Under what conditions can the outer surface of a vertical cylinder be treated as a vertical plate in natural convection calculations?
> A circular grill of diameter 0.25 m has an emissivity of 0.8. If the surface temperature is maintained at 150°C, determine the required electrical power when the room air and surroundings are at 30°C.
> A 12-ft-long, 1.5-kW electrical resistance wire is made of 0.1-in-diameter stainless steel (k = 8.7 Btu/h⋅ft⋅°F). The resistance wire operates in an environment at 85°F. Determine the surface temp
> The demand for electric power is usually much higher during the day than it is at night, and utility companies often sell power at night at much lower prices to encourage consumers to use the available power generation capacity and to avoid building new,
> Repeat Prob. 20–32 for an aluminum plate painted flat black (solar absorptivity 0.98 and emissivity 0.98) and also for a plate painted white (solar absorptivity 0.26 and emissivity 0.90). Evaluate air properties at a film temperature of
> Consider a person who is trying to keep cool on a hot summer day by turning a fan on and exposing his entire body to airflow. The air temperature is 85°F, and the fan is blowing air at a velocity of 6 ft/s. If the person is doing light work an
> A manufacturer makes absorber plates that are 1.2 m × 0.8 m in size for use in solar collectors. The back side of the plate is heavily insulated, while its front surface is coated with black chrome, which has an absorptivity of 0.87 for sola
> A long aluminum wire of diameter 3 mm is extruded at a temperature of 280°C. The wire is subjected to cross airflow at 20°C at a velocity of 6 m/s. Determine the rate of heat transfer from the wire to the air per meter length when i
> Consider a thin 24-cm-long and 20-cm-wide horizontal plate suspended in air at 20°C. The plate is equipped with electric resistance heating elements with a rating of 20 W. Now the heater is turned on and the plate temperature rises. Determine
> Reconsider Prob. 19–42. Using appropriate software, investigate the effect of the wind velocity on the surface temperature of the wire. Let the wind velocity vary from 10 km/h to 80 km/h. Plot the surface temperature as a function of wi
> Reconsider Prob. 20–29. Using appropriate software, investigate the effects of the room temperature and the emissivity of the board on the temperature of the hot surface of the board for different orientations of the board. Let the room
> A 5-mm-diameter electrical transmission line carries an electric current of 50 A and has a resistance of 0.002 ohm per meter length. Determine the surface temperature of the wire during a windy day when the air temperature is 10°C and the wind
> Consider a hot boiled egg in a spacecraft that is filled with air at atmospheric pressure and temperature at all times. Will the egg cool faster or slower when the spacecraft is in space instead of on the ground? Explain.
> In a geothermal power plant, the used geothermal water at 80°C enters a 15-cm-diameter and 400-m-long uninsulated pipe at a rate of 8.5 kg/s and leaves at 70°C before being reinjected back into the ground. Windy air at 15°
> In a hydroelectric power plant, 65 m3/s of water flows from an elevation of 90 m to a turbine, where electric power is generated. The overall efficiency of the turbine–generator is 84 percent. Disregarding frictional losses in piping, e
> Consider a 15-cm × 20-cm printed circuit board (PCB) that has electronic components on one side. The board is placed in a room at 20°C. The heat loss from the back surface of the board is negligible. If the circuit board is dissip
> Reconsider Prob. 19–39E. Using appropriate software, investigate the effects of air temperature and wind velocity on the rate of heat loss from the arm. Let the air temperature vary from 20°F to 80°F and the wind v
> Repeat Prob. 20–27 assuming the circuit board to be positioned horizontally with (a) chips facing up and (b) chips facing down. Data from Prob. 20-27: A 50-cm × 50-cm circuit board that contains 121 square chips on one side is to be cooled by combined
> Consider a hot baked potato. Will the potato cool faster or slower when we blow the warm air coming from our lungs on it instead of letting it cool naturally in the cooler air in the room? Explain.
