A heated 6-mm-thick Pyroceram plate (ρ = 2600 kg/m3, cp = 808 J/kg⋅K, k = 3.98 W/m⋅K, and α = 1.89 × 10−6 m2/s) is being cooled in a room with air temperature of 25°C and convection heat transfer coefficient of 13.3 W/m2⋅K. The heated Pyroceram plate had an initial temperature of 500°C, and it is allowed to cool for 286 s. If the mass of the Pyroceram plate is 10 kg, determine the heat transfer from the Pyroceram plate during the cooling process using the analytical one term approximation method.
> In Betty Crocker’s Cookbook, it is stated that it takes 2 h 45 min to roast a 3.2-kg rib initially at 4.5°C to “rare” in an oven maintained at 163°C. It is recommended that a meat thermometer be used to monitor the cooking, and the rib is considered rare
> A 9-cm-diameter potato (ρ=1100 kg/m3, cp =3900 J/kg⋅K, k = 0.6 W/m⋅K, and α = 1.4 × 10−7 m2/s) that is initially at a uniform temperature of 25°C is baked in an oven at 170°C until a temperature sensor inserted into the center of the potato indicates a r
> Explain how the fins enhance heat transfer from a surface. Also, explain how the addition of fins may actually decrease heat transfer from a surface.
> An experiment is to be conducted to determine the heat transfer coefficient on the surfaces of tomatoes that are placed in cold water at 7°C. The tomatoes (k = 0.59 W/m⋅K, α = 0.141 ×10−6 m2/s, ρ = 999 kg/m3, cp = 3.99 kJ/kg⋅K) with an initial uniform te
> White potatoes (k=0.50 W/m⋅K and α=0.13 × 10−6 m2/s) that are initially at a uniform temperature of 20°C and have an average diameter of 6 cm are to be cooled by refrigerated air a
> The fins attached to a surface are determined to have an effectiveness of 0.9. Do you think the rate of heat transfer from the surface has increased or decreased as a result of the addition of these fins?
> Some engineers have developed a device that provides lighting to rural areas with no access to grid electricity. The device is intended for indoor use. It is driven by gravity, and it works as follows: A bag of rock or sand is raised by human power to a
> Oranges of 2.5-in diameter (k = 0.26 Btu/h⋅ft⋅°F and α = 1.4 × 10−6 ft2/s) initially at a uniform temperature of 78°F are to be cooled by refrigerated air at 25°F flowing at a velocity of 1 ft/s. The average heat transfer coefficient between the oranges
> What is the difference between the fin effectiveness and the fin efficiency?
> Consider heat transfer between two identical hot solid bodies and the air surrounding them. The first solid is being cooled by a fan while the second one is allowed to cool naturally. For which solid is the lumped system analysis more likely to be applic
> What is the reason for the widespread use of fins on surfaces?
> Hot air is to be cooled as it is forced to flow through the tubes exposed to atmospheric air. Fins are to be added in order to enhance heat transfer. Would you recommend attaching the fins inside or outside the tubes? Why? When would you recommend attach
> Reconsider Prob. 18–58. Using appropriate software, investigate the effect of the final center temperature of the egg on the time it will take for the center to reach this temperature. Let the temperature vary from 50°C to 95
> Reconsider Prob. 17–93. Using appropriate software, plot the rate of heat transfer from the ball as a function of the plastic insulation thickness in the range of 0.5 mm to 20 mm. Discuss the results. Data from Prob. 17-93: A 4-mm-diam
> An ordinary egg can be approximated as a 5.5-cm diameter sphere whose properties are roughly k = 0.6 W/mâ‹…K and α = 0.14 × 10−6 m2/s. The egg is initially at a uniform temperature of 4Â&
> A 4-mm-diameter spherical ball at 50°C is covered by 1-mm-thick plastic insulation (k = 0.13 W/m⋅K). The ball is exposed to a medium at 15°C, with a combined convection and radiation heat transfer coefficient of 20
> Hailstones are formed in high-altitude clouds at 253 K. Consider a hailstone with diameter of 20 mm that is falling through air at 15°C with convection heat transfer coefficient of 163 W/m2⋅K. Assuming the hailstone can be modeled as a sphere and has pro
> Natural gas, which is mostly methane CH4, is a fuel and a major energy source. Can we say the same about hydrogen gas, H2?
