Question: Consider two cold canned drinks, one wrapped

> 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

> A DC motor delivers mechanical power to a rotating stainless steel shaft (k = 15.1 W/m⋅K) with a length of 25 cm and a diameter of 25 mm. In a surrounding with ambient air temperature of 20°C and convection heat transfer coef

> Reconsider Prob. 17–114E. Using appropriate software, investigate the effects of the thermal conductivity of the spoon material and the length of its extension in the air on the temperature difference across the exposed surface of the s

> Consider a stainless steel spoon (k = 8.7 Btu/hâ‹…ft⋅°F)partially immersed in boiling water at 200°F in a kitchen at 75°F. The handle of the spoon has a cross section of 0.08 in Ã&

> A turbine blade made of a metal alloy (k = 17 W/m⋅K) has a length of 5.3 cm, a perimeter of 11 cm, and a cross sectional area of 5.13 cm2. The turbine blade is exposed to hot gas from the combustion chamber at 973°C with a co

> Two very long, slender rods of the same diameter and length are given. One rod (Rod 1) is made of aluminum and has a thermal conductivity k1 = 200 W/mâ‹…K, but the thermal conductivity of Rod 2, k2, is not known. To determine the thermal

> Consider a very long, slender rod. One end of the rod is attached to a base surface maintained at Tb, while the surface of the rod is exposed to an air temperature of 400°C. Thermocouples imbedded in the rod at locations 25 and 120 mm from the

> Consider a very long rectangular fin attached to a flat surface such that the temperature at the end of the fin is essentially that of the surrounding air, i.e., 20°C. Its width is 5.0 cm; thickness is 1.0 mm; thermal conductivity is 200 W/m⋅K; and base

> Reconsider Prob. 3–52E. Using appropriate software, study the effects of the unit cost of energy, the new combustion efficiency on the annual energy, and cost savings. Let the efficiency vary from 0.7 to 0.9, and let the unit cost vary from $12 to $14 pe

> Consider a surface of area A at which the convection and radiation heat transfer coefficients are hconv and hrad, respectively. Explain how you would determine (a) the single equivalent heat transfer coefficient, and (b) the equivalent thermal resistance

> A 4-mm-diameter and 10-cm-long aluminum fin (k = 237 W/mâ‹…K) is attached to a surface. If the heat transfer coefficient is 12 W/m2â‹…K, determine the percent error in the rate of heat transfer from the fin when the infini

> Obtain a relation for the fin efficiency for a fin of constant cross-sectional area Ac, perimeter p, length L, and thermal conductivity k exposed to convection to a medium at T∞ with a heat transfer coefficient h. Assume the fins are sufficiently long so

> Two finned surfaces are identical, except that the convection heat transfer coefficient of one of them is twice that of the other. For which finned surface is the (a) fin effectiveness and (b) fin efficiency higher? Explain.

> Two plate fins of constant rectangular cross section are identical, except that the thickness of one of them is twice the thickness of the other. For which fin is the (a) fin effectiveness and (b) fin efficiency higher? Explain.

> Two pin fins are identical, except that the diameter of one of them is twice the diameter of the other. For which fin is the (a) fin effectiveness and (b) fin efficiency higher? Explain.

> Does the (a) efficiency and (b) effectiveness of a fin increase or decrease as the fin length is increased?

> The heat transfer surface area of a fin is equal to the sum of all surfaces of the fin exposed to the surrounding medium, including the surface area of the fin tip. Under what conditions can we neglect heat transfer from the fin tip?

> Consider two finned surfaces that are identical except that the fins on the first surface are formed by casting or extrusion, whereas they are attached to the second surface afterwards by welding or tight fitting. For which case do you think the fins wil

> Hot water is to be cooled as it flows through the tubes exposed to atmospheric air. Fins are to be attached in order to enhance heat transfer. Would you recommend attaching the fins inside or outside the tubes? Why?

> The steam requirements of a manufacturing facility are being met by a boiler whose rated heat input is 5.5 × 106 Btu/h. The combustion efficiency of the boiler is measured to be 0.7 by a handheld flue gas analyzer. After tuning up the boiler, the combust

> How does the overall effectiveness of a finned surface differ from the effectiveness of a single fin?

> Consider heat conduction through a wall of thickness Land area A. Under what conditions will the temperature distributions in the wall be a straight line?

> Does any of the energy of the sun reach the earth by conduction or convection?

> How does heat conduction differ from convection?

