Question: Thick fluids such as asphalt and waxes
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 cm in calm, ambient air at 0°C. The pipe is heated electrically, and a thermostat keeps the outer surface temperature of the pipe constant at 25°C. The emissivity of the outer surface of the pipe is 0.8, and the effective sky temperature is −30°C. Determine the power rating of the electric resistance heater, in kW, that needs to be used. Also, determine the cost of electricity associated with heating the pipe during a 15-h period under the above conditions if the price of electricity is $0.09/kWh.
> Show that the thermal resistance of a rectangular enclosure can be expressed as R = Lc /(AkNu), where k is the thermal conductivity of the fluid in the enclosure.
> A rigid tank with a volume of 0.117 m3 contains 1 kg of refrigerant-134a vapor at 240 kPa. The refrigerant is now allowed to cool. Determine the pressure when the refrigerant first starts condensing. Also, show the process on a P-v diagram with respect t
> Liquid glycerin is flowing through a 25-mm-diameter and 10-m-long tube. The liquid glycerin enters the tube at 20°C with a mass flow rate of 0.5 kg/s. If the outlet mean temperature is 40°C and the tube surface temperature is constant, determine the surf
> What does the effective conductivity of an enclosure represent? How is the ratio of the effective conductivity to thermal conductivity related to the Nusselt number?
> In a manufacturing plant that produces cosmetic products, glycerin is being heated by flowing through a 25-mm diameter and 10-m-long tube. With a mass flow rate of 0.5 kg/s, the flow of glycerin enters the tube at 25°C. The tube surface is maintained at
> Consider a double-pane window consisting of two glass sheets separated by a 1-cm-wide airspace. Someone suggests inserting a thin vinyl sheet between the two glass sheets to form two 0.5-cm wide compartments in the window in order to reduce natural conve
> A computer cooled by a fan contains eight printed circuit boards (PCBs), each dissipating 12 W of power. The height of the PCBs is 12 cm and the length is 15 cm. The clearance between the tips of the components on the PCB and the back surface of the adja
> Someone claims that the airspace in a double-pane window enhances the heat transfer from a house because of the natural convection currents that occur in the airspace and recommends that the double-pane window be replaced by a single sheet of glass whose
> Consider a 10-m-long smooth rectangular tube, with a = 50 mm and b = 25 mm, that is maintained at a constant surface temperature. Liquid water enters the tube at 20°C with a mass flow rate of 0.01 kg/s. Determine the tube surface temperature n
> The upper and lower compartments of a well-insulated container are separated by two parallel sheets of glass with an airspace between them. One of the compartments is to be filled with a hot fluid and the other with a cold fluid. If it is desired that he
> In a thermal system, water enters a 25-mm-diameter and 23-m-long circular tube with a mass flow rate of 0.1 kg/s at 25°C. The heat transfer from the tube surface to the water can be expressed in terms of heat flux as qs(x) = ax. The coefficient a is 400
> A hot liquid is poured into a spherical tank with an inner diameter of 3 m and a wall thickness of 3 cm. The tank wall is made of a material with a thermal conductivity of 0.15 W/m⋅K. The hot liquid in the tank causes the inner surface temperature to be
> One kilogram of R-134a fills a 0.090-m3 rigid container at an initial temperature of –40°C. The container is then heated until the pressure is 280 kPa. Determine the initial pressure and final temperature.
> Consider a 25-mm-diameter and 15-m-long smooth tube that is maintained at a constant surface temperature. Fluids enter the tube at 50°C with a mass flow rate of 0.01 kg/s. Determine the tube surface temperatures necessary to heat water, engine oil, and
> Consider two fluids, one with a large coefficient of volume expansion and the other with a small one. In what fluid will a hot surface initiate stronger natural convection currents? Why? Assume the viscosity of the fluids to be the same.
> Consider a 25-mm-diameter and 15-m-long smooth tube that is used for heating fluids. The wall is heated electrically to provide a constant surface heat flux along the entire tube. Fluids enter the tube at 50°C and exit at 150°C. If the mass flow rate is
> A 2-m-diameter, thin-walled stainless steel spherical tank is filled with chemicals undergoing a reaction. The reaction releases heat through the tank, where the tank outer surface temperature is 50°C and is exposed to air at 20°C. The stainless steel su
> Reconsider Prob. 19–70. Using appropriate software, evaluate the effect of the tube length on the average convection heat transfer coefficient of air. By varying the tube length from 3 to 18 m, plot the average convection heat transfer
> The water in a 40-L tank is to be heated from 15°C to 45°C by a 6-cm-diameter spherical heater whose surface temperature is maintained at 85°C. Determine how long the heater should be kept on.
