass and two tube passes. One hundred thin-walled tubes each have a diameter of 20 mm and a length (per pass) of 2 m. Under normal operating conditions water enters the tubes at 10 kg/s and 290 K and is heated by condensing saturated steam at 1 atm on the outer surface of the tubes. The convection coefficient of the saturated steam is $10,000 \mathrm{W} / \mathrm{m}^{2} \cdot \mathrm{K}$. (a) Determine the water outlet temperature. (b) With all other conditions remaining the same, but accounting for changes in the overall heat transfer coefficient, plot the water outlet temperature as a function of the water flow rate for $5 \leq m_{c} \leq 20 \mathrm{kg} / \mathrm{s}$. (c) On the plot of part (b), generate two additional curves for the water outlet temperature as a function of flow rate for fouling factors of $R_{f}^{\prime \prime}=0.0002$ and $0.0005 \mathrm{m}^{2} \cdot \mathrm{K} / \mathrm{W}$.

A very long solid nonconducting cylinder of radius $R_1$ is uniformly charged with a volume charge density $\rho_{\mathrm{E}}$. It is surrounded by a concentric cylindrical tube of inner radius $R_2$ and outer radius $R_3$ and it too carries a uniform charge density $\rho_{\mathrm{E}}$. Determine the electric field as a function of the distance $R$ from the center of the cylinders for $\text{(b) } R_1<R<R_2$. Assume the cylinders are very long compared to $R_3$.

Steam at a pressure of 0.08 bar and a quality of 93.2% enters a shell-and-tube heat exchanger where it condenses on the outside of tubes through which cooling water flows, exiting as saturated liquid at 0.08 bar. The mass flow rate of the condensing steam is $3.4 \times 10^5 kg/h.$ Cooling water enters the tubes at $15^{\circ}C$ and exits at $35^{\circ}C$ with negligible change in pressure. Neglecting stray heat transfer and ignoring kinetic and potential energy effects, determine the mass flow rate of the cooling water, in kg/h, for steady-state operation.

A shell-and-tube heat exchanger is to heat 10,000 kg/h of water from 16 to $84^{\circ} \mathrm{C}$ by hot engine oil flowing through the shell. The oil makes a single shell pass, entering at $160^{\circ} \mathrm{C}$ and leaving at $94^{\circ} \mathrm{C}$, with an average heat transfer coefficient of $400 \mathrm{W} / \mathrm{m}^{2} \cdot \mathrm{K}$. The water flows through 11 brass tubes of 22.9-mm inside diameter and 25.4-mm outside diameter, with each tube making four passes through the shell. (a) Assuming fully developed flow for the water, determine the required tube length per pass. (b) For the tube length found in part (a), plot the effectiveness, fluid outlet temperatures, and water-side convection coefficient as a function of the water flow rate for $5000 \leq m_{c} \leq 15,000 \mathrm{kg} / \mathrm{h}$, with all other conditions remaining the same.

The hot and cold inlet temperatures to a concentric tube heat exchanger are $T_{h, i}=200^{\circ} \mathrm{C}, T_{c, i}=100^{\circ} \mathrm{C}$, respectively. The outlet temperatures are $T_{h, o}=110^{\circ} \mathrm{C}$ and $T_{c, o}=125^{\circ} \mathrm{C}$. Is the heat exchanger operating in a parallel flow or in a counterflow configuration? What is the heat exchanger effectiveness? What is the NTU? Phase change does not occur in either fluid.

Water $(c_p = 1.0 Btu/lbm \cdot ^\circ F)$ is to be heated by solar-heated hot air $(c_p = 0.24 Btu/lbm \cdot ^\circ F)$ in a double-pipe counter-flow heat exchanger. Air enters the heat exchanger at $190^\circ F$ at a rate of 0.7 lbm/s and leaves at $135^\circ F.$ Water enters at $70^\circ F$ at a rate of 0.35 lbm/s. The overall heat transfer coefficient based on the inner side of the tube is given to be $20 Btu/h \cdot ft^2 \cdot ^\circ F.$ Determine the length of the tube required for a tube internal diameter of 0.5 in.

