Heat Transfer 10th edition Jack Holman - Solutions

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An air-conditioning system operating on the reversed Carnot cycle is required to transfer heat from a house at a rate of 750 kJ/min to maintain its temperature at 24°C. If the outdoor air temperature is 35°C, determine the power required to operate this air-conditioning system.
An inventor claims to have developed a heat pump that produces a 200-kW heating effect for a 293 K heated zone while only using 75 kW of power and a heat source at 273 K. Justify the validity of this claim.
A heat pump operates on a Carnot heat pump cycle with a COP of 8.7. It keeps a space at 24°C by consuming 2.15 kW of power. Determine the temperature of the reservoir from which the heat is absorbed and the heating load provided by the heat pump.
A refrigerator is to remove heat from the cooled space at a rate of 300 kJ/min to maintain its temperature at -8°C. If the air surrounding the refrigerator is at 25°C, determine the minimum power input required for this refrigerator.
An inventor claims to have developed a refrigeration system that removes heat from the closed region at -12°C and transfers it to the surrounding air at 25°C while maintaining a COP of 6.5. Is this claim reasonable? Why?
A heat pump is used to maintain a house at 25°C by extracting heat from the outside air on a day when the outside air temperature is 4°C. The house is estimated to lose heat at a rate of 110,000 kJ/h, and the heat pump consumes 4.75 kW of electric power when running. Is this heat pump
A completely reversible refrigerator operates between thermal energy reservoirs at 450 R and 540 R. How many kilowatts of power are required for this device to produce a 15,000-Btu/h cooling effect?
An air-conditioning system is used to maintain a house at 72°F when the temperature outside is 90°F. If this air-conditioning system draws 5 hp of power when operating, determine the maximum rate of heat removal from the house that it can accomplish.
Air flows at Mach 0.2 through a circular duct with an internal diameter of 50 cm. The total pressure of the flow is 500 kPa and the total temperature is 200oC. Calculate the mass flow rate (m) through the channel.
Determine the velocity of sound in steam at 800 kPa and 350oC assuming (a) 1% variation of temperature across the wave and using the PC model, (b) Steam to behave as a perfect gas. Use the PC Flow State TESTcalc to evaluate steam properties.
Determine the velocity of sound in steam at 800 kPa and 350oC assuming (a) 1% variation of pressure across the wave and using the PC model, (b) steam to behave as a perfect gas. Use the PC Flow State TESTcalc to evaluate steam properties.
Refrigerant R-134a flows at 100 m/s at the exit of a nozzle where the pressure and temperature are 500 kPa and 30oC, respectively. Determine the Mach number of the flow state. Use the PC model for R-134a and assume a 1% variation in temperature across a sound wave.
A needle nose projectile traveling at a speed with M = 2 passes 250 m above the observer. Determine (a) The projectile's velocity (V), and (b) How far beyond the observer the projectile will first be heard. Assume the static temperature as 15oC.
Air flows through a device such that the total pressure is 700 kPa, the total temperature is 300oC and the velocity is 500 m/s. Determine (a) The static temperature (T) of air at this state. (b) The static pressure (p)
Air enters a diffuser with a velocity of 180 m/s and a inlet temperature of 303 K. Determine (a) The velocity of sound and (b) The flow Mach number at the diffuser inlet.
Determine the total temperature for the following substances flowing through a duct: (a) Helium at 180 kPa, 40oC and 250 m/s, (b) Nitrogen at 180 kPa, 40oC and 250 m/s, and (c) Steam at 3 MPa, 300oC and 400 m/s.
Air leaves a compressor in a pipe with a total temperature and pressure of 180oC, 350 kPa and a velocity of 150 m/s. The pipe has a cross sectional area of 0.02 m2. Determine (a) the static temperature (T) and (b) the static pressure (p), (c) the mass flow rate (m).
Steam at 1.2 MPa and 450oC flows through a pipe with a velocity of 300 m/s. Treating the superheated steam as a perfect gas, determine (a) the velocity of sound and (b) the flow Mach number for the steam.