> In a gas-fired boiler, water is being boiled at 120°C by hot air flowing through a 5-m-long, 5-cm diameter tube submerged in water. Hot air enters the tube at 1 atm and 300°C at a mean velocity of 7 m/s and leaves at 150°
> An incandescent lightbulb is an inexpensive but highly inefficient device that converts electrical energy into light. It converts about 5 percent of the electrical energy it consumes into light while converting the remaining 95 percent into heat. The gla
> An average man has a body surface area of 1.8 m2 and a skin temperature of 33°C. The convection heat transfer coefficient for a clothed person walking in still air is expressed as h = 8.6V0.53 for 0.5 < V < 2 m/s, where V is the walking velocity in m/s.
> An average person generates heat at a rate of 240 Btu/h while resting in a room at 70°F. Assuming one-quarter of this heat is lost from the head and taking the emissivity of the skin to be 0.9, determine the average surface temperature of the head when i
> A rigid tank contains nitrogen gas at 227°C and 100 kPa gage. The gas is heated until the gage pressure reads 250 kPa. If the atmospheric pressure is 100 kPa, determine the final temperature of the gas, in °C.
> Reconsider Prob. 19–68. Using appropriate software, evaluate the effect of the cooling water mean velocity on the rate of steam condensation in the condenser. By varying the cooling water mean velocity for 0 Data from Prob. 19-68: Insi
> A hot liquid (cp = 1000 J/kg⋅K) flows at a flow rate of 0.05 kg/s inside a copper pipe with an inner diameter of 45 mm and a wall thickness of 5 mm. At the pipe exit, the liquid temperature decreases by 10°C from its temperature at the inlet. The outer s
> Inside a condenser, there is a bank of seven copper tubes with cooling water flowing in them. Steam condenses at a rate of 0.6 kg/s on the outer surfaces of the tubes, which are at a constant temperature of 68°C. Each copper tube is 5 m long a
> A hot fluid (kfluid = 0.72 W/m⋅K) is flowing as a laminar fully developed flow inside a pipe with an inner diameter of 35 mm and a wall thickness of 5 mm. The pipe is 10 m long, and the outer surface is exposed to air at 10°C. The average temperature dif
> Reconsider Prob. 19–65. Using appropriate software, investigate the effect of the cooling water average (mean) velocity on the number of tubes needed to achieve the indicated heat transfer rate in the condenser. By varying the cooling water average veloc
> Reconsider Prob. 20–52. Using appropriate software, evaluate the effect of the insulation layer thickness on the outer surface temperature. By varying the insulation layer thickness from 5 to 15 mm, plot the outer surface temperature as a function of the
> Repeat Prob. 19–65 for steam condensing at a rate of 0.60 kg/s. Data from Prob. 19-65: Cooling water available at 10°C is used to condense steam at 30°C in the condenser of a power plant at a rate of 0.15 kg/s by circulating the cooling water through a
> Hot engine oil is being transported in a horizontal pipe (k = 15 W/m⋅K, Di = 5 cm) with a wall thickness of 5 mm. The pipe is covered with a 5-mm-thick layer of insulation (k = 0.15 W/m⋅K). A length of 2 m of the outer surface is exposed to cool air at 1
> Cooling water available at 10°C is used to condense steam at 30°C in the condenser of a power plant at a rate of 0.15 kg/s by circulating the cooling water through a bank of 5-m-long, 1.2-cm internal-diameter thin copper tubes. Water enters the tubes at
> Hot water is being transported in a horizontal pipe (k = 0.15 W/m⋅K, Di = 2.5 cm, Do = 4.5 cm), where the pipe inner surface temperature is at 100°C. A length of 2 m of the pipe’s outer surface is exposed to cool air at 12°C. Assuming that the properties
> What is quality? Does it have any meaning in the superheated vapor region?
> Repeat Prob. 19–63 for a heat transfer coefficient of 40 W/m2⋅K. Data from Prob. 19-63: Combustion gases passing through a 5-cm-internal diameter circular tube are used to vaporize wastewater at atmospheric pressure. Hot gases enter the tube at 115 kPa
> A 1.5-m-diameter, 4-m-long cylindrical propane tank is initially filled with liquid propane, whose density is 581 kg/m3. The tank is exposed to the ambient air at 25°C in calm weather. The outer surface of the tank is polished so that the radi
> Combustion gases passing through a 5-cm-internal diameter circular tube are used to vaporize wastewater at atmospheric pressure. Hot gases enter the tube at 115 kPa and 250°C at a mean velocity of 5 m/s and leave at 150°C. If the average heat transfer co
> What is buoyancy force? Compare the relative magnitudes of the buoyancy force acting on a body immersed in these media: (a) air, (b) water, (c) mercury, and (d) an evacuated chamber.
> Air enters an 18-cm-diameter, 12-m-long underwater duct at 50°C and 1 atm at a mean velocity of 7 m/s and is cooled by the water outside. If the average heat transfer coefficient is 65 W/m2⋅K and the tube temperature is nearly equal to the water temper
> Reconsider Prob. 20–48. Using appropriate software, investigate the effect of the surface temperature of the steam pipe on the rate of heat loss from the pipe and the annual cost of this heat loss. Let the surface temperature vary from
> 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?
> 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 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
