Introduction To Thermodynamics and Heat Transfer

Yunus A. Cengel

Chapter 14 Natural Convection - all with Video Answers

Educators

Chapter Questions

Problem 1

What is natural convection? How does it differ from forced convection? What force causes natural convection currents?

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Problem 2

In which mode of heat transfer is the convection heat transfer coefficient usually higher, natural convection or forced convection? Why?

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02:15

Consider a hot boiled egg in a spacecraft that is filled with air at atmospheric pressure and temperature at all times. Will the egg cool faster or slower when the spacecraft is in space instead of on the ground? Explain.

Yaqub Khan

Numerade Educator

02:12

Problem 4

What is buoyancy force? Compare the relative magnitudes of the buoyancy force acting on a body immersed in these mediums: (a) air, (b) water, (c) mercury, and (d) an evacuated chamber.

Baskar P

Numerade Educator

00:48

Problem 5

When will the hull of a ship sink in water deeper: when the ship is sailing in fresh water or in seawater? Why?

Surjit Tewari

Numerade Educator

03:21

Problem 6

A person weighs himself on a waterproof spring scale placed at the bottom of a 1-m-deep swimming pool. Will the person weigh more or less in water? Why?

Prabhu Ramji

Numerade Educator

Problem 7

Consider two fluids, one with a large coefficient of volume expansion and the other with a small one. In what fluid will a hot surface initiate stronger natural convection currents? Why? Assume the viscosity of the fluids to be the same.

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Problem 8

Consider a fluid whose volume does not change with temperature at constant pressure. What can you say about natural convection heat transfer in this medium?

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02:54

Problem 9

What do the lines on an interferometer photograph represent? What do closely packed lines on the same photograph represent?

Ben Nicholson

Numerade Educator

01:17

Problem 10

Physically, what does the Grashof number represent? How does the Grashof number differ from the Reynolds number?

Penny Riley

Numerade Educator

04:45

Problem 11

Show that the volume expansion coefficient of an ideal gas is $\beta=1 / T$, where $T$ is the absolute temperature.

João Gabriel Alencar Caribé

Numerade Educator

01:58

Problem 12

How does the Rayleigh number differ from the Grashof number?

Narayan Hari

Numerade Educator

Problem 13

Under what conditions can the outer surface of a vertical cylinder be treated as a vertical plate in natural convection calculations?

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01:17

Problem 14

Will a hot horizontal plate whose back side is insulated cool faster or slower when its hot surface is facing down instead of up?

Evan Schroeder

Numerade Educator

Problem 15

Consider laminar natural convection from a vertical hot-plate. Will the heat flux be higher at the top or at the bottom of the plate? Why?

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Problem 16

Consider a thin $16-\mathrm{cm}$-long and $20-\mathrm{cm}$-wide horizontal plate suspended in air at $20^{\circ} \mathrm{C}$. The plate is equipped with electric resistance heating elements with a rating of 20 W . Now the heater is turned on and the plate temperature rises. Determine the temperature of the plate when steady operating conditions are reached. The plate has an emissivity of 0.90 and the surrounding surfaces are at $17^{\circ} \mathrm{C}$.

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Problem 17

Flue gases from an incinerator are released to atmosphere using a stack that is 0.6 m in diameter and 10.0 m high. The outer surface of the stack is at $40^{\circ} \mathrm{C}$ and the surrounding air is at $10^{\circ} \mathrm{C}$. Determine the rate of heat transfer from the stack assuming (a) there is no wind and $(b)$ the stack is exposed to $20 \mathrm{~km} / \mathrm{h}$ winds.

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Problem 18

Thermal energy generated by the electrical resistance of a $5-\mathrm{mm}$-diameter and $4-\mathrm{m}$-long bare cable is dissipated to the surrounding air at $20^{\circ} \mathrm{C}$. The voltage drop and the electric current across the cable in steady operation are measured to be 60 V and 1.5 A , respectively. Disregarding radiation, estimate the surface temperature of the cable.

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Problem 19

A 10 -m-long section of a 6-cm-diameter horizontal hot-water pipe passes through a large room whose temperature is $27^{\circ} \mathrm{C}$. If the temperature and the emissivity of the outer surface of the pipe are $73^{\circ} \mathrm{C}$ and 0.8 , respectively, determine the rate of heat loss from the pipe by (a) natural convection and (b) radiation.

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03:02

Problem 20

Consider a wall-mounted power transistor that dissipates 0.18 W of power in an environment at $35^{\circ} \mathrm{C}$. The transistor is 0.45 cm long and has a diameter of 0.4 cm . The emissivity of the outer surface of the transistor is 0.1 , and the average temperature of the surrounding surfaces is $25^{\circ} \mathrm{C}$. Disregarding any heat transfer from the base surface, determine the surface temperature of the transistor. Use air properties at $100^{\circ} \mathrm{C}$.

Shahab Ullah

Numerade Educator

03:02

Problem 21

Reconsider Prob. 14-20. Using EES (or other) software, investigate the effect of ambient temperature on the surface temperature of the transistor. Let the environment temperature vary from $10^{\circ} \mathrm{C}$ to $40^{\circ} \mathrm{C}$ and assume that the surrounding surfaces are $10^{\circ} \mathrm{C}$ colder than the environment temperature. Plot the surface temperature of the transistor versus the environment temperature, and discuss the results.

Jincy M Saji

Numerade Educator

Problem 22

Consider a $2-\mathrm{ft} \times 2$-ft thin square plate in a room at $75^{\circ} \mathrm{F}$. One side of the plate is maintained at a temperature of $130^{\circ} \mathrm{F}$, while the other side is insulated. Determine the rate of heat transfer from the plate by natural convection if the plate is (a) vertical; (b) horizontal with hot surface facing up; and (c) horizontal with hot surface facing down.

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05:52

Problem 23

Reconsider Prob. 14-22E. Using EES (or other) software, plot the rate of natural convection heat transfer for different orientations of the plate as a function of the plate temperature as the temperature varies from $80^{\circ} \mathrm{F}$ to $180^{\circ} \mathrm{F}$, and discuss the results.

Bret Rosen

Numerade Educator

Problem 24

A $300-\mathrm{W}$ cylindrical resistance heater is 0.75 m long and 0.5 cm in diameter. The resistance wire is placed horizontally in a fluid at $20^{\circ} \mathrm{C}$. Determine the outer surface temperature of the resistance wire in steady operation if the fluid is (a) air and (b) water. Ignore any heat transfer by radiation. Use properties at $500^{\circ} \mathrm{C}$ for air and $40^{\circ} \mathrm{C}$ for water.

