A hot dog can be considered to be a 12-cm-long cylinder whose diameter is 2 cm and whose properties are ρ = 980 kg/m3, cp = 3.9 kJ/kg⋅K, k = 0.76 W/m⋅K, and α = 2 × 10−7 m2/s. A hot dog initially at 5°C is dropped into boiling water at 100°C. The heat transfer coefficient at the surface of the hot dog is estimated to be 600 W/m2⋅K. If the hot dog is considered cooked when its center temperature reaches 80°C, determine how long it will take to cook it in the boiling water. Solve this problem using the analytical one-term approximation method.
> 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
> To warm up some milk for a baby, a mother pours milk into a thin-walled cylindrical container whose diameter is 6 cm. The height of the milk in the container is 7 cm. She then places the container into a large pan filled with hot water at 70°C. The milk
> Clothing made of several thin layers of fabric with trapped air in between, often called ski clothing, is commonly used in cold climates because it is light, fashionable, and a very effective thermal insulator. So it is no surprise that such clothing has
> Steel rods (ρ = 7832 kg/m3, cp = 434 J/kg⋅K, and k = 63.9 W/m⋅K) are heated in a furnace to 850°C and then quenched in a water bath at 50°C for 40 s as part of a hardening process. The convection heat transfer coefficient is 650 W/m2⋅K. If the steel rods
> Consider a 10-in × 12-in epoxy glass laminate (k = 0.10 Btu/h⋅ft⋅°F) whose thickness is 0.05 in. In order to reduce the thermal resistance across its thickness, cylindrical copper fillings (k =
> Springs in automobile suspension systems are made of steel rods heated and wound into coils while ductile. Consider steel rods (ρ = 7832 kg/m3, cp = 434 J/kg⋅K, and k = 63.9 W/m⋅K) with diameter of 2.5 cm and length of 1.27 m. The steel rods are heated
> Water is pumped from a lower reservoir to a higher reservoir by a pump that provides 20 kW of shaft power. The free surface of the upper reservoir is 45 m higher than that of the lower reservoir. If the flow rate of water is measured to be 0.03 m3/s, det
> A 10-cm-thick wall is to be constructed with 2.5-m-long wood studs (k = 0.11 W/m⋅K) that have a cross section of 10 cm × 10 cm. At some point the builder ran out of those studs and started using pairs of 2.5-m-long wood studs that have a cross section of
> What is lumped system analysis? When is it applicable?
> When plotting the thermal resistance network associated with a heat transfer problem, explain when two resistances are in series and when they are in parallel.
> A long copper rod of diameter 2.0 cm is initially at a uniform temperature of 100°C. It is now exposed to an airstream at 20°C with a heat transfer coefficient of 200 W/m2⋅K. How long would it take for the copper rod to cool to an average temperature of
> The thermal resistance networks can also be used approximately for multidimensional problems. For what kind of multidimensional problems will the thermal resistance approach give adequate results?
> A batch of 2-cm-thick stainless steel plates (k=21W/m⋅K, ρ=8000 kg/m3, and cp =570 J/kg⋅K) are conveyed through a furnace to be heat treated. The plates enter the furnace at 18°C, and they travel
> What are the two approaches used in the development of the thermal resistance network for two-dimensional problems?