In 15-1-16[BAV] determine the total pressure in each case. Problem 15-1-16 Determine the total temperature for the following substances flowing through a duct: (a) Helium at 180 kPa, 40oC and 250 m/s, (b) Nitrogen at 180 kPa, 40oC and 250 m/s
Determine (a) The velocity (V) of sound, (b) The Mach number, (c) The total temperature (T) and (d) The total pressure (p) of air that is flowing at 50 kPa, 250 K and 500 m/s.
Air flows in a duct at a pressure of 200 kPa with a velocity of 200 m/s. The temperature of air is 300 K. Determine (a) The total temperature (T). (b) The total pressure (p) and
Steam at 250oC and quality 95% is flowing through a duct with a velocity of 250 m/s. Determine the total properties (a) Temperature (T), (b) Pressure (p), (c) Quality and (d) Density. Use the PC model for steam. (e) What-if Scenario: What would the temperature be if steam were treated as a perfect
Determine (a) The total temperature (T) and (b) The total pressure (p) of air that is flowing at 40 kPa, -25oC and 400 m/s.
An aircraft is cruising at a velocity of 1000 km/h at an altitude of 10 km, where the static temperature and pressure are -50oC and 26.5 kPa, respectively. Determine (a) the Mach number of the aircraft. Also determine (b) the pressure (p) and (c) temperature (T) of the air brought to rest is
Steam at 450oC and 1 MPa is flowing through a nozzle with a velocity of 300 m/s. Determine (a) The total temperature (T) and (b) Pressure (p) of the flow. Use the PG model for steam.
A subsonic airplane is flying at a 3500 m altitude where the atmospheric conditions are 72 kPa and 260 K. A pitot tube measures the difference between the static and total pressures to be 10 kPa. Determine The speed of the airplane and The flight Mach number.
Saturated steam at 200 kPa is flowing with a velocity of 500 m/s. A pitot tube brings the flow to stagnation and the stagnation pressure is measured as 350 kPa. Determine the total pressure (p), the total temperature (T) and (c) the stagnation temperature. Use the PC model.
Air flowing at 100 kPa and 298 K is brought to rest, and the stagnation pressure and temperature are measured as 130 kPa and 329 K, respectively. Determine (a) The flow velocity and (b) The total pressure (p) of the flow.
Determine the back pressure necessary for a normal shock to appear at the exit of a converging-diverging nozzle, with an exit to throat area ratio of 2, if the reservoir conditions are 1 MPa and 850 K.
Carbon dioxide enters an adiabatic nozzle at 1200 K with a velocity of 100 m/s and leaves at 500 K. Determine the Mach number (a) At the inlet and (b) At the exit of the nozzle.
Air enters an adiabatic nozzle at 1200 K with a velocity of 100 m/s and leaves at 500 K. Determine (a) The Mach number at the inlet, (b) The Mach number at the exit of the nozzle. (c) The velocity (V2) and
Determine the velocity of sound in air (a) At 273 K and (b) At 1000 K?
Air at 1 MPa and 550oC enters a converging nozzle of throat area 50 cm2 with a velocity of 100 m/s. Determine the mass flow rate for a back pressure of (a) 0.7 MPa, (b) 0.4 MPa and (c) 0.2 MPa.
Air enters a converging-diverging nozzle of a supersonic wind tunnel at 1000 kPa and 35oC with a low velocity. The flow area of the test section is equal to the exit area of the nozzle, which is 0.5 m2. Determine (a) Velocity (V) and (b) The mass flow rate (m) in the test section where M = 2.
Compressed air is discharged through a converging nozzle as shown in the accompanying figure. The conditions in the tank are 1 MPa and 500 K while the outside pressure is 100 kPa. The inlet area of the nozzle is 100 cm2 and the exit area is 35 cm2. Determine (a) The exit temperature and (b) The
For the converging-diverging nozzle shown in the accompanying figure, (a) find the maximum back pressure below which the flow is choked and (b) the mass flow rate for a choked nozzle. The throat area is 10 cm2 and the exit area is 40 cm2.