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Problem 25

Water is boiling in a 12-cm-deep pan with an outer diameter of 25 cm that is placed on top of a stove. The ambient air and the surrounding surfaces are at a temperature of $25^{\circ} \mathrm{C}$, and the emissivity of the outer surface of the pan is 0.80 . Assuming the entire pan to be at an average temperature of $98^{\circ} \mathrm{C}$, determine the rate of heat loss from the cylindrical side surface of the pan to the surroundings by (a) natural convection and (b) radiation. (c) If water is boiling at a rate of $1.5 \mathrm{~kg} / \mathrm{h}$ at $100^{\circ} \mathrm{C}$, determine the ratio of the heat lost from the side surfaces of the pan to that by the evaporation of water. The enthalpy of vaporization of water at $100^{\circ} \mathrm{C}$ is $2257 \mathrm{~kJ} / \mathrm{kg}$.

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Problem 26

Repeat Prob. 14-25 for a pan whose outer surface is polished and has an emissivity of 0.1 .

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Problem 27

In a plant that manufactures canned aerosol paints, the cans are temperature-tested in water baths at $55^{\circ} \mathrm{C}$ before they are shipped to ensure that they withstand temperatures up to $55^{\circ} \mathrm{C}$ during transportation and shelving. The cans, moving on a conveyor, enter the open hot water bath, which is 0.5 m deep, 1 m wide, and 3.5 m long, and move slowly in the hot water toward the other end. Some of the cans fail the test and explode in the water bath. The water container is made of sheet metal, and the entire container is at about the same temperature as the hot water. The emissivity of the outer surface of the container is 0.7 . If the temperature of the surrounding air and surfaces is $20^{\circ} \mathrm{C}$, determine the rate of heat loss from the four side surfaces of the container (disregard the top surface, which is open).

The water is heated electrically by resistance heaters, and the cost of electricity is $\$ 0.085 / \mathrm{kWh}$. If the plant operates 24 h a day 365 days a year and thus 8760 h a year, determine the annual cost of the heat losses from the container for this facility.

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Problem 28

Reconsider Prob. 14-27. In order to reduce the heating cost of the hot water, it is proposed to insulate the side and bottom surfaces of the container with 5 -cm-thick fiberglass insulation ( $\left.k=0.035 \mathrm{~W} / \mathrm{m} \cdot{ }^{\circ} \mathrm{C}\right)$ and to wrap the insulation with aluminum foil ( $\varepsilon=0.1$ ) in order to minimize the heat loss by radiation. An estimate is obtained from a local insulation contractor, who proposes to do the insulation job for $\$ 350$, including materials and labor. Would you support this proposal? How long will it take for the insulation to pay for itself from the energy it saves?

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Problem 29

Consider a $15-\mathrm{cm} \times 20-\mathrm{cm}$ printed circuit board (PCB) that has electronic components on one side. The board is placed in a room at $20^{\circ} \mathrm{C}$. The heat loss from the back surface of the board is negligible. If the circuit board is dissipating 8 W of power in steady operation, determine the average temperature of the hot surface of the board, assuming the board is (a) vertical; (b) horizontal with hot surface facing up; and (c) horizontal with hot surface facing down. Take the emissivity of the surface of the board to be 0.8 and assume the surrounding surfaces to be at the same temperature as the air in the room.

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Problem 30

Reconsider Prob. 14-29. Using EES (or other) software, investigate the effects of the room temperature and the emissivity of the board on the temperature of the hot surface of the board for different orientations of the board. Let the room temperature vary from $5^{\circ} \mathrm{C}$ to $35^{\circ} \mathrm{C}$ and the emissivity from 0.1 to 1.0 . Plot the hot surface temperature for different orientations of the board as the functions of the room temperature and the emissivity, and discuss the results.

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01:31

Problem 31

A manufacturer makes absorber plates that are $1.2 \mathrm{~m} \times 0.8 \mathrm{~m}$ in size for use in solar collectors. The back side of the plate is heavily insulated, while its front surface is coated with black chrome, which has an absorptivity of 0.87 for solar radiation and an emissivity of 0.09 . Consider such a plate placed horizontally outdoors in calm air at $25^{\circ} \mathrm{C}$. Solar radiation is incident on the plate at a rate of $700 \mathrm{~W} / \mathrm{m}^2$. Taking the effective sky temperature to be $10^{\circ} \mathrm{C}$, determine the equilibrium temperature of the absorber plate. What would your answer be if the absorber plate is made of ordinary aluminum plate that has a solar absorptivity of 0.28 and an emissivity of 0.07 ?

Mayukh Banik

Numerade Educator

Problem 32

Repeat Prob. 14-31 for an aluminum plate painted flat black (solar absorptivity 0.98 and emissivity 0.98 ) and also for a plate painted white (solar absorptivity 0.26 and emissivity 0.90 ).

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Problem 33

The following experiment is conducted to determine the natural convection heat transfer coefficient for a horizontal cylinder that is 80 cm long and 2 cm in diameter. A $80-\mathrm{cm}$ long resistance heater is placed along the centerline of the cylinder, and the surfaces of the cylinder are polished to minimize the radiation effect. The two circular side surfaces of the cylinder are well insulated. The resistance heater is turned on, and the power dissipation is maintained constant at 60 W . If the average surface temperature of the cylinder is measured to be $120^{\circ} \mathrm{C}$ in the $20^{\circ} \mathrm{C}$ room air when steady operation is reached, determine the natural convection heat transfer coefficient. If the emissivity of the outer surface of the cylinder is 0.1 and a 5 percent error is acceptable, do you think we need to do any correction for the radiation effect? Assume the surrounding surfaces to be at $20^{\circ} \mathrm{C}$ also.

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Problem 34

Thick fluids such as asphalt and waxes and the pipes in which they flow are often heated in order to reduce the viscosity of the fluids and thus to reduce the pumping costs. Consider the flow of such a fluid through a $100-\mathrm{m}$-long pipe of outer diameter 30 cm in calm ambient air at $0^{\circ} \mathrm{C}$. The pipe is heated electrically, and a thermostat keeps the outer surface temperature of the pipe constant at $25^{\circ} \mathrm{C}$. The emissivity of the outer surface of the pipe is 0.8 , and the effective sky temperature is $-30^{\circ} \mathrm{C}$. Determine the power rating of the electric resistance heater, in kW, that needs to be used. Also, determine the cost of electricity associated with heating the pipe during a 10 -h period under the above conditions if the price of electricity is $\$ 0.09 / \mathrm{kWh}$.

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Problem 35

Reconsider Prob. 14-34. To reduce the heating cost of the pipe, it is proposed to insulate it with sufficiently thick fiberglass insulation ( $k=0.035 \mathrm{~W} / \mathrm{m} \cdot{ }^{\circ} \mathrm{C}$ ) wrapped with aluminum foil $(\varepsilon=0.1)$ to cut down the heat losses by 85 percent. Assuming the pipe temperature to remain constant at $25^{\circ} \mathrm{C}$, determine the thickness of the insulation that needs to be used. How much money will the insulation save during this 10 -h period?