> A 50-cm × 50-cm circuit board that contains 121 square chips on one side is to be cooled by combined natural convection and radiation by mounting it on a vertical surface in a room at 25°C. Each chip dissipates 0.18 W of power, and the emissivity of the
> A person extends his uncovered arms into the windy air outside at 54°F and 30 mph in order to feel nature closely. Initially, the skin temperature of the arm is 84°F. Treating the arm as a 2-ft long and 3-in-diameter cylinder, deter
> Consider a vertical plate with length L, placed in quiescent air. If the film temperature is 20°C and the average Nusselt number in natural convection is of the form Nu = CRaLn, show that the average heat transfer coefficient can be expressed
> A heated long cylindrical rod is placed in a crossflow of air at 20°C (1 atm) with velocity of 10 m/s. The rod has a diameter of 5 mm, and its surface has an emissivity of 0.95. If the surrounding temperature is 20°C and the heat flux dissipated from the
> The side surfaces of a 3-m-high cubic industrial furnace burning natural gas are not insulated, and the temperature at the outer surface of this section is measured to be 110°C. The temperature of the furnace room, including its surfaces, is 3
> A long 12-cm-diameter steam pipe whose external surface temperature is 90°C passes through some open area that is not protected against the winds. Determine the rate of heat loss from the pipe per unit of its length when the air is at 1 atm pressure and
> A grist mill of the 1800s employed a waterwheel that was 14 m high; 480 L/min of water flowed onto the wheel near the top. How much power, in kW, could this waterwheel have produced?
> Reconsider Prob. 20–23E. Using appropriate software, plot the rate of natural convection heat transfer for different orientations of the plate as a function of the plate temperature as the temperature varies from 80°F to 180°F, and discuss the results.
> Consider laminar flow of air across a hot circular cylinder. At what point on the cylinder will the heat transfer be highest? What would your answer be if the flow were turbulent?
> Consider a 2-ft × 2-ft thin square plate in a room at 75°F. One side of the plate is maintained at a temperature of 130°F, while the other side is insulated. Determine the rate of heat transfer from the plate by natural convection if the plate is (a) ver
> A 15-cm × 15-cm circuit board dissipating 20 W of power uniformly is cooled by air, which approaches the circuit board at 20°C with a velocity of 6 m/s. Disregarding any heat transfer from the back surface of the board, determine the surface temperature
> Consider a 1.2-m-high and 2-m-wide glass window with a thickness of 6 mm, thermal conductivity k = 0.78 W/m⋅K, and emissivity ε = 0.9. The room and the walls that face the window are maintained at 25°C, and the a
> Reconsider Prob. 19–33. Using appropriate software, evaluate the local convection heat transfer coefficient, the local surface temperature, and the local film temperature along the plate. By varying the location along the plate for 0.2
> Reconsider Prob. 20–20. Using appropriate software, evaluate the effect of the uniform surface heat flux on the plate midpoint temperature for (a) the highly polished surface and (b) the black oxidized surface. By varying the surface he
> Air is flowing in parallel over the upper surface of a flat plate with a length of 4 m. The first half of the plate length, from the leading edge, has a constant surface temperature of 50°C. The second half of the plate length is subjected to
> A 0.5-m-long thin vertical copper plate is subjected to a uniform heat flux of 1000 W/m2 on one side, while the other side is exposed to air at 5°C. Determine the plate midpoint temperature for (a) a highly polished surface and (b) a black oxi
> A 15-mm × 15-mm silicon chip is mounted such that the edges are flush in a substrate. The chip dissipates 1.4 W of power uniformly, while air at 20°C (1 atm) with a velocity of 25 m/s is used to cool the upper surface of the chip. If the substrate provid
> Consider a vertical elevator whose cabin has a total mass of 800 kg when fully loaded and 150 kg when empty. The weight of the elevator cabin is partially balanced by a 400-kg counter weight that is connected to the top of the cabin by cables that pass t
> In which mode of heat transfer is the convection heat transfer coefficient usually higher, natural convection or forced convection? Why?
> Water vapor at 250°C is flowing with a velocity of 5 m/s in parallel over a 2-m-long flat plate where there is an unheated starting length of 0.5 m. The heated section of the flat plate is maintained at a constant temperature of 50°C. Determine (a) the l
> A 0.5-m-long thin vertical plate is subjected to uniform heat flux on one side, while the other side is exposed to cool air at 5°C. The plate surface has an emissivity of 0.73, and its midpoint temperature is 55°C. Determine the hea
> Liquid mercury at 250°C is flowing in parallel over a flat plate at a velocity of 0.3 m/s. The surface temperature of the 0.1-m-long flat plate is constant at 50°C. Determine (a) the local convection heat transfer coefficient at 5 cm from the leading edg
> Reconsider Prob. 20–17. Using appropriate software, evaluate the effect of the plate thickness on the surface temperature exposed to the cold air. By varying the plate thickness from 0.01 to 0.1 m, plot the plate surface temperature on
> In which mode of heat transfer is the convection heat transfer coefficient usually higher, natural convection or forced convection? Why?
