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NATURAL CONVECTION TEST 1
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Question 1 of 20
1. Question
1 pointsA 6mlong section of an 8cmdiameter horizontal hot water pipe shown in Figure passes through a large room whose temperature is 20˚C. If the outer surface temperature of the pipe is 70˚C, determine the rate of heat loss from the pipe by natural convection.
Assumptions 1 Steady operating conditions exist. 2 Air is an ideal gas. 3 The local atmospheric pressure is 1 atm.
Properties The properties of air at the film temperature of Tf = (Ts+ T∞)/2 =(70 +20)/2 = 45˚C and 1 atm
Correct
SOLUTION A horizontal hot water pipe passes through a large room. The rate of heat loss from the pipe by natural convection is to be determined.
Analysis The characteristic length in this case is the outer diameter of the pipe, Lc = D = 0.08 m. Then the Rayleigh number becomes
Therefore, the pipe will lose heat to the air in the room at a rate of 443 W by natural convection
Incorrect
SOLUTION A horizontal hot water pipe passes through a large room. The rate of heat loss from the pipe by natural convection is to be determined.
Analysis The characteristic length in this case is the outer diameter of the pipe, Lc = D = 0.08 m. Then the Rayleigh number becomes
Therefore, the pipe will lose heat to the air in the room at a rate of 443 W by natural convection

Question 2 of 20
2. Question
1 pointsA 12cmwide and 18cmhigh vertical hot surface in 30˚C air is to be cooled by a heat sink with equally spaced fins of rectangular profile (Fig.). The fin are 0.1 cm thick and 18 cm long in the vertical direction and have a height of 2.4 cm 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 80˚C (ANSWER UPTO ONE DECIMAL)
Assumptions 1 Steady operating conditions exist. 2 Air is an ideal gas. 3 The atmospheric pressure at that location is 1 atm. 4 The thickness t of the fins is very small relative to the fin spacing S so that for optimum fin spacing is applicable. 5 All fin surfaces are isothermal at base temperature
Properties The properties of air at the film temperature of Tf = (Ts +T∞)/2 = (80+ 30)/2 = 55˚C and 1 atm pressure
K=0.02772 W/m .˚C Pr=0.7215
V=1.846 x 10^ 5 m²/s β=1/Tƒ=1/328 K
Correct
SOLUTION A heat sink with equally spaced rectangular fins is to be used to cool a hot surface. The optimum fin spacing and the rate of heat transfer are to be determined
Analysis We take the characteristic length to be the length of the fins in the vertical direction (since we do not know the fin spacing). Then the Rayleigh number becomes
Therefore, this heat sink can dissipate heat by natural convection at a rate of 1.30 W.
Incorrect
SOLUTION A heat sink with equally spaced rectangular fins is to be used to cool a hot surface. The optimum fin spacing and the rate of heat transfer are to be determined
Analysis We take the characteristic length to be the length of the fins in the vertical direction (since we do not know the fin spacing). Then the Rayleigh number becomes
Therefore, this heat sink can dissipate heat by natural convection at a rate of 1.30 W.

Question 3 of 20
3. Question
1 pointsThe vertical 0.8mhigh, 2mwide doublepane window shown in Fig. consists of two sheets of glass separated by a 2cm air gap at atmospheric pressure. If the glass surface temperatures across the air gap are measured to be 12˚C and 2˚C, determine the rate of heat transfer through the window.(answer upto one decimal)
Assumptions 1 Steady operating conditions exist. 2 Air is an ideal gas. 3 Radiation heat transfer is not considered.
Properties The properties of air at the average temperature of Tave = (T1 + T2)/2 = (12 +2)/2 = 7˚C and 1 atm pressure
K=0.02416 W/m ˚C Pr=0.7344
V=1.399 x 10^5 m²/s β=1/Tave =1/280K
Correct
SOLUTION Two glasses of a doublepane window are maintained at specified temperatures. The rate of heat transfer through the window is to be determined.
Analysis We have a rectangular enclosure filled with air. The characteristic length in this case is the distance between the two glasses, L =0.02 m. Then the Rayleigh number becomes
Incorrect
SOLUTION Two glasses of a doublepane window are maintained at specified temperatures. The rate of heat transfer through the window is to be determined.
Analysis We have a rectangular enclosure filled with air. The characteristic length in this case is the distance between the two glasses, L =0.02 m. Then the Rayleigh number becomes