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Problem 36

Consider an industrial furnace that resembles a 13 - ft -long horizontal cylindrical enclosure 8 ft in diameter whose end surfaces are well insulated. The furnace burns natural gas at a rate of 48 therms $/ \mathrm{h}$. The combustion efficiency of the furnace is 82 percent (i.e., 18 percent of the chemical energy of the fuel is lost through the flue gases as a result of incomplete combustion and the flue gases leaving the furnace at high temperature). If the heat loss from the outer surfaces of the furnace by natural convection and radiation is not to exceed 1 percent of the heat generated inside, determine the highest allowable surface temperature of the furnace. Assume the air and wall surface temperature of the room to be $75^{\circ} \mathrm{F}$, and take the emissivity of the outer surface of the furnace to be 0.85 . If the cost of natural gas is $$\$ 1.15 /$$ therm and the furnace operates 2800 h per year, determine the annual cost of this heat loss to the plant.

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Problem 37

Consider a 1.2-m-high and 2-m-wide glass window with a thickness of 6 mm , thermal conductivity $k=0.78 \mathrm{~W} / \mathrm{m} \cdot{ }^{\circ} \mathrm{C}$, and emissivity $\varepsilon=0.9$. The room and the walls that face the window are maintained at $25^{\circ} \mathrm{C}$, and the average temperature of the inner surface of the window is measured to be $5^{\circ} \mathrm{C}$. If the temperature of the outdoors is $-5^{\circ} \mathrm{C}$, determine (a) the convection heat transfer coefficient on the inner surface of the window, (b) the rate of total heat transfer through the window, and (c) the combined natural convection and radiation heat transfer coefficient on the outer surface of the window. Is it reasonable to neglect the thermal resistance of the glass in this case?

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Problem 38

A 3-mm-diameter and 12-m-long electric wire is tightly wrapped with a 1.5 -mm-thick plastic cover whose thermal conductivity and emissivity are $k=0.20 \mathrm{~W} / \mathrm{m} \cdot{ }^{\circ} \mathrm{C}$ and $\varepsilon=0.9$. Electrical measurements indicate that a current of 10 A passes through the wire and there is a voltage drop of 7 V along the wire. If the insulated wire is exposed to calm atmospheric air at $T_{\infty}=30^{\circ} \mathrm{C}$, determine the temperature at the interface of the wire and the plastic cover in steady operation. Take the surrounding surfaces to be at about the same temperature as the air.

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Problem 39

During a visit to a plastic sheeting plant, it was observed that a $60-\mathrm{m}$-long section of a 2 -in nominal ( $6.03-\mathrm{cm}$ -outer-diameter) steam pipe extended from one end of the plant to the other with no insulation on it. The temperature measurements at several locations revealed that the average temperature of the exposed surfaces of the steam pipe was $170^{\circ} \mathrm{C}$, while the temperature of the surrounding air was $20^{\circ} \mathrm{C}$. The outer surface of the pipe appeared to be oxidized, and its emissivity can be taken to be 0.7 . Taking the temperature of the surrounding surfaces to be $20^{\circ} \mathrm{C}$ also, determine the rate of heat loss from the steam pipe.

Steam is generated in a gas furnace that has an efficiency of 78 percent, and the plant pays $$\$ 1.10$$ per therm ( 1 therm $=105,500 \mathrm{~kJ}$ ) of natural gas. The plant operates 24 h a day 365 days a year, and thus 8760 h a year. Determine the annual cost of the heat losses from the steam pipe for this facility.

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03:58

Problem 40

Reconsider Prob. 14-39. Using EES (or other)
software, investigate the effect of the surface temperature of the steam pipe on the rate of heat loss from the pipe and the annual cost of this heat loss. Let the surface temperature vary from $100^{\circ} \mathrm{C}$ to $200^{\circ} \mathrm{C}$. Plot the rate of heat loss and the annual cost as a function of the surface temperature, and discuss the results.

Jincy M Saji

Numerade Educator

Problem 41

Reconsider Prob. 14-39. In order to reduce heat losses, it is proposed to insulate the steam pipe with $5-\mathrm{cm}$ thick fiberglass insulation ( $k=0.038 \mathrm{~W} / \mathrm{m} \cdot{ }^{\circ} \mathrm{C}$ ) and to wrap it with aluminum foil ( $\varepsilon=0.1$ ) in order to minimize the radiation losses. Also, an estimate is obtained from a local insulation contractor, who proposed to do the insulation job for $\$ 750$, including materials and labor. Would you support this proposal? How long will it take for the insulation to pay for itself from the energy it saves? Assume the temperature of the steam pipe to remain constant at $170^{\circ} \mathrm{C}$.

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01:27

Problem 42

A $50-\mathrm{cm} \times 50-\mathrm{cm}$ circuit board that contains 121 square chips on one side is to be cooled by combined natural convection and radiation by mounting it on a vertical surface in a room at $25^{\circ} \mathrm{C}$. Each chip dissipates 0.18 W of power, and the emissivity of the chip surfaces is 0.7 . Assuming the heat transfer from the back side of the circuit board to be negligible, and the temperature of the surrounding surfaces to be the same as the air temperature of the room, determine the surface temperature of the chips.

Mayukh Banik

Numerade Educator

01:55

Problem 43

Repeat Prob. 14-42 assuming the circuit board to be positioned horizontally with (a) chips facing up and (b) chips facing down.

Amit Srivastava

Numerade Educator

Problem 44

The side surfaces of a 2-m-high cubic industrial furnace burning natural gas are not insulated, and the temperature at the outer surface of this section is measured to be $110^{\circ} \mathrm{C}$. The temperature of the furnace room, including its surfaces, is $30^{\circ} \mathrm{C}$, and the emissivity of the outer surface of the furnace is 0.7 . It is proposed that this section of the furnace wall be insulated with glass wool insulation ( $k=$ $0.038 \mathrm{~W} / \mathrm{m}$ * ${ }^{\circ} \mathrm{C}$ ) wrapped by a reflective sheet ( $\varepsilon=0.2$ ) in order to reduce the heat loss by 90 percent. Assuming the outer surface temperature of the metal section still remains at about $110^{\circ} \mathrm{C}$, determine the thickness of the insulation that needs to be used.

The furnace operates continuously throughout the year and has an efficiency of 78 percent. The price of the natural gas is $$\$ 0.55 /$$ therm ( 1 therm $=105,500 \mathrm{~kJ}$ of energy content). If the installation of the insulation will cost $$\$ 550$$ for materials and labor, determine how long it will take for the insulation to pay for itself from the energy it saves.

