Question: In a geothermal power plant, the used

> What is the physical significance of the number of transfer units NTU = hAs/mcp? What do small and large NTU values tell us about a heat transfer system?

> During a visit to a plastic sheeting plant, it was observed that a 45-m-long section of a 2-in nominal (6.03-cm-outer-diameter) steam pipe extended from one end of the plant to the other with no insulation on it. The temperature measurements at several l

> Consider fluid flow in a tube whose surface temperature remains constant. What is the appropriate temperature difference for use in Newton’s law of cooling with an average heat transfer coefficient?

> A 3-mm-diameter and 12-m-long electric wire is tightly wrapped with a 1.5-mm-thick plastic cover whose thermal conductivity and emissivity are k = 0.20 W/m⋅K and ε = 0.9. Electrical measurements indicate that a current of 10 A passes through the wire, an

> A propane tank is filled with a mixture of liquid and vapor propane. Can the contents of this tank be considered a pure substance? Explain.

> When is heat transfer through a fluid conduction and when is it convection? For what case is the rate of heat transfer higher? How does the convection heat transfer coefficient differ from the thermal conductivity of a fluid?

> Reconsider Prob. 20–45. To reduce the cost of heating the pipe, it is proposed to insulate it with enough fiberglass insulation (k = 0.035 W/m⋅K) wrapped in aluminum foil (ε = 0.1) to cut down the heat losses by 85 percent. Assuming the pipe temperature

> What does the logarithmic mean temperature difference represent for flow in a tube whose surface temperature is constant? Why do we use the logarithmic mean temperature instead of the arithmetic mean temperature?

> Thick fluids such as asphalt and waxes and the pipes in which they flow are often heated in order to reduce the viscosity of the fluids and thus to reduce the pumping costs. Consider the flow of such a fluid through a 100-m-long pipe of outer diameter 30

> Consider turbulent forced convection in a circular tube. Will the heat flux be higher near the inlet of the tube or near the exit? Why?

> A 12-m-long section of a 5-cm-diameter horizontal hot-water pipe passes through a large room whose temperature is 27°C. If the temperature and the emissivity of the outer surface of the pipe are 73°C and 0.8, respectively, determine the rate of heat loss

> Consider laminar forced convection in a circular tube. Will the heat flux be higher near the inlet of the tube or near the exit? Why?

> How is the thermal entry length defined for flow in a tube? In what region is the flow in a tube fully developed?

> A 300-W cylindrical resistance heater is 0.75 m long and 0.5 cm in diameter. The resistance wire is placed horizontally in a fluid at 20°C. Determine the outer surface temperature of the resistance wire in steady operation if the fluid is (a) air and (b)

> A 0.4-m-diameter spherical tank of negligible thickness contains iced water at 0°C. Air at 25°C flows over the tank with a velocity of 3 m/s. Determine the rate of heat transfer to the tank and the rate at which ice melts. The heat of fusion of water at

> Electric power is to be generated by installing a hydraulic turbine–generator at a site 120 m below the free surface of a large water reservoir that can supply water at a rate of 1500 kg/s steadily. Determine the power generation potential.

> Thermal energy generated by the electrical resistance of a 5-mm-diameter and 4-m-long bare cable is dissipated to the surrounding air at 20°C. The voltage drop and the electric current across the cable in steady operation are measured to be 60 V and 1.5

> An incandescent lightbulb is an inexpensive but highly inefficient device that converts electrical energy into light. It converts about 10 percent of the electrical energy it consumes into light while converting the remaining 90 percent into heat. (A flu

> An aluminum soda can 150 mm in length and 60 mm in diameter is placed horizontally inside a refrigerator compartment that maintains a temperature of 4°C. If the surface temperature of the can is 36°C, estimate the heat transfer rate from the can. Neglect

> An average person generates heat at a rate of 84 W while resting. Assuming one-quarter of this heat is lost from the head and disregarding radiation, determine the average surface temperature of the head when it is not covered and is subjected to winds a