> A 5-mm-thick stainless steel strip (k = 21 W/m⋅K, ρ = 8000 kg/m3, and cp = 570 J/kg⋅K) is being heat treated as it moves through a furnace at a speed of 1 cm/s. The air temperature in the furnace is maintain
> Inconel® refers to a class of nickel-chromium-based superalloys that are used in high temperature applications, such as gas turbine blades. For further improvement in the performance of gas turbine engines, the outer blade surface is coated with ceramic-
> Metal plates (k = 180 W/m⋅K, ρ = 2800 kg/m3, and cp = 880 J/kg⋅K) with a thickness of 1 cm are being heated in an oven for 2 min. Air in the oven is maintained at 800°C with a convection heat transfer coefficient of 200 W/m2⋅K. If the initial temperatu
> Reconsider Prob. 3–60. Using appropriate software, investigate the effect of wind velocity and the blade span diameter on wind power generation. Let the velocity vary from 5 to 20 m/s in increments of 5 m/s, and let the diameter vary from 20 to 120 m in
> Consider an engine cover that is made with two layers of metal plates. The inner layer is stainless steel (k1 = 14 W/m⋅K) with a thickness of 10 mm, and the outer layer is aluminum (k2 = 237W/m⋅K) with a thickness of 5 mm. Both metal plates have a surfac
> Reconsider Prob. 18–14. Using appropriate software, investigate the effects of the heat transfer coefficient and the final plate temperature on the time it will take for the plate to reach this temperature. Let the heat transfer coeffic
> Consider an 800-W iron whose base plate is made of 0.5-cm-thick aluminum alloy 2024–T6 (ρ = 2770 kg/m3, cp = 875 J/kg⋅K, α = 7.3 × 10−5 m2/s). The base plate has
> A thin electronic component with a surface area of 950 cm2 is cooled by having a heat sink attached on its top surface. The thermal contact conductance of the interface between the electronic component and the heat sink is 2000 W/m2⋅K. According to the m
> A brick of 203 × 102 × 57 mm in dimension is being burned in a kiln to 1100°C and then allowed to cool in a room with ambient air temperature of 30°C and convection heat transfer coefficient of 5 W/m2⋅K. If the brick has properties of ρ = 1920 kg/m3, cp
> Consider steady heat transfer through the wall of a room in winter. The convection heat transfer coefficient at the outer surface of the wall is three times that of the inner surface as a result of the winds. On which surface of the wall do you think the
> Obtain a relation for the time required for a lumped system to reach the average temperature 1/2 (Ti + T∞), where Ti is the initial temperature and T∞ is the temperature of the environment.
> An aluminum plate and a stainless steel plate are pressed against each other at an average pressure of 20 MPa. Both plates have a surface roughness of 2 μm. Determine the impact on the temperature drop at the interface if the surface roughness of the pla
> Obtain relations for the characteristic lengths of a large plane wall of thickness 2L, a very long cylinder of radius ro, and a sphere of radius ro.
> An aluminum plate 25 mm thick (k = 235 W/mâ‹…K) is attached to a copper plate with thickness of 10 mm. The copper plate is heated electrically to dissipate a uniform heat flux of 5300 W/m2. The upper surface of the aluminum plate is expos
> At a certain location, wind is blowing steadily at 7 m/s. Determine the mechanical energy of air per unit mass and the power generation potential of a wind turbine with 80-m-diameter blades at that location. Also determine the actual electric power gene
> Consider the engine block of a car made of cast iron (k = 52 W/m⋅K and α = 1.7 × 10−5 m2/s). The engine can be considered to be a rectangular block whose sides are 80 cm, 40 cm, and 40 cm. The engine is at a temperature of 150°C when it is turned off. Th
> A two-layer wall is made of two metal plates, with surface roughness of about 25 μm, pressed together at an average pressure of 10 MPa. The first layer is a stainless steel plate with a thickness of 5 mm and a thermal conductivity of 14 W/m⋅K. The second
> Two identical aluminum plates with thickness of 30 cm are pressed against each other at an average pressure of 1 atm. The interface, sandwiched between the two plates, is filled with glycerin. On the left outer surface, it is subjected to a uniform heat
> A large iron slab (ρ = 7870 kg/m3, cp = 447 J/kg⋅K, and k = 80.2 W/m⋅K) was initially heated to a uniform temperature of 150°C and then placed on a concrete floor (ρ = 1600 kg/m3, cp
> A 1-mm-thick copper plate (k = 401 W/m⋅K) is sandwiched between two 7-mm-thick epoxy boards (k = 0.26 W/m⋅K) that are 15 cm × 20 cm in size. If the thermal contact conductance on both sides of the copper p
> In a volcano eruption, lava at 1200°C is found flowing on the ground. The ground was initially at 15°C, and the lava flow has a convection heat transfer coefficient of 3500 W/m2⋅K. Determine the ground surface (a) temperature and (b) heat flux after 2 s
> Two 5-cm-diameter, 15-cm-long aluminum bars (k = 176 W/m⋅K) with ground surfaces are pressed against each other with a pressure of 20 atm. The bars are enclosed in an insulation sleeve and, thus, heat transfer from the lateral surfaces is negligible. If
> A 40-cm-thick brick wall (k = 0.72 W/m⋅K, and α = 1.6 × 10−6 m2/s) is heated to an average temperature of 18°C by the heating system and the solar radiation incident on it during the day. During the night, the outer surface of the wall is exposed to cold
> The thermal contact conductance at the interface of two 1-cm-thick aluminum plates is measured to be 11,000 W/m2â‹…K. Determine the thickness of the aluminum plate whose thermal resistance is equal to the thermal resistance of the interfa
> Portable electric heaters are commonly used to heat small rooms. Explain the energy transformation involved during this heating process.