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00:42

Problem 45

A $1.5-\mathrm{m}$-diameter, 4-m-long cylindrical propane tank is initially filled with liquid propane, whose density is $581 \mathrm{~kg} / \mathrm{m}^3$. The tank is exposed to the ambient air at $25^{\circ} \mathrm{C}$ in calm weather. The outer surface of the tank is polished so that the radiation heat transfer is negligible. Now a crack develops at the top of the tank, and the pressure inside drops to 1 atm while the temperature drops to $-42^{\circ} \mathrm{C}$, which is the boiling temperature of propane at 1 atm . The heat of vaporization of propane at 1 atm is $425 \mathrm{~kJ} / \mathrm{kg}$. The propane is slowly vaporized as a result of the heat transfer from the ambient air into the tank, and the propane vapor escapes the tank at $-42^{\circ} \mathrm{C}$ through the crack. Assuming the propane tank to be at about the same temperature as the propane inside at all times, determine how long it will take for the tank to empty if it is not insulated.

Mayukh Banik

Numerade Educator

02:58

Problem 46

An average person generates heat at a rate of $240 \mathrm{Btu} / \mathrm{h}$ while resting in a room at $70^{\circ} \mathrm{F}$. Assuming onequarter of this heat is lost from the head and taking the emissivity of the skin to be 0.9 , determine the average surface temperature of the head when it is not covered. The head can be approximated as a 12 -in-diameter sphere, and the interior surfaces of the room can be assumed to be at the room temperature.

Dading Chen

Numerade Educator

01:42

Problem 47

An incandescent lightbulb is an inexpensive but highly inefficient device that converts electrical energy into light. It converts about 10 percent of the electrical energy it consumes into light while converting the remaining 90 percent into heat. The glass bulb of the lamp heats up very quickly as a result of absorbing all that heat and dissipating it to the surroundings by convection and radiation. Consider an $8-\mathrm{cm}-$ diameter $60-\mathrm{W}$ lightbulb in a room at $25^{\circ} \mathrm{C}$. The emissivity of the glass is 0.9 . Assuming that 10 percent of the energy passes through the glass bulb as light with negligible absorption and the rest of the energy is absorbed and dissipated by the bulb itself by natural convection and radiation, determine the equilibrium temperature of the glass bulb. Assume the interior surfaces of the room to be at room temperature.

Ajay Singhal

Numerade Educator

Problem 48

A 40 -cm-diameter, $110-\mathrm{cm}$-high cylindrical hotwater tank is located in the bathroom of a house maintained at $20^{\circ} \mathrm{C}$. The surface temperature of the tank is measured to be $44^{\circ} \mathrm{C}$ and its emissivity is 0.4 . Taking the surrounding surface temperature to be also $20^{\circ} \mathrm{C}$, determine the rate of heat loss from all surfaces of the tank by natural convection and radiation.

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Problem 49

A $28-\mathrm{cm}$-high, 18 -cm-long, and $18-\mathrm{cm}$-wide rectangular container suspended in a room at $24^{\circ} \mathrm{C}$ is initially filled with cold water at $2^{\circ} \mathrm{C}$. The surface temperature of the container is observed to be nearly the same as the water temperature inside. The emissivity of the container surface is 0.6 , and the temperature of the surrounding surfaces is about the same as the air temperature. Determine the water temperature in the container after 3 h , and the average rate of heat transfer to the water. Assume the heat transfer coefficient on the top and bottom surfaces to be the same as that on the side surfaces.

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Problem 50

Reconsider Prob. 14-49. Using EES (or other) software, plot the water temperature in the container as a function of the heating time as the time varies from 30 min to 10 h , and discuss the results.

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01:51

Problem 51

A room is to be heated by a coal-burning stove, which is a cylindrical cavity with an outer diameter of 32 cm and a height of 70 cm . The rate of heat loss from the room is estimated to be 1.5 kW when the air temperature in the room is maintained constant at $24^{\circ} \mathrm{C}$. The emissivity of the stove surface is 0.85 and the average temperature of the surrounding wall surfaces is $14^{\circ} \mathrm{C}$. Determine the surface temperature of the stove. Neglect the transfer from the bottom surface and take the heat transfer coefficient at the top surface to be the same as that on the side surface.

The heating value of the coal is $30,000 \mathrm{~kJ} / \mathrm{kg}$, and the combustion efficiency is 65 percent. Determine the amount of coal burned a day if the stove operates 14 h a day.

Suzanne W.

Numerade Educator

04:15

Problem 52

The water in a 40-L tank is to be heated from $15^{\circ} \mathrm{C}$ to $45^{\circ} \mathrm{C}$ by a $6-\mathrm{cm}$-diameter spherical heater whose surface temperature is maintained at $85^{\circ} \mathrm{C}$. Determine how long the heater should be kept on.

Vipender Yadav

Numerade Educator

Problem 53

Why are finned surfaces frequently used in practice? Why are the finned surfaces referred to as heat sinks in the electronics industry?

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Problem 54

Why are heat sinks with closely packed fins not suitable for natural convection heat transfer, although they increase the heat transfer surface area more?

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03:30

Problem 55

Consider a heat sink with optimum fin spacing. Explain how heat transfer from this heat sink will be affected by (a) removing some of the fins on the heat sink and (b) doubling the number of fins on the heat sink by reducing the fin spacing. The base area of the heat sink remains unchanged at all times.

Anand Jangid

Numerade Educator

03:30

Problem 56

Aluminum heat sinks of rectangular profile are commonly used to cool electronic components. Consider a $7.62-\mathrm{cm}$-long and $9.68-\mathrm{cm}$-wide commercially available heat sink whose cross section and dimensions are as shown in Fig. P14-56. The heat sink is oriented vertically and is used to cool a power transistor that can dissipate up to 125 W of power. The back surface of the heat sink is insulated. The surfaces of the heat sink are untreated, and thus they have a low emissivity (under 0.1 ). Therefore, radiation heat transfer from the heat sink can be neglected. During an experiment conducted in room air at $22^{\circ} \mathrm{C}$, the base temperature of the heat sink was measured to be $120^{\circ} \mathrm{C}$ when the power dissipation of the transistor was 15 W . Assuming the entire heat sink to be at the base temperature, determine the average natural convection heat transfer coefficient for this case.

Anand Jangid

Numerade Educator

Problem 57

Reconsider the heat sink in Prob. 14-56. In order to enhance heat transfer, a shroud (a thin rectangular metal plate) whose surface area is equal to the base area of the heat sink is placed very close to the tips of the fins such that the interfin spaces are converted into rectangular channels. The base temperature of the heat sink in this case was measured to be $108^{\circ} \mathrm{C}$. Noting that the shroud loses heat to the ambient air from both sides, determine the average natural convection heat transfer coefficient in this shrouded case. (For complete details, see Çengel and Zing, 1987.)