> Repeat Prob. 17–91E, assuming a thermal contact resistance of 0.01 h⋅ft2⋅°F/Btu at the interface of the wire and the insulation. Data from Prob. 17-91: A 0.083-in-diameter electrical wire at 90°F is covered by 0.02-in-thick plastic insulation (k = 0.075
> Chickens with an average mass of 1.7 kg (k = 0.45 W/m⋅K and α = 0.13 × 10−6 m2/s) initially at a uniform temperature of 15°C are to be chilled in agitated brine at −7°C. The average heat transfer coefficient between the chicken and the brine is determine
> A 0.083-in-diameter electrical wire at 90°F is covered by 0.02-in-thick plastic insulation (k = 0.075 Btu/h⋅ft⋅°F). The wire is exposed to a medium at 50°F, with a combined convection and radiation heat transfer coefficient of 2.5 Btu/h⋅ft2⋅°F. Determine
> Citrus fruits are very susceptible to cold weather, and extended exposure to subfreezing temperatures can destroy them. Consider an 8-cm-diameter orange that is initially at 15°C. A cold front moves in one night, and the ambient temperature suddenly drop
> A pipe is insulated such that the outer radius of the insulation is less than the critical radius. Now the insulation is taken off. Will the rate of heat transfer from the pipe increase or decrease for the same pipe surface temperature?
> For heat transfer purposes, an egg can be considered to be a 5.5-cm-diameter sphere having the properties of water. An egg that is initially at 4.3°C is dropped into boiling water at 100°C. The heat transfer coefficient at the surface of the egg is estim
> Someone comments that a microwave oven can be viewed as a conventional oven with zero convection resistance at the surface of the food. Is this an accurate statement?
> Steel rods, 2 m in length and 60 mm in diameter, are being drawn through an oven that maintains a temperature of 800°C and convection heat transfer coefficient of 128 W/m2⋅K. The steel rods (ρ = 7832 kg/m3, cp = 434 J/kg⋅K, k = 63.9 W/m⋅K, and α = 18.8 ×
> Consider a pipe at a constant temperature whose radius is greater than the critical radius of insulation. Someone claims that the rate of heat loss from the pipe has increased when some insulation is added to the pipe. Is this claim valid?
> Reconsider Prob. 18–51. Using appropriate software, investigate the effect of the cooling time on the final center temperature of the shaft and the amount of heat transfer. Let the time vary from 5 min to 60 min. Plot the center temperature and the heat
> A wind turbine is rotating at 15 rpm under steady winds flowing through the turbine at a rate of 42,000 kg/s. The tip velocity of the turbine blade is measured to be 250 km/h. If 180 kW of power is produced by the turbine, determine (a) the average veloc
> A pipe is insulated to reduce the heat loss from it. However, measurements indicate that the rate of heat loss has increased instead of decreasing. Can the measurements be right?
> A long 35-cm-diameter cylindrical shaft made of stainless steel 304 (k = 14.9 W/m⋅K, ρ = 7900 kg/m3, cp = 477 J/kg⋅K, and α = 3.95 × 10−6 m2/s) comes out of an oven at a uniform temperature of 500°C. The shaft is then allowed to cool slowly in a chambe
> Consider an insulated pipe exposed to the atmosphere. Will the critical radius of insulation be greater on calm days or on windy days? Why?
> A 30-cm-diameter, 4-m-high cylindrical column of a house made of concrete (k = 0.79 W/m⋅K, α = 5.94 × 10−7 m2/s, ρ = 1600 kg/m3, and cp = 0.84 kJ/kg⋅K) cooled to 14°C during a cold night is heated again during the day by being exposed to ambient air at a
> What is the critical radius of insulation? How is it defined for a cylindrical layer?
> For which kinds of bodies made of the same material is the lumped system analysis more likely to be applicable: slender ones or well-rounded ones of the same volume? Why?
