What is the difference between the fin effectiveness and the fin efficiency?
> A 20-mm × 20-mm silicon chip is mounted such that the edges are flush in a substrate. The substrate provides an unheated starting length of 20 mm that acts as a turbulator. A turbulator is a device that trips the velocity boundary layer to turbulence. He
> A semi-infinite aluminum cylinder (k = 237 W/m⋅K, α = 9.71 × 10−5 m2/s) of diameter D = 15 cm is initially at a uniform temperature of Ti = 115°C. The cylinder is now placed in water at 10°C, where heat transfer takes place by convection with a heat tra
> The local atmospheric pressure in Denver, Colorado (elevation 1610 m), is 83.4 kPa. Air at this pressure and 20°C flows with a velocity of 8 m/s over a 1.5-m × 6-m flat plate whose temperature is 140°C. Determine the ra
> The U.S. Department of Energy estimates that 570,000 barrels of oil would be saved per day if every household in the United States lowered the thermostat setting in winter by 6°F (3.3°C). Assuming the average heating season to be 180 days and the cost of
> Reconsider Prob. 18–91. Using appropriate software, investigate the effect of the cooling time on the center temperature of the cylinder, the center temperature of the top surface of the cylinder, and the total heat transfer. Let the ti
> To defrost ice accumulated on the outer surface of an automobile windshield, warm air is blown over the inner surface of the windshield. Consider an automobile windshield (kw = 1.4 W/mâ‹…K) with an overall height of 0.5 m and thickness of
> A short brass cylinder (ρ = 8530 kg/m3, cp = 0.389 kJ/kg⋅K, k = 110 W/m⋅K, and α = 3.39 × 10−5 m2/s) of diameter 4 cm and height 20 cm is initially at a uniform t
> A 2-cm-high cylindrical ice block (k = 2.22 W/m⋅K and α = 0.124 × 10−7 m2/s) is placed on a table on its base of diameter 2 cm in a room at 24°C. The heat transfer coefficient on the exposed surfaces of the ice block is 13 W/m2⋅K, and heat transfer from
> The upper surface of a 50-cm-thick solid plate (k = 237 W/m⋅K) is being cooled by water with temperature of 20°C. The upper and lower surfaces of the solid plate are maintained at constant temperatures of 60°C and
> Consider two identical 4-kg pieces of roast beef. The first piece is baked as a whole, while the second is baked after being cut into two equal pieces in the same oven. Will there be any difference between the cooking times of the whole and cut roasts? W
> What is forced convection? How does it differ from natural convection? Is convection that is caused by winds forced or natural convection?
> A hot dog can be considered to be a cylinder 5 in long and 0.8 in in diameter whose properties are ρ = 61.2 lbm/ft3, cp = 0.93 Btu/lbm⋅°F, k = 0.44 Btu/h⋅ft⋅°F, and α = 0.0077 ft2/h. A hot dog initially at 40°F is dropped into boiling water at 212°F. If
> Repeat Prob. 18–87 with the heat transfer coefficient at the top and the bottom surfaces of each block being doubled to 80 W/m2⋅K. Data from Prob. 18-87: Consider a cubic block whose sides are 5 cm long and a cylindri
> Consider a cubic block whose sides are 5 cm long and a cylindrical block whose height and diameter are also 5 cm. Both blocks are initially at 20°C and are made of granite (k = 2.5 W/mâ‹…K and α = 1.15 Ã
> A homeowner is considering these heating systems for heating his house: Electric resistance heating with $0.12/kWh and 1 kWh = 3600 kJ, gas heating with $1.24/therm and 1 therm = 105,500 kJ, and oil heating with $2.3/gal and 1 gal of oil = 138,500 kJ. As
> 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
> A short cylinder initially at a uniform temperature Ti is subjected to convection from all of its surfaces to a medium at temperature T∞. Explain how you can determine the temperature of the midpoint of the cylinder at a specified time t.
> How is the product solution used to determine the variation of temperature with time and position in three-dimensional systems?
> What is the product solution method? How is it used to determine the transient temperature distribution in a two dimensional system?
