Question: Reconsider Prob. 17–31. Using appropriate software,

> 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

> 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 tr

> 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

> 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‹&#1

> 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/

> Steam in a heating system flows through tubes whose outer diameter is 3 cm and whose walls are maintained at a temperature of 120°C. Circular aluminum alloy fins (k = 180 W/m⋅K) of outer diameter 6 cm and constant thickness t

> A room is cooled by circulating chilled water through a heat exchanger located in the room. The air is circulated through the heat exchanger by a 0.25-hp (shaft output) fan. Typical efficiency of small electric motors driving 0.25-hp equipment is 60 perc

> A plane wall surface at 200°C is to be cooled with aluminum pin fins of parabolic profile with blunt tips. Each fin has a length of 25 mm and a base diameter of 4 mm. The fins are exposed to ambient air at 25°C, and the heat transfer coefficient is 45 W/

> A plane wall with surface temperature of 300°C is attached with straight aluminum triangular fins (k = 236 W/m⋅K). The fins are exposed to an ambient air condition of 25°C, and the convection heat transfer coeffici

> A total of 10 rectangular aluminum fins (k = 203 W/m⋅K) are placed on the outside flat surface of an electronic device. Each fin is 100 mm wide, 20 mm high, and 4 mm thick. The fins are located parallel to each other at a center-to-center distance of 8 m

> Circular fins of uniform cross section, with diameter of 10 mm and length of 50 mm, are attached to a wall with surface temperature of 350°C. The fins are made of material with thermal conductivity of 240 W/m⋅K, they are expo

> A 12-cm-long bar with a square cross section, as shown in Fig. P17–133, consists of a 1-cm-thick copper layer (k = 380W/m⋅K) and a 1-cm-thick epoxy composite layer (k = 0.4 W/m⋅K). Calculate the rate

> A typical section of a building wall is shown in Fig. P17–132. 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 suppo

> A 4-m-high and 6-m-long wall is constructed of two large 0.8-cm-thick steel plates (k = 15 W/mâ‹…K) separated by 1-cm thick and 22-cm-wide steel bars placed 99 cm apart. The remaining space between the steel plates is filled with fibergla

> One wall of a refrigerated warehouse is 10.0 m high and 5.0 m wide. The wall is made of three layers: 1.0-cm-thick aluminum (k = 200W/m⋅K), 8.0-cm thick fiberglass (k = 0.038W/m⋅K), and 3.0-cm-thick gypsum board (k = 0.48 W/m⋅K). The warehouse inside and

> Consider a window glass consisting of two 4-mm thick glass sheets pressed tightly against each other. Compare the heat transfer rate through this window with that of one consisting of a single 8-mm-thick glass sheet under identical conditions.

> A spherical vessel, 3.0 m in diameter (and negligible wall thickness), is used for storing a fluid at a temperature of 0°C. The vessel is covered with a 5.0-cm-thick layer of an insulation (k = 0.20 W/m⋅K). The surrounding air is at 22°C. The inside and

> An exercise room has six weight-lifting machines that have no motors and seven treadmills each equipped with a 2.5-hp (shaft output) motor. The motors operate at an average load factor of 0.7, at which their efficiency is 0.77. During peak evening hours,

> Steam at 260°C is flowing inside a steel pipe (k = 61 W/m⋅K) whose inner and outer diameters are 10 cm and 12 cm, respectively, in an environment at 20°C. The heat transfer coefficients inside and outside the pipe are 120 W/m2⋅K and 14 W/m2⋅K, respective

> The plumbing system of a house involves a 0.5-m section of a plastic pipe (k = 0.16 W/mâ‹…K) of inner diameter 2 cm and outer diameter 2.4 cm exposed to the ambient air. During a cold and windy night, the ambient air temperature remains a

> Hot water is flowing at an average velocity of 1.5 m/s through a cast iron pipe (k = 52 W/m⋅K) whose inner and outer diameters are 3 cm and 3.5 cm, respectively. The pipe passes through a 15 m-long section of a basement whose temperature is 15°C. If the

> Cold conditioned air at 12°C is flowing inside a 1.5-cm-thick square aluminum (k = 237 W/m⋅K) duct of inner cross section 22 cm × 22 cm at a mass flow rate of 0.8 kg/s. The duct is exposed to air at 33°C with a combined convection radiation heat transfer

> Consider two identical people each generating 60 W of metabolic heat steadily while doing sedentary work and dissipating it by convection and perspiration. The first person is wearing clothes made of 1-mm-thick leather (k = 0.159 W/m⋅K) that covers half

> A 40-W power transistor is to be cooled by attaching it to one of the commercially available heat sinks shown in Table 17–6. Select a heat sink that will allow the case temperature of the transistor not to exceed 90°C in the

> Reconsider Prob. 17–121. Using appropriate software, investigate the effect of the center-to center distance of the fins on the rate of heat transfer from the surface and the overall effectiveness of the fins. Let the center-to center d

> A hot surface at 100°C is to be cooled by attaching 3-cm-long, 0.25-cm-diameter aluminum pin fins (k = 237 W/m⋅K) to it, with a center-to-center distance of 0.6 cm. The temperature of the surrounding medium is 30°C

> A 0.4-cm-thick, 12-cm-high, and 18-cm-long circuit board houses 80 closely spaced logic chips on one side, each dissipating 0.04 W. The board is impregnated with copper fillings and has an effective thermal conductivity of 30 W/m⋅K. All the heat generate

> Consider steady one-dimensional heat transfer through a multilayer medium. If the rate of heat transfer Q is known, explain how you would determine the temperature drop across each layer.

> A 75-hp (shaft output) motor that has an efficiency of 91.0 percent is worn out and is replaced by a high-efficiency 75-hp motor that has an efficiency of 95.4 percent. Determine the reduction in the heat gain of the room due to higher efficiency under f

> Steam in a heating system flows through tubes whose outer diameter is 5 cm and whose walls are maintained at a temperature of 130°C. Circular aluminum alloy 2024-T6 fins (k = 186 W/m⋅K) of outer diameter 6 cm and constant thi

> Pipes with inner and outer diameters of 50 mm and 60 mm, respectively, are used for transporting superheated vapor in a manufacturing plant. The pipes with thermal conductivity of 16 W/mâ‹…K are connected together by flanges with combined

> A plane wall with surface temperature of 350°C is attached with straight rectangular fins (k = 235 W/m⋅K). The fins are exposed to an ambient air condition of 25°C, and the convection heat transfer coefficient is 1