A converging-diverging nozzle with an exit area of 35 cm2 and a throat area of 10 cm2, is attached to a reservoir which contains air at 700 kPa and 20oC absolute. Determine (a) The associated exit temperatures and (b) Velocities. (c) The two exit pressures that result in M = 1 at the throat for
A rocket nozzle has an exit-to-throat area ratio of 4.0 and a throat area of 100 cm2. The exhaust gases are generated in a combustion chamber with stagnation pressure equal to 4 MPa and stagnation temperature equal to 2000 K. Assume the working fluid to behave as a perfect gas with k = 1.3 and
On a test stand, a nozzle operates is entropically with a chamber pressure of 2 MPa and chamber temperature of 2500 K. If the products of combustion are assumed to behave as a perfect gas with k = 1.3 and molar mass = 20 kg/kmol, determine the rocket motor thrust that is transmitted to the stand.
Nitrogen enters a duct with varying flow area at 500 K, 100 kPa and Mach number 0.4. Assuming a steady isentropic flow, determine (a) The Mach number, (b) Pressure (p) and (c) The temperature (T) at a location where the flow area has been reduced by 30%.
Products of combustion enters the nozzle of a gas turbine at the design conditions of 420 kPa, 1200 K and 200 m/s, and they exit at a pressure of 290 kPa at a rate of 3 kg/s. Take k = 1.34 and cp = 1.16 kJ/kg-k for the combustion products. Assuming an isentropic flow, determine Whether the nozzle
Air enters a converging-diverging nozzle at 700 K and 1000 kPa with negligible velocity. The exit Mach number is 2 and the throat area is 20 cm2. Assuming steady isentropic flow, determine (a) The throat velocity, (b) Mass flow rate (m) and (c) The exit area.
Combustion products enter a nozzle with total temperature of 700 K and total pressure of 200 kPa. For a back pressure of 60 kPa and a nozzle efficiency of 90%, determine the exit velocity. Assume the combustion gases to have the properties of air with k = 1.33.
A converging-diverging nozzle has an exit area to throat area ratio of 1.8. Air enters the nozzle with a total pressure of 1100 kPa and a total temperature of 400 K. The throat area is 5 cm2. If the velocity at the throat is sonic, and the diverging section acts as a nozzle, determine (a) The mass
A jetliner is flying at 275 m/s at a high altitude where the atmospheric pressure and temperature are 50 kPa and 250 K, respectively. Air is first decelerated in a diffuser, before it is compressed by an isentropic compressor with a compression ratio of 10. Determine (a) The pressure at the
Carbon dioxide flows steadily through a variable-area duct with a mass flow rate of 2 kg/s. It enters the duct at 1400 kPa and 250oC with negligible velocity and expands to a pressure of 200 kPa is entropically. Determine The exit Mach number, Flow area and The critical flow area.
A converging-diverging nozzle has a throat area of 100 mm2 and an an exit area of 160 mm2. The inlet flow is helium at a total pressure of 1 MPa and total temperature of 375 K. Determine the back pressure that will give sonic condition at the throat, but subsonic everywhere else.
Oxygen flows at Mach 0.5 in a channel with a cross-sectional area of 0.16 m2. The temperature and pressure are 800 K and 800 kPa, respectively. (a) Calculate the mass flow rate through the channel. The cross-sectional area is now reduced to 0.15 m2. Determine the (b) Flow velocity at the reduced
Air flows at Mach 0.5 in a channel with cross-sectional area of 0.16 m2. The temperature and pressure are 800 K and 800 kPa, respectively. (a) Calculate the mass flow rate () through the channel. (b) What should the cross-sectional area be reduced to before the mass flow rate is affected? Assume
Air enters a diffuser with a velocity of 200 m/s, a static pressure of 80 kPa and a temperature of 268 K. The velocity leaving the diffuser is 50 m/s and the static pressure at the diffuser exit is 90 kPa. Determine (a) The total pressure (p) at the exit and (b) The static temperature (T) at the
Helium enters a variable-area duct at 400 K, 100 kPa and M = 0.3. Assuming steady isentropic flow, determine the Mach number at a location where the area is 20% smaller.