> Water mains must be placed at sufficient depth below the earth’s surface to avoid freezing during extended periods of subfreezing temperatures. Determine the minimum depth at which the water main must be placed at a location where the soil is initially a
> Consider two surfaces pressed against each other. Now the air at the interface is evacuated. Will the thermal contact resistance at the interface increase or decrease as a result?
> Spherical glass beads coming out of a kiln are allowed to cool in a room temperature of 30°C. A glass bead with a diameter of 10 mm and an initial temperature of 400°C is allowed to cool for 3 min. If the convection heat transfer coefficient is 28 W/m2⋅K
> A plate consists of two thin metal layers pressed against each other. Do we need to be concerned about the thermal contact resistance at the interface in a heat transfer analysis or can we just ignore it?
> A watermelon initially at 35°C is to be cooled by dropping it into a lake at 15°C. After 4 h and 40 min of cooling, the center temperature of the watermelon is measured to be 20°C. Treating the watermelon as a 20-cm-diameter sphere and using the properti
> In Betty Crocker’s Cookbook, it is stated that it takes 5 h to roast a 14-lb stuffed turkey initially at 40°F in an oven maintained at 325°F. It is recommended that a meat thermometer be used to monitor the cooking, and the turkey is considered done when
> A wall consists of two layers of insulation pressed against each other. Do we need to be concerned about the thermal contact resistance at the interface in a heat transfer analysis or can we just ignore it?
> Consider a sphere and a cylinder of equal volume made of copper. Both the sphere and the cylinder are initially at the same temperature and are exposed to convection in the same environment. Which do you think will cool faster, the cylinder or the sphere
> Can we define the convection resistance for a unit surface area as the inverse of the convection heat transfer coefficient?
> What is the physical significance of the Biot number? Is the Biot number more likely to be larger for highly conducting solids or poorly conducting ones?
> A geothermal pump is used to pump brine whose density is 1050 kg/m3 at a rate of 0.3 m3/s from a depth of 200 m. For a pump efficiency of 74 percent, determine the required power input to the pump. Disregard frictional losses in the pipes, and assume the
> Explain how the thermal contact resistance can be minimized.
> Will the thermal contact resistance be greater for smooth or rough plain surfaces?
> What is thermal contact resistance? How is it related to thermal contact conductance?
> Consider a house whose walls are 12 ft high and 40 ft long. Two of the walls of the house have no windows, while each of the other two walls has four windows made of 0.25-in-thick glass (k = 0.45 /Btuâ‹…hâ‹…ftâ‹
> Consider a house that has a 10-m × 20-m base and a 4-m-high wall. All four walls of the house have an R-value of 2.31 m2⋅°C/W. The two 10-m × 4-m walls have no windows. The third wall has five windows made of 0.5-cm-thick glass (k = 0.78 W/m⋅K), 1.2 m ×
> A 0.05-in-thick copper plate (k = 223 Btu/h⋅ft⋅°F) is sandwiched between two 0.15-in-thick epoxy boards (k = 0.15 Btu/h⋅ft⋅°F) that are 7 in × 9 in
> Heat is to be conducted along a circuit board that has a copper layer on one side. The circuit board is 15 cm long and 15 cm wide, and the thicknesses of the copper and epoxy layers are 0.1 mm and 1.2 mm, respectively. Disregarding heat transfer from sid
> Reconsider Prob. 17–31. Using appropriate software, investigate the effects of the thermal conductivities of the insulation material and the sheet metal on the thickness of the insulation. Let the thermal conductivity vary from 0.02 W/m
> The wall of a refrigerator is constructed of fiberglass insulation (k = 0.035 W/m⋅K) sandwiched between two layers of 1-mm-thick sheet metal (k = 15.1 W/m⋅K). The refrigerated space is maintained at 2°C, and
> A 2-m × 1.5-m section of wall of an industrial furnace burning natural gas is not insulated, and the temperature at the outer surface of this section is measured to be 110°C. The temperature of the furnace room is 32°C, and the combined convection and ra
> A 7-hp (shaft) pump is used to raise water to an elevation of 15 m. If the mechanical efficiency of the pump is 82 percent, determine the maximum volume flow rate of water.
> What does the thermal resistance of a medium represent?