> A 0.2-m-long and 25-mm-thick vertical plate (k = 1.5W/m⋅K) separates the hot water from the cold air at 2°C. The plate surface exposed to the hot water has a temperature of 100°C, and the surface exposed to the col
> Solar radiation is incident on the glass cover of a solar collector at a rate of 700 W/m2. The glass transmits 88 percent of the incident radiation and has an emissivity of 0.90. The entire hot water needs of a family in summer can be met by two collecto
> Reconsider Prob. 20–15. Using appropriate software, investigate the effect of the plate thermal conductivity on the surface temperature exposed to the cold water. By varying the plate thermal conductivity from 3 to 200 W/mâ‹&
> Reconsider Prob. 19–27. Using appropriate software, investigate the effects of the train velocity and the rate of absorption of solar radiation on the equilibrium temperature of the top surface of the car. Let the train velocity vary fr
> Consider the falling of a rock off a cliff into seawater, and eventually settling at the bottom of the sea. Starting with the potential energy of the rock, identify the energy transfers and transformations involved during this process.
> A 0.2-m-long and 25-mm-thick vertical plate (k = 15 W/mâ‹…K) separates the hot water from the cold water. The plate surface exposed to the hot water has a temperature of 100°C, and the temperature of the cold water is 7Â&
> The top surface of the passenger car of a train moving at a velocity of 95 km/h is 2.8 m wide and 8 m long. The top surface is absorbing solar radiation at a rate of 380 W/m2, and the temperature of the ambient air is 30°C. Assuming the roof o
> Warm air is blown over the inner surface of an automobile windshield to defrost ice accumulated on the outer surface of the windshield. Consider an automobile windshield (kw = 0.8 Btu/h⋅ft⋅R) with an overall height of 20 in and thickness of 0.2 in. The o
> Consider laminar natural convection from a vertical hot plate. Will the heat flux be higher at the top or at the bottom of the plate? Why?
> The local atmospheric pressure in Denver, Colorado (elevation 1610 m), is 83.4 kPa. Air at this pressure and at 30°C flows with a velocity of 6 m/s over a 2.5-m × 8-m flat plate whose temperature is 120°C. Determine the rate of heat transfer from the pla
> Will a hot horizontal plate whose back side is insulated cool faster or slower when its hot surface is facing down instead of up?
> Reconsider Prob. 19–23. Using appropriate software, evaluate the effect of the sheet metal velocity on its surface temperature. By varying the sheet metal velocity from 3 to 30 m/s, plot the surface temperature of the sheet metal as a f
> A long 2-in-diameter rod with surface temperature of 200°F is submerged in a bath of fluid. Determine the Grashof and Rayleigh numbers if the fluid is (a) liquid water at 40°F, (b) liquid ammonia at 40°F, (c) engine oil at 50°F, and (d) air at 40°F (1 at
> A 5-m-long strip of sheet metal is being transported on a conveyor at a velocity of 5 m/s, while the coating on the upper surface is being cured by infrared lamps. The coating on the upper surface of the metal strip has an absorptivity of 0.6 and an emis
> Water is pumped from a 200-ft-deep well into a 100-ft high storage tank. Determine the power, in kW, that would be required to pump 200 gal/min.
> Two concentric spheres with diameters of 5 cm and 10 cm are having the surface temperatures maintained at 200°C and 100°C, respectively (see Fig. P20–100). The enclosure between the two concentric spherical surface
> Consider a hot automotive engine, which can be approximated as a 0.5-m-high, 0.40-m-wide, and 0.8-m-long rectangular block. The bottom surface of the block is at a temperature of 100°C and has an emissivity of 0.95. The ambient air is at 20°C, and the ro
> A 10-cm × 10-cm plate has a constant surface temperature of 150°C. Determine the Grashof number if the chip is placed in the following fluids: air (1 atm, 30°C), liquid water (30°C), engine oil (10°C). Discuss how the Grashof number affects the natural
> Consider a refrigeration truck traveling at 70 mph at a location where the air temperature is 80°F. The refrigerated compartment of the truck can be considered to be a 9-ft-wide, 7-ft high, and 20 ft-long rectangular box. The refrigeration sys
> What is natural convection? How does it differ from forced convection? What force causes natural convection currents?
> Repeat Prob. 19–19 for a location at an elevation of 1610 m where the atmospheric pressure is 83.4 kPa. Data from Prob. 19-19: An array of power transistors, dissipating 5 W of power each, are to be cooled by mounting them on a 25-cm
> What is external forced convection? How does it differ from internal forced convection? Can a heat transfer system involve both internal and external convection at the same time? Give an example.