A converging-diverging nozzle has an area ratio of 3:1 and a throat area of 50 cm2. The nozzle is supplied from a tank containing helium at 100 kPa and 270 K. Find (a) The range of back pressures over which the mass flow can be attained. (b) The maximum mass flow rate possible through the nozzle
Stationary nitrogen at 0.9 MPa and 450 K is accelerated is entropically to a Mach number of 0.6. Determine the temperature (T) and the pressure (p) of nitrogen after acceleration.
A symmetric converging diverging duct with an area ratio of 2 is placed in a wind tunnel where it encounters a 300 m/s flow of air at 50 kPa, 300 K. Determine the bypass ratio (diverted flow / incoming flow).
In problem 15-2-30[BIO], determine the air speed below which flow bypass is not necessary. Problem 15-2-30 A symmetric converging diverging duct with an area ratio of 2 is placed in a wind tunnel where it encounters a 300 m/s flow of air at 50 kPa, 300 K. Determine the bypass ratio (diverted flow /
Air is expanded in an isentropic nozzle from 1.0 MPa and 800 K to an exhaust pressure of 100 kPa. If air enters the nozzle with a velocity of 80 m/s, determine the exhaust velocity.
Helium enters a converging-diverging nozzle at a pressure of 800 kPa, 700 K and 100 m/s. Determine The lowest temperature and The lowest pressure that can be obtained at the throat of the nozzle.
Nitrogen flows steadily through a variable-area duct with a mass flow rate of 3 kg/s. It enters the duct at 1200 kPa and 250oC with a low velocity and expands to a pressure of 300 kPa. The duct is designed so that the flow can be approximated as isentropic. Determine (a) The Mach number, (b) The
A convergent nozzle has an exit area of 4 cm2. Air enters the nozzle with a total pressure of 1200 kPa, and a total temperature of 400 K. Assuming isentropic flow, determine the mass flow rate (m) for back pressure of (a) 900 kPa, (b) 634 kPa and (c) 400 kPa.
Air enters a nozzle at 3000 kPa, 400 K and a velocity of 180 m/s. Assuming isentropic flow, determine (a) The temperature (T), (b) The pressure (p) of the air at a location where the air velocity equals to the velocity of sound, and (c) The ratio of area at this location to the entrance area.
An ideal gas with k = 1.5 is flowing through a nozzle such that the Mach number is 3 where the flow area is 30 cm2. Assuming the flow to be isentropic, determine The flow area at the location where the Mach number is 1.4.
An airstream with a velocity of 600 m/s, a pressure of 50 kPa and a temperature of 250 K undergoes a normal shock. Determine (a) The velocity (V) and (b) The pressure (p) at the exit. (c) Also determine the loss of total pressure due to the shock.
Consider the convergent-divergent nozzle of problem 15-3-9 [BNU]. Assume that there is a normal shock wave standing at the point where M = 1.5, determine The exit plane pressure, Temperature and Mach number.
Air flowing steadily in a nozzle experiences a normal shock at a Mach number of 2.5. If the pressure and temperature of air are 60 kPa and 273 K, respectively, upstream of the shock, determine (a) The pressure (p), temperature (T), (b) Velocity (V), (c) Mach number and (d) The total pressure
An airstream at Mach 2.0, with pressure of 100 kPa and temperature of 300 K, enters a diverging channel with a area ratio of 3 between the exit and inlet. Determine the back pressure necessary to produce a normal shock in the channel at an area equal to twice the inlet area.
A supersonic flow of air at M = 3.0 is to be slowed down via a normal shock in a diverging channel with an exit to inlet area ratio of 2. At the exit M = 0.5. Find the ratio of exit to inlet pressure.
Air approaches a diffuser with a pressure of 20 kPa at a Mach number of 2. A normal shock occurs at the inlet of the channel as shown in the accompanying figure. For an exit to inlet area ratio of 3, find The loss of total pressure and The Mach number at the exit.