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03:30

Problem 58

A 6 -in-wide and 8 -in-high vertical hot surface in $78^{\circ} \mathrm{F}$ air is to be cooled by a heat sink with equally spaced fins of rectangular profile. The fins are 0.08 in thick and 8 in long in the vertical direction and have a height of 1.2 in from the base. Determine the optimum fin spacing and the rate of heat transfer by natural convection from the heat sink if the base temperature is $180^{\circ} \mathrm{F}$.

Anand Jangid

Numerade Educator

Problem 59

Reconsider Prob. 14-58E. Using EES (or other) software, investigate the effect of the length of the fins in the vertical direction on the optimum fin spacing and the rate of heat transfer by natural convection. Let the fin length vary from 2 in to 10 in . Plot the optimum fin spacing and the rate of convection heat transfer as a function of the fin length, and discuss the results.

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03:30

Problem 60

A $15-\mathrm{cm}$-wide and 18 -cm-high vertical hot surface in $25^{\circ} \mathrm{C}$ air is to be cooled by a heat sink with equally spaced fins of rectangular profile. The fins are 0.1 cm thick and 18 cm long in the vertical direction. Determine the optimum fin height and the rate of heat transfer by natural convection from the heat sink if the base temperature is $85^{\circ} \mathrm{C}$.

The criteria for optimum fin height $H$ in the literature is given by $H=\sqrt{h A_c / p k}$. Take the thermal conductivity of fin material to be $177 \mathrm{~W} / \mathrm{m} \cdot{ }^{\circ} \mathrm{C}$

Natural Convection inside Enclosures

Anand Jangid

Numerade Educator

03:04

Problem 61

The upper and lower compartments of a wellinsulated container are separated by two parallel sheets of glass with an air space between them. One of the compartments is to be filled with a hot fluid and the other with a cold fluid. If it is desired that heat transfer between the two compartments be minimal, would you recommend putting the hot fluid into the upper or the lower compartment of the container? Why?

Prabhu Ramji

Numerade Educator

01:24

Problem 62

Someone claims that the air space in a double-pane window enhances the heat transfer from a house because of the natural convection currents that occur in the air space and recommends that the double-pane window be replaced by a single sheet of glass whose thickness is equal to the sum of the thicknesses of the two glasses of the double-pane window to save energy. Do you agree with this claim?

William Mead

Numerade Educator

01:24

Problem 63

Consider a double-pane window consisting of two glass sheets separated by a $1-\mathrm{cm}$-wide air space. Someone suggests inserting a thin vinyl sheet in the middle of the two glasses to form two $0.5-\mathrm{cm}$-wide compartments in the window in order to reduce natural convection heat transfer through the window. From a heat transfer point of view, would you be in favor of this idea to reduce heat losses through the window?

William Mead

Numerade Educator

Problem 64

What does the effective conductivity of an enclosure represent? How is the ratio of the effective conductivity to thermal conductivity related to the Nusselt number?

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Problem 65

Show that the thermal resistance of a rectangular enclosure can be expressed as $R=L_c /(A k \mathrm{Nu})$, where $k$ is the thermal conductivity of the fluid in the enclosure.

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Problem 66

Determine the $U$-factors for the center-of-glass section of a double-pane window and a triple-pane window. The heat transfer coefficients on the inside and outside surfaces are 6 and $25 \mathrm{~W} / \mathrm{m}^2 \cdot{ }^{\circ} \mathrm{C}$, respectively. The thickness of the air layer is 1.5 cm and there are two such air layers in triplepane window. The Nusselt number across an air layer is estimated to be 1.2. Take the thermal conductivity of air to be $0.025 \mathrm{~W} / \mathrm{m} \cdot{ }^{\circ} \mathrm{C}$ and neglect the thermal resistance of glass sheets. Also, assume that the effect of radiation through the air space is of the same magnitude as the convection.

Considering that about 70 percent of total heat transfer through a window is due to center-of-glass section, estimate the percentage decrease in total heat transfer when triplepane window is used in place of double-pane window.

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Problem 67

A vertical $1.5-\mathrm{m}$-high and $3.0-\mathrm{m}$-wide enclosure consists of two surfaces separated by a $0.4-\mathrm{m}$ air gap at atmospheric pressure. If the surface temperatures across the air gap are measured to be 280 K and 336 K and the surface emissivities to be 0.15 and 0.90 , determine the fraction of heat transferred through the enclosure by radiation.

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02:38

Problem 68

A vertical 4-ft-high and 6-ft-wide double-pane window consists of two sheets of glass separated by a 1-in air gap at atmospheric pressure. If the glass surface temperatures across the air gap are measured to be $65^{\circ} \mathrm{F}$ and $40^{\circ} \mathrm{F}$, determine the rate of heat transfer through the window by (a) natural convection and (b) radiation. Also, determine the $R$-value of insulation of this window such that multiplying the inverse of the $R$-value by the surface area and the temperature difference gives the total rate of heat transfer through the window. The effective emissivity for use in radiation calculations between two large parallel glass plates can be taken to be 0.82 .

Manish Jain

Numerade Educator

04:54

Problem 69

Reconsider Prob. 14-68E. Using EES (or other) software, investigate the effect of the air gap thickness on the rates of heat transfer by natural convection and radiation, and the $R$-value of insulation. Let the air gap thickness vary from 0.2 in to 2.0 in . Plot the rates of heat transfer by natural convection and radiation, and the $R$ value of insulation as a function of the air gap thickness, and discuss the results.

Bret Rosen

Numerade Educator

Problem 70

Two concentric spheres of diameters 15 cm and 25 cm are separated by air at 1 atm pressure. The surface temperatures of the two spheres enclosing the air are $T_1=350 \mathrm{~K}$ and $T_2=275 \mathrm{~K}$, respectively. Determine the rate of heat transfer from the inner sphere to the outer sphere by natural convection.

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Problem 71

Reconsider Prob. 14-70. Using EES (or other) software, plot the rate of natural convection heat transfer as a function of the hot surface temperature of the sphere as the temperature varies from 300 K to 500 K , and discuss the results.

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Problem 72

Flat-plate solar collectors are often tilted up toward the sun in order to intercept a greater amount of direct solar radiation. The tilt angle from the horizontal also affects the rate of heat loss from the collector. Consider a $1.5-\mathrm{m}$-high and 3 -m-wide solar collector that is tilted at an angle $\theta$ from the horizontal. The back side of the absorber is heavily insulated. The absorber plate and the glass cover, which are spaced 2.5 cm from each other, are maintained at temperatures of $80^{\circ} \mathrm{C}$ and $40^{\circ} \mathrm{C}$, respectively. Determine the rate of heat loss from the absorber plate by natural convection for $\theta=0^{\circ}, 30^{\circ}$, and $90^{\circ}$.