> An electric heater with the total surface area of 0.25 m2 and emissivity 0.75 is in a room where the air has a temperature of 20°C and the walls are at 10°C. When the heater consumes 500 W of electric power, its surface has a steady

> Consider a flat-plate solar collector placed on the roof of a house. The temperatures at the inner and outer surfaces of the glass cover are measured to be 28°C and 25°C, respectively. The glass cover has a surface area of 2.5 m2, a thickness of 0.6 cm,

> A thin metal plate is insulated on the back and exposed to solar radiation on the front surface. The exposed surface of the plate has an absorptivity of 0.7 for solar radiation. If solar radiation is incident on the plate at a rate of 550 W/m2 and the su

> A soldering iron has a cylindrical tip of 2.5 mm in diameter and 20 mm in length. With age and usage, the tip has oxidized and has an emissivity of 0.80. Assuming that the average convection heat transfer coefficient over the soldering iron tip is 25 W/m

> Consider a 3-m × 3-m × 3-m cubical furnace whose top and side surfaces closely approximate black surfaces at a temperature of 1200 K. The base surface has an emissivity of ε = 0.7 and is maintained at 800 K. Determine the net rate of radiation heat trans

> Consider a 2.4-kW hooded electric open burner in an area where the unit costs of electricity and natural gas are $0.10/kWh and $1.20/therm (1 therm = 105,500 kJ), respectively. The efficiency of open burners can be taken to be 73 percent for electric bur

> Consider a person standing in a room maintained at 20°C at all times. The inner surfaces of the walls, floors, and ceiling of the house are observed to be at an average temperature of 12°C in winter and 23°C in summer. Determine the rates of radiation he

> A cylindrical fuel rod 2 cm in diameter is encased in a concentric tube and cooled by water. The fuel generates heat uniformly at a rate of 150 MW/m3. The convection heat transfer coefficient on the fuel rod is 5000 W/m2â‹…K, and the aver

> Consider an electrical wire submerged in liquid water at atmospheric conditions. The wire has a diameter of 1 mm and a length of 15 cm. The current through the wire is increased until the water reaches a temperature of 100°C. For this situatio

> An engine block with a surface area measured to be 0.95 m2 generates a power output of 50 kW with a net engine efficiency of 35 percent. The engine block operates inside a compartment at 157°C, and the average convection heat transfer coefficient is 50

> It is well known that wind makes the cold air feel much colder as a result of the wind-chill effect that is due to an increase in the convection heat transfer coefficient with increasing air velocity. The wind-chill effect is usually expressed in terms o

> Write down the expressions for the physical laws that govern each mode of heat transfer, and identify the variables involved in each relation.

> A 40-cm-long, 800-W electric resistance heating element with diameter 0.5 cm and surface temperature 120°C is immersed in 75 kg of water initially at 20°C. Determine how long it will take for this heater to raise the water temperature to 80°C. Also, dete

> A 0.3-cm-thick, 12-cm-high, and 18-cm-long circuit board houses 80 closely spaced logic chips on one side, each dissipating 0.06 W. The board is impregnated with copper fillings and has an effective thermal conductivity of 16 W/m·K. All the heat generate

> The heat generated in the circuitry on the surface of a silicon chip (k = 130 W/m⋅K) is conducted to the ceramic substrate to which it is attached. The chip is 6 mm × 6 mm in size and 0.5 mm thick and dissipates 3 W of powe

> A cylindrical resistor element on a circuit board dissipates 0.8 W of power. The resistor is 2 cm long and has a diameter of 0.4 cm. Assuming heat to be transferred uniformly from all surfaces, determine (a) the amount of heat this resistor dissipates du

> Can the combined turbine–generator efficiency be greater than either the turbine efficiency or the generator efficiency? Explain.

> The inner and outer surfaces of a 25-cm-thick wall in summer are at 27°C and 44°C, respectively. The outer surface of the wall exchanges heat by radiation with surrounding surfaces at 40°Cand by convection with ambient ai

> The roof of a house consists of a 15-cm-thick concrete slab (k = 2 W/m⋅K) that is 15 m wide and 20 m long. The emissivity of the outer surface of the roof is 0.9, and the convection heat transfer coefficient on that surface is estimated to be 15 W/m2⋅K.

> An AISI 304 stainless steel sheet is going through an annealing process inside an electrically heated oven. The ambient air inside the oven is 600°C, while the surrounding surfaces of the oven are at a uniform temperature of 750°C. If the emissivity of t

> Consider a flat-plate solar collector placed horizontally on the flat roof of a house. The collector is 5 ft wide and 15 ft long, and the average temperature of the exposed surface of the collector is 100°F. The emissivity of the exposed surfa

> A flat-plate solar collector is used to heat water by having water flow through tubes attached at the back of the thin solar absorber plate. The absorber plate has a surface area of 2 m2 with emissivity and absorptivity of 0.9. The surface temperature o

> Solar radiation is incident on a 5-m2 solar absorber plate surface at a rate of 800 W/m2. Ninety three percent of the solar radiation is absorbed by the absorber plate, while the remaining 7 percent is reflected away. The solar absorber plate has a surfa

> What are the mechanisms of heat transfer? How are they distinguished from each other?