In problem 15-3-14 [BNF] determine the diffuser efficiency if the shock is (a) at the inlet and (b) at the exit (%). Problem 15-3-14 Air approaches a diffuser with a pressure of 20 kPa at a Mach number of 2. A normal shock occurs at the inlet of the channel as shown in the accompanying figure. For
A rocket nozzle has an exit-to-throat area ratio of 4.0. The exhaust gases are generated in a combustion chamber with stagnation pressure equal to 4 MPa and stagnation temperature equal to 2000 K. Assume the working fluid to behave as a perfect gas with k = 1.3 and molar mass = 20 kg/kmol.
In problem 15-3-16 [BNQ] (a) determine the thrust if the outside pressure is 0 kPa. (b) What-if Scenario: What would the thrust be if the normal shock did not exist? Problem 15-3-16 A rocket nozzle has an exit-to-throat area ratio of 4.0. The exhaust gases are generated in a combustion chamber with
For the converging-diverging nozzle shown in the accompanying figure,(a) Find the range of back pressure for which a normal shock appears in the diverging section, and(b) The mass flow rate () when the shock is present. The throat area is 10 cm2 and the exit area is 40 cm2.
For the converging-diverging nozzle shown in the accompanying figure, find the exit Mach number.
Air enters a normal shock at 30 kPa, 220 K and 700 m/s. Determine (a) The total pressure and Mach number upstream of the shock, (b) Pressure, temperature, (c) Velocity, Mach number and ( d) Total pressure downstream of the shock. pi = 30kPa, Ti = 220K and Vi = 700m/s
A symmetric converging diverging duct with an area ratio of 2 is placed in wind tunnel where it encounters a 700 m/s flow of air at 50 kPa and 300 K. Determine the bypass ratio (diverted flow / incoming flow).
Supersonic air at Mach 3 and 75 kPa impinges on a two dimensional wedge of half angle 10o. Determine (a) The Mach number downstream of the oblique shock for each case. (b) The pressure downstream of the oblique shock for each case and
An airflow with velocity, temperature and pressure of 850 m/s, 25oC and 50 kPa absolute, respectively, is turned with an oblique shock emanating from the wall, which makes an abrupt 20o corner. For a weak shock, determine (a) the downstream Mach number and (b) the pressure (p).
A meteorite is entering the earth's atmosphere at a Mach number of 25 at the outer atmosphere where the pressure and temperature are 1 kPa and 200 K respectively. Determine (a) The velocity (V) of the meteorite with respect to ground, (b) The relative velocity of the meteorite with respect to the
Air enters a converging-diverging nozzle at 700 K and 1000 kPa with negligible velocity. The exit Mach number is designed to be 2 and the throat area is 20 cm2. Now suppose the air experiences a normal shock at the exit plane. Determine (a) The total pressure (p) after the shock, (b) Mass flow
Air enters a converging-diverging nozzle of a supersonic wind tunnel at 400 K and 1 MPa with a low velocity. If a normal shock wave occurs at the exit plane of the nozzle at Mach equal to 2, determine (a) The pressure (p), the temperature (T), (b) The velocity (V) and (c) The Mach number, (d)
Air enters a converging-diverging nozzle with a low velocity at 1.5 MPa and 120oC. If the exit area of the nozzle is 3 times the throat area, determine The back pressure to produce a normal shock at the exit plane of the nozzle.
Carbon dioxide enters converging-diverging nozzle at 900 kPa and 900 K with a negligible velocity. The flow is steady and isentropic. For a exit Mach number of 2.5 and a throat area of 25 cm2, determine (a) The exit area, (b) The exit velocity. (c) Mass flow rate () and
Air enters a converging-diverging nozzle at 700 K and 1000 kPa with a velocity of 75 m/s. The exit Mach number is designed to be 2 and the throat area is 20 cm2. Suppose the air experiences a normal shock at the exit plane. Determine (a) The mass flow rate (m) and (b) The nozzle efficiency (%).