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Problem 73

A simple solar collector is built by placing a $5-\mathrm{cm}-$ diameter clear plastic tube around a garden hose whose outer diameter is 1.6 cm . The hose is painted black to maximize solar absorption, and some plastic rings are used to keep the spacing between the hose and the clear plastic cover constant. During a clear day, the temperature of the hose is measured to be $65^{\circ} \mathrm{C}$, while the ambient air temperature is $26^{\circ} \mathrm{C}$. Determine the rate of heat loss from the water in the hose per meter of its length by natural convection. Also, discuss how the performance of this solar collector can be improved.

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Problem 74

Reconsider Prob. 14-73. Using EES (or other) software, plot the rate of heat loss from the water by natural convection as a function of the ambient air temperature as the temperature varies from $4^{\circ} \mathrm{C}$ to $40^{\circ} \mathrm{C}$, and discuss the results.

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00:39

Problem 75

A vertical 1.3 -m-high, $2.8-\mathrm{m}$-wide double-pane window consists of two layers of glass separated by a $2.2-\mathrm{cm}$ air gap at atmospheric pressure. The room temperature is $26^{\circ} \mathrm{C}$ while the inner glass temperature is $18^{\circ} \mathrm{C}$. Disregarding radiation heat transfer, determine the temperature of the outer glass layer and the rate of heat loss through the window by natural convection.

Mayukh Banik

Numerade Educator

Problem 76

Consider two concentric horizontal cylinders of diameters 55 cm and 65 cm , and length 125 cm . The surfaces of the inner and outer cylinders are maintained at $54^{\circ} \mathrm{C}$ and $106^{\circ} \mathrm{C}$, respectively. Determine the rate of heat transfer between the cylinders by natural convection if the annular space is filled with (a) water and (b) air.

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Problem 77

A 10-cm-diameter and 10-m-long cylinder with a surface temperature of $10^{\circ} \mathrm{C}$ is placed horizontally in air at $40^{\circ} \mathrm{C}$. Calculate the steady rate of heat transfer for the cases of (a) free-stream air velocity of $10 \mathrm{~m} / \mathrm{s}$ due to normal winds and (b) no winds and thus a free stream velocity of zero.

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Problem 78

A spherical vessel, with $30.0-\mathrm{cm}$ outside diameter, is used as a reactor for a slow endothermic reaction. The vessel is completely submerged in a large water-filled tank, held at a constant temperature of $30^{\circ} \mathrm{C}$. The outside surface temperature of the vessel is $20^{\circ} \mathrm{C}$. Calculate the rate of heat transfer in steady operation for the following cases: (a) the water in the tank is still, (b) the water in the tank is still (as in a part a), however, the buoyancy force caused by the difference in water density is assumed to be negligible, and (c) the water in the tank is circulated at an average velocity of $20 \mathrm{~cm} / \mathrm{s}$.

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Problem 79

A vertical cylindrical pressure vessel is 1.0 m in diameter and 3.0 m in height. Its outside average wall temperature is $60^{\circ} \mathrm{C}$, while the surrounding air is at $0^{\circ} \mathrm{C}$. Calculate the rate of heat loss from the vessel's cylindrical surface when there is (a) no wind and (b) a crosswind of $20 \mathrm{~km} / \mathrm{h}$.

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Problem 80

Consider a solid sphere, 50 cm in diameter embedded with electrical heating elements such that its surface temperature is always maintained constant at $60^{\circ} \mathrm{C}$. The sphere is placed in a large pool of oil held at a constant temperature of $20^{\circ} \mathrm{C}$. Using the oil properties tabulated below, calculate the rate of heat transfer in steady operation for each of the following scenarios.
(a) Heat flow in the oil is assumed to occur only by conduction.
(b) The oil is circulated across the sphere at an average velocity of $1.50 \mathrm{~m} / \mathrm{s}$.
(c) The pump causing the oil circulation in part (b) has broken down.
$$
\begin{array}{cccccc}
T,{ }^{\circ} \mathrm{C} & k, \mathrm{~W} / \mathrm{m} \cdot \mathrm{~K} & \rho, \mathrm{~kg} / \mathrm{m}^3 & c_p, \mathrm{~J} / \mathrm{kg} \cdot \mathrm{~K} & \mu, \mathrm{mPa} \cdot \mathrm{~s} & \beta, \mathrm{~K}^{-1} \\
\hline 20.0 & 0.22 & 888.0 & 1880 & 10.0 & 0.00070 \\
40.0 & 0.21 & 876.0 & 1965 & 7.0 & 0.00070 \\
60.0 & 0.20 & 864.0 & 2050 & 4.0 & 0.00070
\end{array}
$$

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Problem 81

A 0.1-W small cylindrical resistor mounted on a lower part of a vertical circuit board is 0.3 in long and has a diameter of 0.2 in . The view of the resistor is largely blocked by another circuit board facing it, and the heat transfer through the connecting wires is negligible. The air is free to flow through the large parallel flow passages between the boards as a result of natural convection currents. If the air temperature at the vicinity of the resistor is $120^{\circ} \mathrm{F}$, determine the approximate surface temperature of the resistor.

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01:59

Problem 82

An ice chest whose outer dimensions are $30 \mathrm{~cm} \times$ $40 \mathrm{~cm} \times 40 \mathrm{~cm}$ is made of 3-cm-thick Styrofoam $\left(k=0.033 \mathrm{~W} / \mathrm{m} \cdot{ }^{\circ} \mathrm{C}\right)$. Initially, the chest is filled with 30 kg of ice at $0^{\circ} \mathrm{C}$, and the inner surface temperature of the ice chest can be taken to be $0^{\circ} \mathrm{C}$ at all times. The heat of fusion of water at $0^{\circ} \mathrm{C}$ is $333.7 \mathrm{~kJ} / \mathrm{kg}$, and the surrounding ambient air is at $20^{\circ} \mathrm{C}$. Disregarding any heat transfer from the 40 cm $\times 40 \mathrm{~cm}$ base of the ice chest, determine how long it will take for the ice in the chest to melt completely if the ice chest is subjected to (a) calm air and (b) winds at $50 \mathrm{~km} / \mathrm{h}$. Assume the heat transfer coefficient on the front, back, and top surfaces to be the same as that on the side surfaces.

Khoobchandra Agrawal

Numerade Educator

Problem 83

An electronic box that consumes 200 W of power is cooled by a fan blowing air into the box enclosure. The dimensions of the electronic box are $15 \mathrm{~cm} \times 50 \mathrm{~cm} \times 50$ cm , and all surfaces of the box are exposed to the ambient except the base surface. Temperature measurements indicate that the box is at an average temperature of $32^{\circ} \mathrm{C}$ when the ambient temperature and the temperature of the surrounding walls are $25^{\circ} \mathrm{C}$. If the emissivity of the outer surface of the box is 0.75 , determine the fraction of the heat lost from the outer surfaces of the electronic box.