> Repeat Prob. 17–84 for liquid oxygen, which has a boiling temperature of −183°C, a heat of vaporization of 213 kJ/kg, and a density of 1140 kg/m3 at 1 atm pressure. Data from Prob. 17-84: The boiling temper
> A 65-kg beef carcass (k = 0.47 W/m⋅K and α = 0.13 ×10−6 m2/s) initially at a uniform temperature of 37°C is to be cooled by refrigerated air at −10°C f
> The boiling temperature of nitrogen at atmospheric pressure at sea level (1 atm pressure) is −196°C. Therefore, nitrogen is commonly used in low-temperature scientific studies since the temperature of liquid nitrogen in a tan
> A 2-cm-diameter plastic rod has a thermocouple inserted to measure temperature at the center of the rod. The plastic rod (ρ = 1190 kg/m3, cp = 1465 J/kg⋅K, and k = 0.19 W/m⋅K) was initially heated to a uni
> An oil pump is drawing 44 kW of electric power while pumping oil with ρ = 860 kg/m3 at a rate of 0.1 m3/s. The inlet and outlet diameters of the pipe are 8 cm and 12 cm, respectively. If the pressure rise of oil in the pump is measured to be 5
> An 8-m-internal-diameter spherical tank made of 1.5-cm-thick stainless steel (k = 15 W/m⋅K) is used to store iced water at 0°C. The tank is located in a room whose temperature is 25°C. The walls of the room are als
> A long iron rod (ρ = 7870 kg/m3, cp = 447 J/kg⋅K, k = 80.2 W/m⋅K, and α = 23.1 × 10−6 m2/s) with diameter of 25 mm is initially heated to a uniform temperature
> Liquid hydrogen is flowing through an insulated pipe (k = 23 W/m⋅K, Di = 3 cm, Do = 4 cm, and L = 20 m). The pipe is situated in a chemical plant, where the average air temperature is 40°C. The convection heat transfer coefficients of the liquid hydrogen
> Long cylindrical AISI stainless steel rods (k = 7.74 Btu/h⋅ft⋅°F and α = 0.135 ft2/h) of 4-in diameter are heat treated by drawing them at a velocity of 7 ft/min through a 21 ft long oven maint
> In a pharmaceutical plant, a copper pipe (kc = 400 W/mâ‹…K)with inner diameter of 20 mm and wall thickness of 2.5 mm is used for carrying liquid oxygen to a storage tank. The liquid oxygen flowing in the pipe has an average temperature of
> A long cylindrical wood log (k = 0.17 W/m⋅K and α = 1.28 × 10−7 m2/s) is 10 cm in diameter and is initially at a uniform temperature of 25°C. It is exposed to hot gases at 525°C in a fireplace with a heat transfer coefficient of 13.6 W/m2⋅K on the surfac
> Hot water at an average temperature of 90°C is flowing through a 15-m section of a cast iron pipe (k = 52 W/m⋅K) whose inner and outer diameters are 4 cm and 4.6 cm, respectively. The outer surface of the pipe, whose emissivity is 0.7, is exposed to the
> After a long, hard week on the books, you and your friend are ready to relax and enjoy the weekend. You take a steak 50 mm thick from the freezer. (a) How long (in hours) do you have to let the good times roll before the steak has thawed? Assume that the
> Consider steady one-dimensional heat transfer through a plane wall exposed to convection from both sides to environments at known temperatures T∞1 and T∞2 with known heat transfer coefficients h1 and h2. Once the rate of heat transfer Q has been evaluate
> The water behind Hoover Dam in Nevada is 206 m higher than the Colorado River below it. At what rate must water pass through the hydraulic turbines of this dam to produce 50 MW of power if the turbines are 100 percent efficient?
> Steam at 450°F is flowing through a steel pipe (k = 8.7 Btu/h⋅ft⋅°F) whose inner and outer diameters are 3.5 in and 4.0 in, respectively, in an environment at 55°F. The pipe is insulated with 2-in-thick fiberglass insulation (k = 0.020 Btu/h⋅ft⋅°F). If t
> Layers of 23-cm-thick meat slabs (k = 0.47 W/m⋅K and α = 0.13 × 10−6 m2/s) initially at a uniform temperature of 7°C are to be frozen by refrigerated air at −30°C flowing at a velocity of 1.4 m/s. The average heat transfer coefficient between the meat an
> Chilled water enters a thin-shelled 4-cm-diameter, 200-m-long pipe at 7°C at a rate of 0.98 kg/s and leaves at 8°C. The pipe is exposed to ambient air at 30°C with a heat transfer coefficient of 9 W/m2⋅K. If the pipe is to be insulated with glass wool in
> A 10-cm-thick aluminum plate (α = 97.1 × 10−6 m2/s) is being heated in liquid with temperature of 500°C. The aluminum plate has a uniform initial temperature of 25°C. If the surface temperature of the aluminum plate is approximately the liquid temperat
> Consider a 1.5-m-high electric hot-water heater that has a diameter of 40 cm and maintains the hot water at 60°C. The tank is located in a small room whose average temperature is 27°C, and the heat transfer coefficients on the inner
> In a meat processing plant, 2-cm-thick steaks (k = 0.45 W/m⋅K and α = 0.91 × 10−7 m2/s) that are initially at 25°C are to be cooled by passing them through a refrigeration room at −11°C. The heat transfer coefficient on both sides of the steaks is 9 W/m2
> A 2.2-mm-diameter and 14-m-long electric wire is tightly wrapped with a 1-mm-thick plastic cover whose thermal conductivity is k = 0.15 W/mâ‹…K. Electrical measurements indicate that a current of 13 A passes through the wire, and there is
> For which solid is the lumped system analysis more likely to be applicable: an actual apple or a golden apple of the same size? Why?