Consider the convergent-divergent nozzle of problem 15-2-21 [BHD] in which the diverging section acts as a supersonic nozzle. Assume that a normal shock stands in the exit plane of the nozzle. Determine (a) The static pressure, temperature and (b) Total pressure just downstream of the normal
A certain insulation has a thermal conductivity of 10 W/m· ºC. What thickness is necessary to effect a temperature drop of 500ºC for a heat flow of 400 W/m2?
Assuming that the heat transfer to the sphere in Problem 1-5 occurs by free convection with a heat-transfer coefficient of 2.7 W/m2 · ºC, calculate the temperature difference between the outer surface of the sphere and the environment.
Two perfectly black surfaces are constructed so that all the radiant energy leaving a surface at 800ºC reaches the other surface. The temperature of the other surface is maintained at 250ºC. Calculate the heat transfer between the surfaces per hour and per unit area of the surface maintained at
Two very large parallel planes having surface conditions that very nearly approximate those of a blackbody are maintained at 1100 and 425ºC, respectively. Calculate the heat transfer by radiation between the planes per unit time and per unit surface area.
Two infinite black plates at 500 and 100ºC exchange heat by radiation. Calculate the heat-transfer rate per unit area. If another perfectly black plate is placed between the 500 and 100ºC plates, by how much is the heat transfer reduced? What is the temperature of the center plate?
Water flows at the rate of 0.5 kg/s in a 2.5-cm-diameter tube having a length of 3 m. A constant heat flux is imposed at the tube wall so that the tube wall temperature is 40ºC higher than the water temperature. Calculate the heat transfer and estimate the temperature rise in the water. The water
Steam at 1 atm pressure (Tsat = 100ºC) is exposed to a 30-by-30-cm vertical square plate that is cooled such that 3.78 kg/h is condensed. Calculate the plate temperature. Consult steam tables for any necessary properties.
Boiling water at 1 atm may require a surface heat flux of 3 × 104 Btu/h · ft2 for a surface temperature of 232ºF. What is the value of the heat-transfer coefficient?
A small radiant heater has metal strips 6 mm wide with a total length of 3 m. The surface emissivity of the strips is 0.85. To what temperature must the strips be heated if they are to dissipate 2000Wof heat to a room at 25ºC?
A temperature difference of 85ºC is impressed across a fiberglass layer of 13 cm thickness. The thermal conductivity of the fiberglass is 0.035W/m·ºC. Compute the heat transferred through the material per hour per unit area.
Calculate the energy emitted by a blackbody at 1000ºC.
If the radiant flux from the sun is 1350W/m2, what would be its equivalent blackbody temperature?
A flat wall is exposed to an environmental temperature of 38ºC. The wall is covered with a layer of insulation 2.5 cm thick whose thermal conductivity is 1.4 W/m· ºC, and the temperature of the wall on the inside of the insulation is 315ºC. The wall loses heat to the environment by convection.
One side of a plane wall is maintained at 100ºC, while the other side is exposed to a convection environment having T = 10ºC and h = 10 W/m2 · ºC. The wall has k = 1.6W/m · ºC and is 40 cm thick. Calculate the heat-transfer rate through the wall.
How does the free-convection heat transfer from a vertical plate compare with pure conduction through a vertical layer of air having a thickness of 2.5 cm and a temperature difference the same at Tw − T∞? Use information from Table 1-3.
A 1/4-in steel plate having a thermal conductivity of 25 Btu/h · ft · ºF is exposed to a radiant heat flux of 1500 Btu/h · ft2 in a vacuum space where the convection heat transfer is negligible. Assuming that the surface temperature of the steel exposed to the radiant energy is maintained at
A 5.0-cm-diameter cylinder is heated to a temperature of 200ºC, and air at 30ºC is forced across it at a velocity of 50 m/s. If the surface emissivity is 0.7, calculate the total heat loss per unit length if the walls of the enclosing room are at 10ºC. Comment on this calculation.

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Heat Transfer 10th edition Jack Holman - Solutions

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