A shell-and-tube heat exchanger must be designed to heat 2.5 kg/s of water from 15 to $85^{\circ} \mathrm{C}$. The heating is to be accomplished by passing hot engine oil, which is available at $160^{\circ} \mathrm{C}$, through the shell side of the exchanger. The oil is known to provide an average convection coefficient of $h_{o}=400 \mathrm{W} / \mathrm{m}^{2} \cdot \mathrm{K}$ on the outside of the tubes. Ten tubes pass the water through the shell. Each tube is thin walled, of diameter D=25 mm, and makes eight passes through the shell. If the oil leaves the exchanger at $100^{\circ} \mathrm{C}$, what is its flow rate? How long must the tubes be to accomplish the desired heating?

A shell-and-tube process heater is to be selected to heat water $(c_p = 4190 J/kg \cdot K)$ from $20^\circ C$ to $90^\circ C$ by steam flowing on the shell side. The heat transfer load of the heater is 600 kW. If the inner diameter of the tubes is 1 cm and the velocity of water is not to exceed 3 m/s, determine how many tubes need to be used in the heat exchanger.

The condenser of a room air conditioner is designed to reject heat at a rate of 15,000 kJ/h from refrigerant-134a as the refrigerant is condensed at a temperature of $40^\circ C.$ Air $(c_p = 1005 J/kg \cdot K)$ flows across the finned condenser coils, entering at $25^\circ C$ and leaving at $35^\circ C.$ If the overall heat transfer coefficient based on the refrigerant side is $150 W/m^2 \cdot K,$ determine the heat transfer area on the refrigerant side.

Usa estas preguntas para entrevistar a un(a) compañero/a acerca de la primera persona que conoció de un país hispanohablante. ¿Cómo se llamaba?

Thin-walled aluminum tubes of diameter D=10 mm are used in the condenser of an air conditioner. Under normal operating conditions, a convection coefficient of $h_{i}=5000 \mathrm{W} / \mathrm{m}^{2} \cdot \mathrm{K}$ is associated with condensation on the inner surface of the tubes, while a coefficient of $h_{o}=100 \mathrm{W} / \mathrm{m}^{2} \cdot \mathrm{K}$ is maintained by airflow over the tubes. (a) What is the overall heat transfer coefficient if the tubes are unfinned? (b) What is the overall heat transfer coefficient based on the inner surface, $U_{i}$, if aluminum annular fins of thickness t=1.5 mm, outer diameter $D_{o}=20 \mathrm{mm}$, and pitch S=3.5 mm are added to the outer surface? Base your calculations on a 1-m-long section of tube. Subject to the requirements that $t \geq 1$ and $(S-t) \geq 1.5 \mathrm{mm}$, explore the effect of variations in t and S on $U_{i}$. What combination of t and S would yield the best heat transfer performance?

For a refrigerator with automatic defrost and a top-mounted freezer, the electric power required is approximately 420 watts to operate. If the coefficient of performance is 2.9, determine the rate that energy is removed from the its refrigerated space, in watts. Evaluating electricity at $\$ 0.10 / \mathrm{kW} \cdot \mathrm{h},$ and assuming the unit runs 60% of the time, estimate the cost of one month's operation, in $.

Graph the function. Compare the graph to the graph of

$$f ( x ) = \sqrt [ 3 ] { x }$$

.

$$q ( x ) = \sqrt [ 3 ] { - 4 - x }$$

For a refrigerator with automatic defrost and a top- mounted freezer, the annual cost of electricity is $55. (a) Evaluating electricity at 8 cents per$kW \cdot h$, determine the refrigerator’s annual electricity requirement, in$kW \cdot h$. (b) If the refrigerator’s coefficient of performance is 3, determine the amount of energy removed from its refrigerated space annually, in MJ.