> Reconsider Prob. 17–73E. Using appropriate software, investigate the effects of the thermal conductivity of the pipe material and the outer diameter of the pipe on the length of the tube required. Let the thermal conductivity vary from
> A body at an initial temperature of Ti is brought into a medium at a constant temperature of T∞. How can you determine the maximum possible amount of heat transfer between the body and the surrounding medium?
> A hydraulic turbine has 85 m of elevation difference available at a flow rate of 0.25 m3/s, and its overall turbine–generator efficiency is 91 percent. Determine the electric power output of this turbine.
> Solve Prob. 1–17 using appropriate software. Print out the entire solution, including the numerical results with proper units. Data from Problem 1-17: A 2-kg rock is thrown upward with a force of 200 N at a location where the local gravitational acceler
> Repeat Prob. 17–73E, assuming that a 0.01-in-thick layer of mineral deposit (k = 0.5 Btu/h⋅ft⋅°F) has formed on the inner surface of the pipe. Data from Prob. 17-73: Steam exiting the turb
> The Biot number during a heat transfer process between a sphere and its surroundings is determined to be 0.02. Would you use lumped system analysis or the one-term approximate solutions when determining the midpoint temperature of the sphere? Why?
> Steam exiting the turbine of a steam power plant at 100°F is to be condensed in a large condenser by cooling water flowing through copper pipes (k = 223 Btu/h⋅ft⋅°F) of inner diameter 0.4 in and o
> How can we use the one-term approximate solutions when the surface temperature of the geometry is specified instead of the temperature of the surrounding medium and the convection heat transfer coefficient?
> Superheated steam at an average temperature 200°C is transported through a steel pipe (k = 50 W/m⋅K, Do = 8.0 cm, Di = 6.0 cm, and L = 20.0 m). The pipe is insulated with a 4-cm thick layer of gypsum plaster (k = 0.5 W/m⋅K). The insulated pipe is placed
> Can the one-term approximate solutions for a plane wall exposed to convection on both sides be used for a plane wall with one side exposed to convection while the other side is insulated? Explain.
> A 50-m-long section of a steam pipe whose outer diameter is 10 cm passes through an open space at 15°C. The average temperature of the outer surface of the pipe is measured to be 150°C. If the combined heat transfer coefficient on t
> What is the physical significance of the Fourier number? Will the Fourier number for a specified heat transfer problem double when the time is doubled?
> Reconsider Prob. 17–69. Using appropriate software, investigate the effect of the thickness of the insulation on the rate of heat loss from the steam and the temperature drop across the insulation layer. Let the insulation thickness vary from 1 cm to 10
> What is an infinitely long cylinder? When is it proper to treat an actual cylinder as being infinitely long, and when is it not? For example, is it proper to use this model when finding the temperatures near the bottom or top surfaces of a cylinder? Expl
> Large wind turbines with a power capacity of 8 MW and blade span diameters of over 160 m are available for electric power generation. Consider a wind turbine with a blade span diameter of 100 m installed at a site subjected to steady winds at 8 m/s. Taki
> Why are the convection and the radiation resistances at a surface in parallel instead of being in series?
> An egg is to be cooked to a certain level of doneness by being dropped into boiling water. Can the cooking time be shortened by turning up the heat and bringing water to a more rapid boil?
> Steam at 280°C flows in a stainless steel pipe (k = 15W/m⋅K) whose inner and outer diameters are 5 cm and 5.5 cm, respectively. The pipe is covered with 3-cm-thick glass wool insulation (k = 0.038 W/m⋅K). Heat is lost to the surroundings at 5°C by natura
> An electronic device dissipating 18 W has a mass of 20 g, a specific heat of 850J/kg⋅K, and a surface area of 4 cm2. The device is lightly used, and it is on for 5 min and then off for several hours, during which it cools to the ambient temperature of 25
> Consider a short cylinder whose top and bottom surfaces are insulated. The cylinder is initially at a uniform temperature Ti and is subjected to convection from its side surface to a medium at temperature T∞, with a heat transfer coefficient of h. Is the
> Consider a sphere of diameter 5 cm, a cube of side length 5 cm, and a rectangular prism of dimension 4 cm × 5 cm × 6 cm, all initially at 0°C and all made of silver (k = 429 W/m⋅K, ρ = 10,500 kg/m3, cp = 0.235 kJ/kg⋅K). Now all three of these geometrie
> Can the thermal resistance concept be used for a solid cylinder or sphere in steady operation? Explain.