> An array of power transistors, dissipating 5 W of power each, are to be cooled by mounting them on a 25-cm × 25-cm square aluminum plate and blowing air at 35°C over the plate with a fan at a velocity of 4 m/s. The average tempera
> Hydrogen gas at 1 atm is flowing in parallel over the upper and lower surfaces of a 3-m-long flat plate at a velocity of 2.5 m/s. The gas temperature is 120°C, and the surface temperature of the plate is maintained at 30°C. Using appropriate software, in
> Parallel plates form a solar collector that covers a roof, as shown in the figure. The plates are maintained at 15°C, while ambient air at 10°C flows over the roof with V = 2 m/s. Determine the rate of convective heat loss from (a)
> Consider a TV set that consumes 120 W of electric power when it is on and is kept on for an average of 6 h per day. For a unit electricity cost of 12 cents per kWh, determine the cost of electricity this TV consumes per month (30 days).
> Hot engine oil at 150°C is flowing in parallel over a flat plate at a velocity of 2 m/s. Surface temperature of the 0.5-m-long flat plate is constant at 50°C. Determine (a) the local convection heat transfer coefficient at 0.2 m from the leading edge and
> Hot carbon dioxide exhaust gas at 1 atm is being cooled by flat plates. The gas at 220°C flows in parallel over the upper and lower surfaces of a 1.5-m-long flat plate at a velocity of 3 m/s. If the flat plate surface temperature is maintained at 80°C, d
> Water at 43.3°C flows over a large plate at a velocity of 30.0 cm/s. The plate is 1.0 m long (in the flow direction), and its surface is maintained at a uniform temperature of 10.0°C. Calculate the steady rate of heat transfer per unit width of the plate
> A desktop computer is to be cooled by a fan. The electronic components of the computer consume 80 W of power under full-load conditions. The computer is to operate in environments at temperatures up to 50°C and at elevations up to 3000 m where the atmosp
> In an experiment, the local heat transfer over a flat plate was correlated in the form of the local Nusselt number as expressed by the following correlation Nux = 0.035Rex0.8Pr1/3 Determine the ratio of the average convection heat transfer coefficient (h
> 100 kg/s of crude oil is heated from 20°C to 40°C through the tube side of a multitube heat exchanger. The crude oil flow is divided evenly among all 100 tubes in the tube bundle. The ID of each tube is 10 mm, and the inside tube-wall temperature is main
> Cold air at 5°C enters a 12-cm-diameter, 20-m-long isothermal pipe at a velocity of 2.5 m/s and leaves at 19°C. Estimate the surface temperature of the pipe.
> Geothermal steam at 165°C condenses in the shell side of a heat exchanger over the tubes through which water flows. Water enters the 4-cm-diameter, 14-m-long tubes at 20°C at a rate of 0.8 kg/s. Determine the exit temperature of water and the rate of con
> Hot exhaust gases leaving a stationary diesel engine at 450°C enter a 15-cm-diameter pipe at an average velocity of 7.2 m/s. The surface temperature of the pipe is 180°C. Determine the pipe length if the exhaust gases are to leave the pipe at 250°C after
> Repeat Prob. 19–121 for a pipe made of copper (k = 386 W/m⋅K) instead of cast iron. Data from Prob. 19-121: Hot water at 90°C enters a 15-m section of a cast iron pipe (k = 52 W/m⋅K) whos
> The force required to expand the gas in a gas spring a distance x is given by F = Constant / xk where the constant is determined by the geometry of this device and k is determined by the gas used in the device. Such a gas spring is arranged to have a con
> Hot water at 90°C enters a 15-m section of a cast iron pipe (k = 52 W/m⋅K) whose inner and outer diameters are 4 and 4.6 cm, respectively, at an average velocity of 1.2 m/s. The outer surface of the pipe, whose emissivity is
> Air is flowing through a smooth, thin-walled, 4-in-diameter copper tube that is submerged in water. The water maintains a constant temperature of 60°F and a convection heat transfer coefficient of 176 Btu/hâ‹…ft2â‹&#
> During air cooling of oranges, grapefruit, and tangelos, the heat transfer coefficient for combined convection, radiation, and evaporation for air velocities of 0.11