> A barefooted person whose feet are at 32°C steps on a large aluminum block at 20°C. Treating both the feet and the aluminum block as semi-infinite solids, determine the contact surface temperature. What would your answer be if the person stepped on a woo
> Thick slabs of stainless steel (k = 14.9 W/m⋅K and α = 3.95 × 10−6 m2/s) and copper (k = 401 W/m⋅K and α = 117 ×10−6 m2/s) are p
> We often cut a watermelon in half and put it into the freezer to cool it quickly. But usually we forget to check on it and end up having a watermelon with a frozen layer on top. To avoid this potential problem, a person wants to set a timer so that it wi
> Consider a potato being baked in an oven that is maintained at a constant temperature. The temperature of the potato is observed to rise by 5°C during the first minute. Will the temperature rise during the second minute be less than, equal to, or more th
> Reconsider Prob. 18–78. Using appropriate software, plot the soil temperature as a function of the distance from the earth’s surface as the distance varies from 0 m to 1 m, and discuss the results. Data from Prob. 18-
> The soil temperature in the upper layers of the earth varies with variations in the atmospheric conditions. Before a cold front moves in, the earth at a location is initially at a uniform temperature of 15°C. Then the area is subjected to a te
> Consider a homeowner who is replacing his 25-year-old natural gas furnace that has an efficiency of 55 percent. The home owner is considering a conventional furnace that has an efficiency of 82 percent and costs $1600 and a high-efficiency furnace that h
> A thick wood slab (k = 0.17 W/m⋅K and α = 1.28 ×10−7 m2/s) that is initially at a uniform temperature of 25°C is exposed to hot gases at 550°C for 5 min. The heat transfer coefficient between the gases and the wood slab is 35 W/m2⋅K. If the ignition temp
> Thick slabs of stainless steel (k = 14.9 W/m⋅K and α=3.95 × 10−6 m2/s) and copper (k=401 W/m⋅K and α=117 ×10−6 m2/s) are subject
> Refractory bricks are used as linings for furnaces, and they generally have low thermal conductivity to minimize heat loss through the furnace walls. Consider a thick furnace wall lined with refractory bricks (k = 1.0 W/mâ‹…K and Î&
> A thick aluminum block initially at 20°C is subjected to constant heat flux of 4000 W/m2 by an electric resistance heater whose top surface is insulated. Determine how much the surface temperature of the block will rise after 30 min.
> A highway made of asphalt is initially at a uniform temperature of 55°C. Suddenly the highway surface temperature is reduced to 25°C by rain. Determine the temperature at the depth of 3 cm from the highway surface and the heat flux transferred from the h
> A large cast iron container (k = 52 W/m⋅K and α = 1.70 × 10−5 m2/s) with 4-cm-thick walls is initially at a uniform temperature of 0°C and is filled with ice at 0°C. Now
> In areas where the air temperature remains below 0°C for prolonged periods of time, the freezing of water in underground pipes is a major concern. Fortunately, the soil remains relatively warm during those periods, and it takes weeks for the subfreezing
> Consider a curing kiln whose walls are made of 30-cm thick concrete with a thermal diffusivity of α=0.23 × 10−5 m2/s. Initially, the kiln and its walls are in equilibrium with the surroundings at 6°
> Consider heat transfer between two identical hot solid bodies and their environments. The first solid is dropped in a large container filled with water, while the second one is allowed to cool naturally in the air. For which solid is the lumped system an
> The walls of a furnace are made of 1.5-ft-thick concrete (k = 0.64 Btu/h⋅ft⋅°F and α = 0.023 ft2/h). Initially, the furnace and the surrounding air are in thermal equilibrium at 70°F. The furnace is then fired, and the inner surfaces of the furnace are s
> Consider a classroom for 55 students and one instructor, each generating heat at a rate of 100 W. Lighting is provided by 18 fluorescent lightbulbs, 40 W each, and the ballasts consume an additional 10 percent. Determine the rate of internal heat generat
> Consider a hot semi-infinite solid at an initial temperature of Ti that is exposed to convection to a cooler medium at a constant temperature of T∞, with a heat transfer coefficient of h. Explain how you can determine the total amount of heat transfer fr
> What is a semi-infinite medium? Give examples of solid bodies that can be treated as semi-infinite media for heat transfer purposes.
> Under what conditions can a plane wall be treated as a semi-infinite medium?
> Repeat Prob. 18–64 for a roast rib that is to be “welldone” instead of “rare.” A rib is considered to be well-done when its center temperature reaches 77°C, and the roasting in this case takes about 4 h 15 min. Data from Prob. 18-64: In Betty Crocker’s
> 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
> 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
> 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
> 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