> In a manufacturing facility, 2-in-diameter brass balls (k=64.1 Btu/h⋅ft⋅°F, ρ=532 lbm/ft3, and cp =0.092 Btu/lbm⋅°F) initially at 250°F are quenched in a wa
> What is an infinitely long cylinder? When is it proper to treat an actual cylinder as being infinitely long, and when is it not?
> In what medium is the lumped system analysis more likely to be applicable: in water or in air? Why?
> Water is pumped from a lake to a storage tank 15 m above at a rate of 70 L/s while consuming 15.4 kW of electric power. Disregarding any frictional losses in the pipes and any changes in kinetic energy, determine (a) the overall efficiency of the pump&ac
> In an experiment to measure convection heat transfer coefficients, a very thin metal foil of very low emissivity (e.g., highly polished copper) is attached on the surface of a slab of material with very low thermal conductivity. The other surface of the
> Consider a spherical shell satellite with outer diameter of 4 m and shell thickness of 10 mm that is reentering the atmosphere. The shell satellite is made of stainless steel with properties of ρ = 8238 kg/m3, cp = 468 J/kg⋅K, and k = 13.4 W/m⋅K. During
> Consider a 5-m-high, 8-m-long, and 0.22-m-thick wall whose representative cross section is as given in the figure. The thermal conductivities of various materials used, in W/mâ‹…K, are kA = kF = 2, kB = 8, kC = 20, kD = 15, and kE = 35. T
> Plasma spraying is a process used for coating a material surface with a protective layer to prevent the material from degradation. In a plasma spraying process, the protective layer in powder form is injected into a plasma jet. The powder is then heated
> A 10-in-thick, 30-ft-long, and 10-ft-high wall is to be constructed using 9-in-long solid bricks (k = 0.40 Btu/h⋅ft⋅°F) of cross section 7in × 7in, or identical-size bricks with nine square air
> Oxy-fuel combustion power plants use pulverized coal particles as fuel to burn in a pure oxygen environment to generate electricity. Before entering the furnace, pulverized spherical coal particles with an average diameter of 300 μm are transported at 2
> A 12-m-long and 5-m-high wall is constructed of two layers of 1-cm-thick sheetrock (k = 0.17 W/m⋅K) spaced 16 cm by wood studs (k = 0.11 W/m⋅K) whose cross section is 16 cm × 5 cm. The studs are placed vertically 60 cm apart, and the space between them i
> Pulverized coal particles are used in oxy-fuel combustion power plants for electricity generation. Consider a situation where coal particles are suspended in hot air flowing through a heated tube, where the convection heat transfer coefficient is 100 W/m
> Reconsider Prob. 17–60. Using appropriate software, plot the rate of heat transfer through the wall as a function of the thickness of the rigid foam in the range of 1 cm to 10 cm. Discuss the results. Data from Prob. 17-60: A 4-m-high
> A thermocouple with a spherical junction diameter of 0.5 mm is used for measuring the temperature of hot airflow in a circular duct. The convection heat transfer coefficient of the airflow can be related with the diameter (D) of the spherical junction an
> An 80-percent-efficient pump with a power input of 20 hp is pumping water from a lake to a nearby pool at a rate of 1.5 ft3/s through a constant-diameter pipe. The free surface of the pool is 80 ft above that of the lake. Determine the mechanical power u
> A 4-m-high and 6-m-wide wall consists of a long 15-cm × 25-cm cross section of horizontal bricks (k = 0.72 W/m⋅K) separated by 3-cm-thick plaster layers (k = 0.22 W/m⋅K). There are also 2-cm thick plaster
> In an experiment, the temperature of a hot gas stream is to be measured by a thermocouple with a spherical junction. Due to the nature of this experiment, the response time of the thermos couple to register 99 percent of the initial temperature differenc
> How is the combined heat transfer coefficient defined? What convenience does it offer in heat transfer calculations?
> The temperature of a gas stream is to be measured by a thermocouple whose junction can be approximated as a 1.2-mm diameter sphere. The properties of the junction are k = 35 W/m⋅K, ρ = 8500 kg/m3, and cp = 320 J/kg⋅K, and the heat transfer coefficient be
> A typical section of a building wall is shown in Fig. P17–59. This section extends in and out of the page and is repeated in the vertical direction. The wall support members are made of steel (k = 50 W/m⋅K). The suppor