> Consider a cylinder with a length of 15 cm and a diameter of 10 cm. The cylinder has a surface temperature of 43°C, while the room air temperature is 17°C. Determine whether placing the cylinder horizontally or vertically would achieve a higher heat tran

> Reconsider Prob. 19–51. Using appropriate software, investigate the effect of air velocity on the average convection heat transfer coefficient and the cooling time. Let the air velocity vary from 1 m/s to 10 m/s. Plot the heat transfer coefficient and th

> When will the hull of a ship sink deeper in the water: when the ship is sailing in fresh water or in seawater? Why?

> A stainless steel ball (ρ = 8055 kg/m3, cp = 480 J/kg⋅K) of diameter D = 15 cm is removed from the oven at a uniform temperature of 125°C. The ball is then subjected to the flow of air at 1 atm pressure and 30°C with a velocity of 6 m/s. The surface temp

> A room is to be heated by a coal-burning stove, which is a cylindrical cavity with an outer diameter of 50 cm and a height of 120 cm. The rate of heat loss from the room is estimated to be 1.5 kW when the air temperature in the room is maintained constan

> A 10-cm-diameter, 30-cm-high cylindrical bottle contains cold water at 3°C. The bottle is placed in windy air at 27°C. The water temperature is measured to be 11°C after 45 min of cooling. Disregarding radiation effects and heat transfer from the top and

> The pump of a water distribution system is powered by a 15-kW electric motor whose efficiency is 90 percent. The water flow rate through the pump is 50 L/s. The diameters of the inlet and outlet pipes are the same, and the elevation difference across the

> A 150-lbm astronaut took his bathroom scale (a spring scale) and a beam scale (compares masses) to the moon, where the local gravity is g = 5.48 ft/s2. Determine how much he will weigh (a) on the spring scale and (b) on the beam scale.

> An office worker claims that a cup of cold coffee on his table warmed up to 80°C by picking up energy from the surrounding air, which is at 25°C. Is there any truth to his claim? Does this process violate any thermodynamic laws?

> Reconsider Prob. 20–37. In order to reduce the heating cost of the hot water, it is proposed to insulate the side and bottom surfaces of the container with 5-cm-thick fiberglass insulation (k = 0.035 W/m⋅K) and to wrap

> What is the physical significance of the Nusselt number? How is it defined?

> In a plant that manufactures canned aerosol paints, the cans are temperature-tested in water baths at 60°C before they are shipped to ensure that they withstand temperatures up to 55°Cduring transportation and shelving (as shown in

> Reconsider Prob. 19–48. Using appropriate software, plot the temperature of the tank as a function of the cooling time as the time varies from 30 min to 5 h, and discuss the results. Data from Prob. 19-48: Consider a 50-cm-diameter and 95-cm-long hot wa

> Flue gases from an incinerator are released to atmosphere using a stack that is 0.6 m in diameter and 10.0 m high. The outer surface of the stack is at 40°C and the surrounding air is at 10°C. Determine the rate of heat transfer from the stack, assuming

> Consider a 50-cm-diameter and 95-cm-long hot water tank. The tank is placed on the roof of a house. The water inside the tank is heated to 80°C by a flat-plate solar collector during the day. The tank is then exposed to windy air at 18°C with an average

> A can of engine oil with a length of 150 mm and a diameter of 100 mm is placed vertically in the trunk of a car. On a hot summer day, the temperature in the trunk is 43°C. If the surface temperature of the can is 17°C, determine heat transfer rate from t

> A 0.4-W cylindrical electronic component with diameter 0.3 cm and length 1.8 cm and mounted on a circuit board is cooled by air flowing across it at a velocity of 240 m/min. If the air temperature is 35°C, determine the surface temperature of the compone

> 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 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

> Under what conditions can the outer surface of a vertical cylinder be treated as a vertical plate in natural convection calculations?

> 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