Question 4 of 20
4. Question
1 pointsThe two concentric spheres of diameters Di = 20 cm and Do = 30 cm shown in Fig. are separated by air at 1 atm pressure. The surface temperatures of the two spheres enclosing the air are Ti = 320 K and To =280 K, respectively. Determine the rate of heat transfer from the inner sphere to the outer sphere by natural convection.(answer upto one decimal)
Assumptions 1 Steady operating conditions exist. 2 Air is an ideal gas. 3 Radiation heat transfer is not considered.
Properties The properties of air at the average temperature of Tave = (Ti+ To)/2 = (320 +280)/2=300 K =27˚C and 1 atm pressure are
k=0.02566 W/m ˚C Pr=0.7290
v=1.580 x 10^5 m²/s β=1/Tave=1/300k
Correct
SOLUTION Two surfaces of a spherical enclosure are maintained at specified temperatures. The rate of heat transfer through the enclosure is to be determined.
Analysis We have a spherical enclosure filled with air. The characteristic length in this case is the distance between the two spheres,
Lc=(Do Di)/2=(0.3 0.2)/2=0.05 m
The Rayleigh number is
Therefore, heat will be lost from the inner sphere to the outer one at a rate of 16.7 W.
Incorrect
SOLUTION Two surfaces of a spherical enclosure are maintained at specified temperatures. The rate of heat transfer through the enclosure is to be determined.
Analysis We have a spherical enclosure filled with air. The characteristic length in this case is the distance between the two spheres,
Lc=(Do Di)/2=(0.3 0.2)/2=0.05 m
The Rayleigh number is
Therefore, heat will be lost from the inner sphere to the outer one at a rate of 16.7 W.

Question 5 of 20
5. Question
1 pointsDetermine the Ufactor for the centerofglass section of a doublepane window with a 6mm air space for winter design conditions (Fig.). The glazings are made of clear glass that has an emissivity of 0.84. Take the average air space temperature at design conditions to be 0°C.(answer upto two decimal)
Assumptions 1 Steady operating conditions exist. 2 Heat transfer through the window is onedimensional. 3 The thermal resistance of glass sheets is negligible.
Properties The emissivity of clear glass is 0.84.
Correct
SOLUTION The Ufactor for the centerofglass section of a doublepane window is to be determined.
Analysis Disregarding the thermal resistance of glass sheets, which are small, the Ufactor for the center region of a doublepane window is determined from
1/Ucenter =1/h1+1/hspace+1/ho
where hi, hspace, and ho are the heat transfer coefficients at the inner surface of the window, the air space between the glass layers, and the outer surface of the window, respectively. The values of hi and ho for winter design conditions were given earlier to be hi= 8.29 W/m² · °C and ho = 34.0 W/m² · °C. The effective emissivity of the air space of the doublepane window is
εeffective=1/1/ε1+1/ε21=1/1/0.84+1/0.841=0.72
For this value of emissivity and an average air space temperature of 0°C, we read hspace = 7.2 W/m² · °C from 6mmthick air space.
Therefore,1/Ucenter=1/8.29+1/7.2+1/34.0 → Ucenter=3.46 W/m² · °C
Incorrect
SOLUTION The Ufactor for the centerofglass section of a doublepane window is to be determined.
Analysis Disregarding the thermal resistance of glass sheets, which are small, the Ufactor for the center region of a doublepane window is determined from
1/Ucenter =1/h1+1/hspace+1/ho
where hi, hspace, and ho are the heat transfer coefficients at the inner surface of the window, the air space between the glass layers, and the outer surface of the window, respectively. The values of hi and ho for winter design conditions were given earlier to be hi= 8.29 W/m² · °C and ho = 34.0 W/m² · °C. The effective emissivity of the air space of the doublepane window is
εeffective=1/1/ε1+1/ε21=1/1/0.84+1/0.841=0.72
For this value of emissivity and an average air space temperature of 0°C, we read hspace = 7.2 W/m² · °C from 6mmthick air space.
Therefore,1/Ucenter=1/8.29+1/7.2+1/34.0 → Ucenter=3.46 W/m² · °C