> The exhaust gases of an automotive engine leave the combustion chamber and enter an 8-ft-long and 3.5-in-diameter thin-walled steel exhaust pipe at 800°F and 15.5 psia at a rate of 0.05 lbm/s. The surrounding ambient air is at a temperature of 80°F, and
> Water at 1500 kg/h and 10°C enters a 10-mm-diameter smooth tube whose wall temperature is maintained at 49°C. Calculate (a) the tube length necessary to heat the water to 40°C, and (b) the water outlet temperature if the tube length is doubled. Assume av
> Repeat Prob. 19–116 for a flow rate of 20 kg/s. Data from Prob. 19-116: Water is heated at a rate of 10 kg/s from a temperature of 15°C to 35°C by passing it through five identical tubes, each 5.0 cm in diameter, whose surface temperature is 60.0°C. Est
> Water is heated at a rate of 10 kg/s from a temperature of 15°C to 35°C by passing it through five identical tubes, each 5.0 cm in diameter, whose surface temperature is 60.0°C. Estimate (a) the steady rate of heat transfer and (b) the length of tubes ne
> In the effort to find the best way to cool a smooth, thin-walled copper tube, an engineer decided to flow air either through the tube or across the outer tube surface. The tube has a diameter of 5 cm, and the surface temperature is held constant. Determi
> Liquid mercury is flowing at 0.6 kg/s through a 5-cm-diameter tube with inlet and outlet mean temperatures of 100°C and 200°C, respectively. The tube surface temperature is kept constant at 250°C. Determine the tube length using (a) the appropriate Nusse
> To cool a storehouse in the summer without using a conventional air-conditioning system, the owner decided to hire an engineer to design an alternative system that would make use of the water in the nearby lake. The engineer decided to flow air through a
> The force F required to compress a spring a distance x is given by F – F0 = kx where k is the spring constant and F0 is the preload. Determine the work, in kJ, required to compress a spring a distance of 1 cm when its spring constant is 300 N/cm and the
> Air (1 atm) enters a 5-mm-diameter circular tube at an average velocity of 5 m/s. The tube wall is maintained at a constant surface temperature. Determine the convection heat transfer coefficient for (a) a 10-cm-long tube and (b) a 50-cm-long tube. Evalu
> Crude oil at 22°C enters a 20-cm-diameter pipe with an average velocity of 32 cm/s. The average pipe wall temperature is 2°C. Crude oil properties are as given below. Calculate the rate of heat transfer and the pipe length if the cr
> A fluid (ρ = 1000 kg/m3, μ = 1.4 × 10−3 kg/m⋅s, cp = 4.2 kJ/kg⋅K, and k = 0.58 W/m⋅K) flows with an average velocity of 0.3 m/s through a 14-m-long tube with inside diameter of 0.01 m. Heat is uniformly added to the entire tube at the rate of 1500 W/m2.
> Consider airflow over a plate surface maintained at a temperature of 220°C. The temperature profile of the airflow is given as The airflow at 1 atm has a free stream velocity and temperature of 0.08 m/s and 20°C, respectively. Deter
> Repeat Prob. 19–108, assuming the inner surface of the tank to be at 0°C but by taking the thermal resistance of the tank and heat transfer by radiation into consideration. Assume the average surrounding surface temperature f
> During a fire, the trunks of some dry oak trees (k = 0.17 W/mâ‹…K and α = 1.28 × 10−7 m2/s) that are initially at a uniform temperature of 30°C are exposed to hot gases at 600Â
> A 0.55-m-internal-diameter spherical tank made of 1-cm-thick stainless steel (k = 15 W/m⋅K) is used to store iced water at 0°C. The tank is located outdoors at 30°C and is subjected to winds at 8 km/h. Assuming the
> In an annealing process, a 50-mm-thick stainless steel plate (ρ = 8238 kg/m3, cp = 468 J/kg⋅K, k = 13.4 W/m⋅K, and α = 3.48 × 10−6 m2/s ) was reheated in a furnace from an initial uniform temperature of 230°C. The ambient temperature inside the furnace
> Steam at 250°C flows in a stainless steel pipe (k = 15 W/m⋅K) whose inner and outer diameters are 4 cm and 4.6 cm, respectively. The pipe is covered with 3.5-cm-thick glass wool insulation (k = 0.038 W/m⋅K) whose outer surface has an emissivity of 0.3. H
> A transistor with a height of 0.32 in and a diameter of 0.22 in is mounted on a circuit board. The transistor is cooled by air flowing over it at a velocity of 600 ft/min. If the air temperature is 120°F and the transistor case temperature is