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Problem 84

A 6-m-internal-diameter spherical tank made of 1.5 -cm-thick stainless steel $\left(k=15 \mathrm{~W} / \mathrm{m} \cdot{ }^{\circ} \mathrm{C}\right)$ is used to store iced water at $0^{\circ} \mathrm{C}$ in a room at $20^{\circ} \mathrm{C}$. The walls of the room are also at $20^{\circ} \mathrm{C}$. The outer surface of the tank is black (emissivity $\varepsilon=1$ ), and heat transfer between the outer surface of the tank and the surroundings is by natural convection and radiation. Assuming the entire steel tank to be at $0^{\circ} \mathrm{C}$ and thus the thermal resistance of the tank to be negligible, determine (a) the rate of heat transfer to the iced water in the tank and (b) the amount of ice at $0^{\circ} \mathrm{C}$ that melts during a 24 -h period. The heat of fusion of water is $333.7 \mathrm{~kJ} / \mathrm{kg}$

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06:45

Problem 85

Consider a 1.2-m-high and 2-m-wide double-pane window consisting of two 3 -mm-thick layers of glass ( $k=0.78 \mathrm{~W} / \mathrm{m} \cdot{ }^{\circ} \mathrm{C}$ ) separated by a 3 -cm-wide air space. Determine the steady rate of heat transfer through this window and the temperature of its inner surface for a day during which the room is maintained at $20^{\circ} \mathrm{C}$ while the temperature of the outdoors is $0^{\circ} \mathrm{C}$. Take the heat transfer coefficients on the inner and outer surfaces of the window to be $h_1=10 \mathrm{~W} / \mathrm{m}^2 \cdot{ }^{\circ} \mathrm{C}$ and $h_2=25 \mathrm{~W} / \mathrm{m}^2 \cdot{ }^{\circ} \mathrm{C}$ and disregard any heat transfer by radiation.

Cyra Jelle Calleja

Numerade Educator

05:27

Problem 86

An electric resistance space heater is designed such that it resembles a rectangular box 50 cm high, 80 cm long, and 15 cm wide filled with 45 kg of oil. The heater is to be placed against a wall, and thus heat transfer from its back surface is negligible. The surface temperature of the heater is not to exceed $75^{\circ} \mathrm{C}$ in a room at $25^{\circ} \mathrm{C}$ for safety considera-
tions. Disregarding heat transfer from the bottom and top surfaces of the heater in anticipation that the top surface will be used as a shelf, determine the power rating of the heater in W. Take the emissivity of the outer surface of the heater to be 0.8 and the average temperature of the ceiling and wall surfaces to be the same as the room air temperature.

Also, determine how long it will take for the heater to reach steady operation when it is first turned on (i.e., for the oil temperature to rise from $25^{\circ} \mathrm{C}$ to $75^{\circ} \mathrm{C}$ ). State your assumptions in the calculations.

Keshav Singh

Numerade Educator

Problem 87

Skylights or "roof windows" are commonly used in homes and manufacturing facilities since they let natural light in during day time and thus reduce the lighting costs. However, they offer little resistance to heat transfer, and large amounts of energy are lost through them in winter unless they are equipped with a motorized insulating cover that can be used in cold weather and at nights to reduce heat losses. Consider a $1-\mathrm{m}$-wide and $2.5-\mathrm{m}$-long horizontal skylight on the roof of a house that is kept at $20^{\circ} \mathrm{C}$. The glazing of the skylight is made of a single layer of $0.5-\mathrm{cm}-$ thick glass ( $k=0.78 \mathrm{~W} / \mathrm{m} \cdot{ }^{\circ} \mathrm{C}$ and $\varepsilon=0.9$ ). Determine the rate of heat loss through the skylight when the air temperature outside is $-10^{\circ} \mathrm{C}$ and the effective sky temperature is $-30^{\circ} \mathrm{C}$. Compare your result with the rate of heat loss through an equivalent surface area of the roof that has a common R-5.34 construction in SI units (i.e., a thickness-to-effective-thermal-conductivity ratio of $5.34 \mathrm{~m}^2$, $\left.{ }^{\circ} \mathrm{C} / \mathrm{W}\right)$.

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Problem 88

A solar collector consists of a horizontal copper tube of outer diameter 5 cm enclosed in a concentric thin glass tube of 9 cm diameter. Water is heated as it flows through the tube, and the annular space between the copper and glass tube is filled with air at 1 atm pressure. During a clear day, the temperatures of the tube surface and the glass cover are measured to be $60^{\circ} \mathrm{C}$ and $32^{\circ} \mathrm{C}$, respectively. Determine the rate of heat loss from the collector by natural convection per meter length of the tube.

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Problem 89

A solar collector consists of a horizontal aluminum tube of outer diameter 5 cm enclosed in a concentric thin glass tube of 7 cm diameter. Water is heated as it flows through the aluminum tube, and the annular space between the aluminum and glass tubes is filled with air at 1 atm pressure. The pump circulating the water fails during a clear day, and the water temperature in the tube starts rising. The aluminum tube absorbs solar radiation at a rate of 20 W per meter length, and the temperature of the ambient air outside is $30^{\circ} \mathrm{C}$. Approximating the surfaces of the tube and the glass cover as being black (emissivity $\varepsilon=1$ ) in radiation calculations and taking the effective sky temperature to be $20^{\circ} \mathrm{C}$, determine the temperature of the aluminum tube when equilibrium is established (i.e., when the net heat loss from the tube by convection and radiation equals the amount of solar energy absorbed by the tube).

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08:34

Problem 90

The components of an electronic system dissipating 180 W are located in a 4 -ft-long horizontal duct whose cross section is $6 \mathrm{in} \times 6 \mathrm{in}$. The components in the duct are cooled by forced air, which enters at $85^{\circ} \mathrm{F}$ at a rate of 22 cfm and leaves at $100^{\circ} \mathrm{F}$. The surfaces of the sheet metal duct are not painted, and thus radiation heat transfer from the outer surfaces is negligible. If the ambient air temperature is $80^{\circ} \mathrm{F}$, determine ( $a$ ) the heat transfer from the outer surfaces of the duct to the ambient air by natural convection and (b) the average temperature of the duct.

Dading Chen

Numerade Educator

01:20

Problem 91

Repeat Prob. 14-90E for a circular horizontal duct of diameter 4 in .

Dading Chen

Numerade Educator

11:35

Problem 92

Repeat Prob. $14-90 E$ assuming the fan fails and thus the entire heat generated inside the duct must be rejected to the ambient air by natural convection through the outer surfaces of the duct.

