Oil in an engine is being cooled by air in a cross-flow heat exchanger, where both fluids are unmixed. Oil $(c_ph =2047 J/kg \cdot K)$ flowing with a flow rate of 0.026 kg/s enters the heat exchanger at $75^\circ C,$ while air $(c_{pc} = 1007 J/kg \cdot K)$ enters at $30^\circ C$ with a flow rate of 0.21 kg/s. The overall heat transfer coefficient of the heat exchanger is $53 W/m^2 \cdot K$ and the total surface area is $1 m^2.$ Determine (a) the heat transfer effectiveness and (b) the outlet temperature of the oil.

A certain solar-energy collector produces a maximum temperature of 100$^{\circ} \mathrm{C}$. The energy is used in a cycle heat engine that operates in a 10$^{\circ} \mathrm{C}$ environment. What is the maximum thermal efficiency? If the collector is redesigned to focus the incoming light, what should the maximum temperature be to produce a 25% improvement in engine efficiency?

Hot oil $(c_p = 2.1 kJ/kg \cdot K)$ at $110^\circ C$ and 8 kg/s is to be cooled in a heat exchanger by cold water $(c_p = 4.18 kJ/kg \cdot K)$ entering at $10^\circ C$ and at a rate of 2 kg/s. The lowest temperature that oil can be cooled in this heat exchanger is(a) $10.0^\circ C$ (b) $33.5^\circ C$ (c) $46.1^\circ C$ (d) $60.2^\circ C$ (e) $71.4^\circ C$

A double-pipe parallel-flow heat exchanger is to heat water $(c_p = 4180 J/kg \cdot K)$ from $25^\circ C$ to $60^\circ C$ at a rate of 0.2 kg/s. The heating is to be accomplished by geothermal water $(c_p =4310 J/kg \cdot K)$ available at $140^\circ C$ at a mass flow rate of 0.3 kg/s. The inner tube is thin-walled and has a diameter of 0.8 cm. If the overall heat transfer coefficient of the heat exchanger is $550 W/m^2 \cdot K,$ determine the length of the tube required to achieve the desired heating.

A single tube-pass heat exchanger is to be designed to heat water by condensing steam in the shell. The water is to pass through the smooth horizontal tubes in turbulent flow, and the steam is to be condensed dropwise in the shell. The water flow rate, the initial and final water temperatures, the condensation temperature of the steam, and the available tube-side pressure drop (neglecting entrance and exit losses) are all specified. In order to determine the optimum exchanger design, it is desirable to know how the total required area of the exchanger varies with the tube diameter selected. Assuming that the water flow remains turbulent and that the thermal resistance of the tube wall and the steam–condensate film is negligible, determine the effect of tube diameter on the total area required in the exchanger.

Give the phase and the missing properties of P, T, v, and x. These may be a little more difficult to determine if the appendix tables are used instead of the software.a. R-410a, T = 10$^{\circ} \mathrm{C}$, v = 0.02 m3/kgb. H2O, v = 0.2 m3/kg, x = 0.5c. H2O, T = 60$^{\circ} \mathrm{C}$, v = 0.001016 m3/kgd. NH3, T = 30$^{\circ} \mathrm{C}$, P = 60 kPae. R134a, v = 0.005 m3/kg, x = 0.5

Cold water ($c_{p}$ = 4.18 kJ/kgK) leading to a shower enters a thin-walled double-pipe counterflow heat exchanger at 15$^\circ{}$C at a rate of 0.60 kg/s and is heated to 45$^\circ{}$C by hot water ($c_{p}$ = 4.19 kJ/kgK) that enters a 100$^\circ{}$C at a rate of 3 kg/s. Determine the rate of heat transfer in the heat exchanger and the exit temperature of the hot water.

Cold water $(c_p = 4.18 kJ/kg \cdot K)$ enters a cross-flow heat exchanger at $14^\circ C$ at a rate of 0.35 kg/s where it is heated by hot air $(c_p = 1.0 kJ/kg \cdot K)$ that enters the heat exchanger at $65^\circ C$ at a rate of 0.8 kg/s and leaves at $25^\circ C.$ Determine the maximum outlet temperature of the cold water and the effectiveness of this heat exchanger.

Glycerin $(c_p = 2400 J/kg \cdot K)$ at $20^\circ C$ and 0.5 kg/s is to be heated by ethylene glycol $(c_p = 2500 J/kg \cdot K)$ at $60^\circ C$ in a thin-walled double-pipe parallel-flow heat exchanger. The temperature difference between the two fluids is $15^\circ C$ at the outlet of the heat exchanger. If the overall heat transfer coefficient is $240 W/m^2 \cdot K$ and the heat transfer surface area is $3.2 m^2,$ determine (a) the rate of heat transfer, (b) the outlet temperature of the glycerin, and (c) the mass flow rate of the ethylene glycol.

The radiator in an automobile is a cross-flow heat exchanger $(UA_s = 10 kW/K)$ that uses air $(c_p = 1.00 kJ/ kg \cdot K)$ to cool the engine coolant fluid $(c_p = 4.00 kJ/kg \cdot K).$ The engine fan draws $30^\circ C$ air through this radiator at a rate of 10 kg/s while the coolant pump circulates the engine coolant at a rate of 5 kg/s. The coolant enters this radiator at $80^\circ C.$ Under these conditions, what is the number of transfer units (NTU) of this radiator? (a) 1 (b) 2 (c) 3 (d) 4 (e) 5

An automobile radiator may be viewed as a cross-flow heat exchanger with both fluids unmixed. Water, which has a flow rate of 0.05 kg/s, enters the radiator at 400 K and is to leave at 330 K. The water is cooled by air that enters at 0.75 kg/s and 300 K. (a) If the overall heat transfer coefficient is $200 \mathrm{W} / \mathrm{m}^{2} \cdot \mathrm{K}$, what is the required heat transfer surface area? (b) A manufacturing engineer claims ridges can be stamped on the finned surface of the exchanger, which could greatly increase the overall heat transfer coefficient. With all other conditions remaining the same and the heat transfer surface area determined from part (a), generate a plot of the air and water outlet temperatures as a function of U for $200 \leq U \leq 400 \mathrm{W} / \mathrm{m}^{2} \cdot \mathrm{K}$. What benefits result from increasing the overall convection coefficient for this application?

Consider a rectangular fin that is used to cool a motorcycle engine. The fin is 0.15 m long and at a temperature of $250^{\circ} \mathrm{C}$, while the motorcycle is moving at 80 km/h in air at $27^{\circ} \mathrm{C}$. The air is in parallel flow over both surfaces of the fin, and turbulent flow conditions may be assumed to exist throughout. (a) What is the rate of heat removal per unit width of the fin? (b) Generate a plot of the heat removal rate per unit width of the fin for motorcycle speeds ranging from 10 to 100 km/h.

The components of an electronic system are located in a 1.5-m-long horizontal duct whose cross section is 20cm × 20 cm. The components in the duct are not allowed to come into direct contact with cooling air, and thus are cooled by air at $30^\circ C$ flowing over the duct with a velocity of 200 m/min. If the surface temperature of the duct is not to exceed $65^\circ C,$ determine the total power rating of the electronic devices that can be mounted into the duct.

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 $0.0005 \mathrm{m}^{2} \cdot \mathrm{K} / \mathrm{W}$.