> In the metal processing industry, heat treatment of metals is commonly done using electrically heated draw batch furnaces. Consider a furnace that is situated in a room with surrounding air temperature of 30°C and an average convection heat tr

> A 3-m-internal-diameter spherical tank made of 1-cm thick stainless steel is used to store iced water at 0°C. The tank is located outdoors at 25°C. Assuming the entire steel tank to be at 0°C and thus the thermal resistance of the tank to be negligible,

> A 1000-W iron is left on an ironing board with its base exposed to the air at 20°C. The convection heat transfer coefficient between the base surface and the surrounding air is 35 W/m2⋅K. If the base has an emissivity of 0.6

> What is mechanical energy? How does it differ from thermal energy? What are the forms of mechanical energy of a fluid stream?

> A 2-in-diameter spherical ball whose surface is maintained at a temperature of 170°F is suspended in the middle of a room at 70°F. If the convection heat transfer coefficient is 15 Btu/h⋅ft2⋅°F and the emissivity of the surface is 0.8, determine the tota

> Consider a person standing in a room at 23°C. Determine the total rate of heat transfer from this person if the exposed surface area and the skin temperature of the person are 1.7 m2 and 32°C, respectively, and the convection heat transfer coefficient is

> Consider steady heat transfer between two large parallel plates at constant temperatures of T1 = 290 K and T2 = 150 K that are L = 2 cm apart. Assuming the surfaces to be black (emissivity ε = 1), determine the rate of heat transfer between the plates pe

> An electronic package with a surface area of 1 m2 placed in an orbiting space station is exposed to space. The electronics in this package dissipate all 1 kW of its power to the space through its exposed surface. The exposed surface has an emissivity of

> Air at 20°C with a convection heat transfer coefficient of 25 W/m2⋅K blows over a horizontal steel hot plate (k = 43W/m⋅K). The surface area of the plate is 0.38 m2 with a thickness of 2 cm. The plate surfac

> A solid plate, with a thickness of 15 cm and a thermal conductivity of 80 W/m⋅K, is being cooled at the upper surface by air. The air temperature is 10°C, while the temperatures at the upper and lower surfaces of the plate ar

> Consider a 20-cm-thick granite wall with a thermal conductivity of 2.79 W/m⋅K. The temperature of the left surface is held constant at 50°C, whereas the right face is exposed to a flow of 22°C air with a convection

> Why do we characterize the heat conduction ability of insulators in terms of their apparent thermal conductivity instead of their ordinary thermal conductivity?

> We often turn the fan on in summer to help us cool. Explain how a fan makes us feel cooler in the summer. Also explain why some people use ceiling fans also in winter.

> The deep human body temperature of a healthy person remains constant at 37°C while the temperature and the humidity of the environment change with time. Discuss the heat transfer mechanisms between the human body and the environment in both summer and wi

> How is the combined pump–motor efficiency of a pump and motor system defined? Can the combined pump–motor efficiency be greater than either the pump or the motor efficiency?

> Can a medium involve (a) conduction and convection, (b) conduction and radiation, or (c) convection and radiation simultaneously? Give examples for the “yes” answers.

> Can all three modes of heat transfer occur simultaneously (in parallel) in a medium?

> An electronic package in the shape of a sphere with an outer diameter of 100 mm is placed in a large laboratory room. The surface emissivity of the package can assume three different values (0.2, 0.25, and 0.3). The walls of the room are maintained at a

> A spherical interplanetary probe with a diameter of 2 m is sent out into the solar system. The probe surface is made of material having an emissivity of 0.9 and an absorptivity of 0.1. Signals from the sensors monitoring the probe surface temperatures ar

> Two surfaces, one highly polished and the other heavily oxidized, are found to be emitting the same amount of energy per unit area. The highly polished surface has an emissivity of 0.1 at 1070°C, while the emissivity of the heavily oxidized surface is 0.

> Consider a sealed 20-cm-high electronic box whose base dimensions are 40 cm × 40 cm placed in a vacuum chamber. The emissivity of the outer surface of the box is 0.95. If the electronic components in the box dissipate a total of 100 W of pow

> Consider a person whose exposed surface area is 1.7 m2, emissivity is 0.5, and surface temperature is 32°C. Determine the rate of heat loss from that person by radiation in a large room having walls at a temperature of (a) 300 K and (b) 280 K.

> The outer surface of a spacecraft in space has an emissivity of 0.8 and a solar absorptivity of 0.3. If solar radiation is incident on the spacecraft at a rate of 950 W/m2, determine the surface temperature of the spacecraft when the radiation emitted eq

> Why is the thermal conductivity of superinsulation orders of magnitude lower than the thermal conductivity of ordinary insulation?