Khoobchandra Agrawal

Numerade Educator

Problem 93

Consider a cold aluminum canned drink that is initially at a uniform temperature of $5^{\circ} \mathrm{C}$. The can is 12.5 cm high and has a diameter of 6 cm . The emissivity of the outer surface of the can is 0.6 . Disregarding any heat transfer from the bottom surface of the can, determine how long it will take for the average temperature of the drink to rise to $7^{\circ} \mathrm{C}$ if the surrounding air and surfaces are at $25^{\circ} \mathrm{C}$.

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Problem 94

Consider a 2-m-high electric hot-water heater that has a diameter of 40 cm and maintains the hot water at $60^{\circ} \mathrm{C}$. The tank is located in a small room at $20^{\circ} \mathrm{C}$ whose walls and the ceiling are at about the same temperature. The tank is placed in a $44-\mathrm{cm}$-diameter sheet metal shell of negligible thickness, and the space between the tank and the shell is filled with foam insulation. The average temperature and emissivity of the outer surface of the shell are $40^{\circ} \mathrm{C}$ and 0.7 , respectively. The price of electricity is $$\$ 0.08 / \mathrm{kWh}$$. Hot-water tank insulation kits large enough to wrap the entire tank are available on the market for about $$\$ 60$$. If such an insulation is installed on this water tank by the home owner himself, how long will it take for this additional insulation to pay for itself? Disregard any heat loss from the top and bottom surfaces, and assume the insulation to reduce the heat losses by 80 percent.

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Problem 95

During a plant visit, it was observed that a $1.5-\mathrm{m}$ high and 1-m-wide section of the vertical front section of a natural gas furnace wall was too hot to touch. The temperature measurements on the surface revealed that the average temperature of the exposed hot surface was $110^{\circ} \mathrm{C}$, while the temperature of the surrounding air was $25^{\circ} \mathrm{C}$. The surface appeared to be oxidized, and its emissivity can be taken to be 0.7 . Taking the temperature of the surrounding surfaces to be $25^{\circ} \mathrm{C}$ also, determine the rate of heat loss from this furnace.
The furnace has an efficiency of 79 percent, and the plant pays $$\$ 1.20$$ per therm of natural gas. If the plant operates 10 h a day, 310 days a year, and thus 3100 h a year, determine the annual cost of the heat loss from this vertical hot surface on the front section of the furnace wall.

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Problem 96

A group of 25 power transistors, dissipating 1.5 W each, are to be cooled by attaching them to a black-anodized square aluminum plate and mounting the plate on the wall of a room at $30^{\circ} \mathrm{C}$. The emissivity of the transistor and the plate surfaces is 0.9 . Assuming the heat transfer from the back side of the plate to be negligible and the temperature of the surrounding surfaces to be the same as the air temperature of the room, determine the size of the plate if the average surface temperature of the plate is not to exceed $50^{\circ} \mathrm{C}$.

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Problem 97

Repeat Prob. 14-96 assuming the plate to be positioned horizontally with (a) transistors facing up and (b) transistors facing down.

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02:27

Problem 98

Hot water is flowing at an average velocity of $4 \mathrm{ft} / \mathrm{s}$ through a cast iron pipe ( $\left.k=30 \mathrm{Btu} / \mathrm{h} \cdot \mathrm{ft} \cdot{ }^{\circ} \mathrm{F}\right)$ whose inner and outer diameters are 1.0 in and 1.2 in , respectively. The pipe passes through a 50 -ft-long section of a basement whose temperature is $60^{\circ} \mathrm{F}$. The emissivity of the outer surface of the pipe is 0.5 , and the walls of the basement are also at about $60^{\circ} \mathrm{F}$. If the inlet temperature of the water is $150^{\circ} \mathrm{F}$ and the heat transfer coefficient on the inner surface of the pipe is $30 \mathrm{Btu} / \mathrm{h} \cdot \mathrm{ft}^2 \cdot{ }^{\circ} \mathrm{F}$, determine the temperature drop of water as it passes through the basement.

Anand Jangid

Numerade Educator

Problem 99

Consider a flat-plate solar collector placed horizontally on the flat roof of a house. The collector is 1.5 m wide and 6 m long, and the average temperature of the exposed surface of the collector is $42^{\circ} \mathrm{C}$. Determine the rate of heat loss from the collector by natural convection during a calm day when the ambient air temperature is $8^{\circ} \mathrm{C}$. Also, determine the heat loss by radiation by taking the emissivity of the collector surface to be 0.9 and the effective sky temperature to be $-15^{\circ} \mathrm{C}$.

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Problem 100

Solar radiation is incident on the glass cover of a solar collector at a rate of $650 \mathrm{~W} / \mathrm{m}^2$. The glass transmits 88 percent of the incident radiation and has an emissivity of 0.90 . The hot water needs of a family in summer can be met completely by a collector 1.5 m high and 2 m wide, and tilted $40^{\circ}$ from the horizontal. The temperature of the glass cover is measured to be $40^{\circ} \mathrm{C}$ on a calm day when the surrounding air temperature is $20^{\circ} \mathrm{C}$. The effective sky temperature for radiation exchange between the glass cover and the open sky is $-40^{\circ} \mathrm{C}$. Water enters the tubes attached to the absorber plate at a rate of $1 \mathrm{~kg} / \mathrm{min}$. Assuming the back surface of the absorber plate to be heavily insulated and the only heat loss occurs through the glass cover, determine (a) the total rate of heat loss from the collector; (b) the collector efficiency, which is the ratio of the amount of heat transferred to the water to the solar energy incident on the collector; and (c) the temperature rise of water as it flows through the collector.

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01:39

Problem 101

Write a computer program to optimize the spacing between the two glasses of a double-pane window. Assume the spacing is filled with dry air at atmospheric pressure. The program should evaluate the recommended practical value of the spacing to minimize the heat losses and list it when the size of the window (the height and the width) and the temperatures of the two glasses are specified.

Paul Gabriel

Numerade Educator

03:02

Problem 102

Contact a manufacturer of aluminum heat sinks and obtain their product catalog for cooling electronic components by natural convection and radiation. Write an essay on how to select a suitable heat sink for an electronic component when its maximum power dissipation and maximum allowable surface temperature are specified.

Jincy M Saji

Numerade Educator

Problem 103

The top surfaces of practically all flat-plate solar collectors are covered with glass in order to reduce the heat losses from the absorber plate underneath. Although the glass cover reflects or absorbs about 15 percent of the incident solar radiation, it saves much more from the potential heat losses from the absorber plate, and thus it is considered to be an essential part of a well-designed solar collector. Inspired by the energy efficiency of double-pane windows, someone proposes to use double glazing on solar collectors instead of a single glass. Investigate if this is a good idea for the town in which you live. Use local weather data and base your conclusion on heat transfer analysis and economic considerations.

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