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 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 large stationary Brayton-cycle has-turbine power plant delivers a power output of 100 000 hp to an electric generator. The minimum temperature is the cycle is 540 R, and the maximum temperature is 2900 R. The minimum pressure in the cycle is 1 atm, and the compressor pressure ratio is 14 to 1. Calculate the power output of the turbine, the fraction of the turbine output required to drive the compressor, and the thermal efficiency of the cycle.

Consider a heat exchanger in which both fluids have the same specific heats but different mass flow rates. Which fluid will experience a larger temperature change: the one with the lower or higher mass flow rate?

Choose the best answer. Sarah is currently spending $100 per month on electricity. She pays$0.20 per kWh. Her space heater is responsible for 10 percent of her electricity consumption. How many kilowatt-hours does her space heater use in a month? Assume a month is 30 days. (a) 0.07 kWh (b) 2 kWh (c) 20 kWh (d) 50 kWh

Factor out the common factor. 6y-30

An isothermal silicon chip of width W=20 mm on a side is soldered to an aluminum heat sink $( k=180 \mathrm{W} / \mathrm{m} \cdot \mathrm{K})$ of equivalent width. The heat sink has a base thickness of $L_{h}=3 \mathrm{mm}$ and an array of rectangular fins, each of length $L_{f}=15 \mathrm{mm}$. Airflow at $T_{\infty}=20^{\circ} \mathrm{C}$ is maintained through channels formed by the fins and a cover plate, and for a convection coefficient of $h=100 \mathrm{W} / \mathrm{m}^{2} \cdot \mathrm{K}$, a minimum fin spacing of 1.8 mm is dictated by limitations on the flow pressure drop. The solder joint has a thermal resistance of $R_{t, c}^{\prime \prime}=2 \times 10^{-6} \mathrm{m}^{2} \cdot \mathrm{K} / \mathrm{W}$. (a) Consider limitations for which the array has N=11 fins, in which case values of the fin thickness t=0.182 mm and pitch S=1.982 mm are obtained from the requirements that W=(N-1)S+t and S-t=1.8 mm. If the maximum allowable chip temperature is $T_{c}=85^{\circ} \mathrm{C}$, what is the corresponding value of the chip power $q_{c} ?$ An adiabatic fin tip condition may be assumed, and airflow along the outer surfaces of the heat sink may be assumed to provide a convection coefficient equivalent to that associated with airflow through the channels. (b) With (S-t) and h fixed at 1.8 mm and 100 $\mathrm{W} / \mathrm{m}^{2} \cdot \mathrm{K}$, respectively, explore the effect of increasing the fin thickness by reducing the number of fins. With N=11 and S-t fixed at 1.8 mm, but relaxation of the constraint on the pressure drop, explore the effect of increasing the airflow, and hence the convection coefficient.

A 9-ft-high room with a base area of $12 \mathrm{ft} \times 12 \mathrm{ft}$ is to be heated by electric resistance heaters placed on the ceiling, which is maintained at a uniform temperature of $90^{\circ} \mathrm{F}$ at all times. The floor of the room is at $65^{\circ} \mathrm{F}$ and has an emissivity of 0.8. The side surfaces are well insulated. Treating the ceiling as a blackbody, determine the rate of heat loss from the room through the floor.

Find an equation of the parabola that has the indicated vertex and whose graph passes through the given point. Vertex: (-5, -1); point: (-2, 6)

Solve the system by the method of elimination. Then state whether the system is consistent or inconsistent.

$$\left\{\begin{array}{r} {2 x-3 y=4} \\ {-2 x-y=4} \end{array}\right.$$

A pump is to be selected for a waterfall in a garden. The water collects in a pond at the bottom, and the elevation difference between the free surface of the pond and the location where the water is discharged is 3 m. The flow rate of water is to be at least 8 L/s. Select an appropriate motor– pump unit for this job and identify three manufacturers with product model numbers and prices. Make a selection and explain why you selected that particular product. Also estimate the cost of annual power consumption of this unit assuming continuous operation.

A shell-and-tube exchanger (two shells, four tube passes) is used to heat 10,000 kg/h of pressurized water from 35 to $120^{\circ} \mathrm{C}$ with 5000 kg/h pressurized water entering the exchanger at $300^{\circ} \mathrm{C}$. If the overall heat transfer coefficient is $1500 \mathrm{W} / \mathrm{m}^{2} \cdot \mathrm{K}$, determine the required heat exchanger area.

An 8-m-long, uninsulated square duct of cross section $0.2 \mathrm{m} \times 0.2 \mathrm{m}$ and relative roughness $10^{-3}$ passes through the attic space of a house. Hot air enters the duct at 1 atm and $80^{\circ} \mathrm{C}$ at a volume flow rate of $0.15 \mathrm{m}^{3} / \mathrm{s}.$ The duct surface is nearly isothermal at $60^{\circ} \mathrm{C}.$ Determine the rate of heat loss from the duct to the attic space and the pressure difference between the inlet and outlet sections of the duct. Evaluate air properties at a bulk mean temperature of $80^{\circ} \mathrm{C}.$ Is this a good assumption?

Use the given zero of f to find all the zeros of f. $f(x)=x^{4}-2 x^{3}+37 x^{2}-72 x+36$, 6i