> The roof of a house consists of a 15-cm-thick concrete slab (k = 2 W/mâ‹…K) that is 15 m wide and 20 m long. The convection heat transfer coefficients on the inner and outer surfaces of the roof are 5 and 12 W/m2â‹…K, resp
> 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 with thickness of 5 mm and thermal conductivity of 1.4 W/mâ‹…K. The
> A transparent film is to be bonded onto the top surface of a solid plate inside a heated chamber. For the bond to cure properly, a temperature of 70°C is to be maintained at the bond, between the film and the solid plate. The transparent film
> To defog the rear window of an automobile, a very thin transparent heating element is attached to the inner surface of the window. A uniform heat flux of 1300 W/m2 is provided to the heating element for defogging a rear window with thickness of 5 mm. The
> A wall is constructed of two layers of 0.6-in-thick sheetrock (k = 0.10 Btu/h⋅ft⋅°F), which is a plasterboard made of two layers of heavy paper separated by a layer of gypsum, placed 7 in apart. The space be
> Reconsider Prob. 17–22. Using appropriate software, plot the rate of heat transfer through the window as a function of the width of airspace in the range of 2 mm to 20 mm, assuming pure conduction through the air. Discuss the results.
> Repeat Prob. 17–22, assuming the space between the two glass layers is evacuated. Data from Prob. 17-22: Consider a 1.5-m-high and 2.4-m-wide double pane window consisting of two 3-mm-thick layers of glass (k = 0.78 W/mâ‹
> Consider a 1.5-m-high and 2.4-m-wide double pane window consisting of two 3-mm-thick layers of glass (k = 0.78 W/mâ‹…K) separated by a 12-mm-wide stagnant airspace (k = 0.026 W/mâ‹…K). Determine the steady rate of heat tra
> Consider a 1.5-m-high and 2.4-m-wide glass window whose thickness is 6 mm and thermal conductivity is k = 0.78 W/m⋅K. Determine the steady rate of heat transfer through this glass window and the temperature of its inner surface for a day during which the
> The water in a large lake is to be used to generate electricity by the installation of a hydraulic turbine–generator at a location where the depth of the water is 50 m. Water is to be supplied at a rate of 5000 kg/s. If the electric power generated is me
> A 2-kg rock is thrown upward with a force of 200 N at a location where the local gravitational acceleration is 9.79 m/s2. Determine the acceleration of the rock, in m/s2.
> Consider a power transistor that dissipates 0.15 W of power in an environment at 30°C. The transistor is 0.4 cm long and has a diameter of 0.5 cm. Assuming heat to be transferred uniformly from all surfaces, determine (a) the amount of heat th
> Consider heat conduction through a plane wall. Does the energy content of the wall change during steady heat conduction? How about during transient conduction? Explain.
> A cylindrical resistor element on a circuit board dissipates 0.15 W of power in an environment at 35°C. The resistor is 1.2 cm long and has a diameter of 0.3 cm. Assuming heat to be transferred uniformly from all surfaces, determine (a) the amount of hea
> Water is boiling in a 25-cm-diameter aluminum pan (k = 237 W/m⋅K) at 95°C. Heat is transferred steadily to the boiling water in the pan through its 0.5-cm-thick flat bottom at a rate of 800 W. If the inner surface temperature of the bottom of the pan is
> A 12-cm × 18-cm circuit board houses on its surface 100 closely spaced logic chips, each dissipating 0.06 W in an environment at 40°C. The heat transfer from the back surface of the board is negligible. If the heat transfer coefficient on the surface of
> Consider an electrically heated brick house (k = 0.40 Btu/h⋅ft⋅°F) whose walls are 9 ft high and 1 ft thick. Two of the walls of the house are 50 ft long and the others are 35 ft long. The house is maintaine
> Consider a person standing in a room at 20°C with an exposed surface area of 1.7 m2. The deep body temperature of the human body is 37°C, and the thermal conductivity of the human tissue near the skin is about 0.3 W/m⋅K. The body is losing heat at a rate
> Consider a 3-m-high, 6-m-wide, and 0.25-m-thick brick wall whose thermal conductivity is k = 0.8 W/m⋅K. On a certain day, the temperatures of the inner and the outer surfaces of the wall are measured to be 14°C and 5°C, respectively. Determine the rate o
> A 0.2-cm-thick, 10-cm-high, and 15-cm-long circuit board houses electronic components on one side that dissipate a total of 15 W of heat uniformly. The board is impregnated with conducting metal fillings and has an effective thermal conductivity of 12 W/