Question 6 of 20
6. Question
1 pointsConsider a wallmounted power transistor that dissipates 0.18 W of power in an environment at 35°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°C. Disregarding any heat transfer from the base surface, determine the surface temperature of the transistor. Use air properties at 100°C.
Correct
183°C
Incorrect
183°C

Question 7 of 20
7. Question
1 pointsWater is boiling in a 12cmdeep 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°C, and the emissivity of the outer surface of the pan is 0.95. Assuming the entire pan to be at an average temperature of 98°C, determine the rate of heat loss from the cylindrical side surface of the pan to the surroundings by natural convection(answer upto one decimal)
Correct
46.2 w
Incorrect
46.2 w

Question 8 of 20
8. Question
1 pointsWater is boiling in a 12cmdeep 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°C, and the emissivity of the outer surface of the pan is 0.95. Assuming the entire pan to be at an average temperature of 98°C, determine the rate of heat loss from the cylindrical side surface of the pan to the surroundings by radiation.(answer upto one decimal)
Correct
56.1 W
Incorrect
56.1 W

Question 9 of 20
9. Question
1 pointsWater is boiling in a 12cmdeep 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°C, and the emissivity of the outer surface of the pan is 0.95. Assuming the entire pan to be at an average temperature of 98°C, determine the rate of heat loss from the cylindrical side surface of the pan to the surroundings by . If water is boiling at a rate of 2 kg/h at 100°C, determine the ratio of the heat lost from the side surfaces of the pan to that by the evaporation of water. The heat of vaporization of water at 100°C is 2257 kJ/kg.(answer upto three decimal)
Correct
0.082
Incorrect
0.082

Question 10 of 20
10. Question
1 pointsConsider a 15cm x 20cm printed circuit board (PCB) that has electronic components on one side. The board is placed in a room at 20°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 vertical(answer upto one decimal)
Correct
46.6°C
Incorrect
46.6°C

Question 11 of 20
11. Question
1 pointsConsider a 15cm x 20cm printed circuit board (PCB) that has electronic components on one side. The board is placed in a room at 20°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 horizontal with hot surface facing up,(answer upto one decimal)
Correct
42.6°C
Incorrect
42.6°C

Question 12 of 20
12. Question
1 pointsConsider a 15cm x 20cm printed circuit board (PCB) that has electronic components on one side. The board is placed in a room at 20°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 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,(answer upto one decimal)
Correct
50.7°C
Incorrect
50.7°C

Question 13 of 20
13. Question
1 pointsA manufacturer makes absorber plates that are 1.2 m x 0.8 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°C. Solar radiation is incident on the plate at a rate of 700 W/m². Taking the effective sky temperature to be 10°C, determine the equilibrium temperature of the absorber plate
Correct
29.1 kW
Incorrect
29.1 kW

Question 14 of 20
14. Question
1 pointsA manufacturer makes absorber plates that are 1.2 m x 0.8 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°C. Solar radiation is incident on the plate at a rate of 700 W/m². Taking the effective sky temperature to be 10°C, 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?
electricity associated with heating the pipe during a 10h period under the above conditions if the price of electricity is $0.09/kWh.
Correct
$26.2
Incorrect
$26.2

Question 15 of 20
15. Question
1 pointsA 30cm x 30cm 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°C. Each chip dissipates 0.05 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.
Correct
33.4°C
Incorrect
33.4°C

Question 16 of 20
16. Question
1 pointsAn 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 8cmdiameter 60W light bulb in a room at 25°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.
Correct
169°C
Incorrect
169°C

Question 17 of 20
17. Question
1 pointsAluminum heat sinks of rectangular profile are commonly used to cool electronic components. Consider a 7.62cmlong and 9.68cmwide commercially available heat sink whose cross section and dimensions are as shown in Figure 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°C, the base temperature of the heat sink was measured to be 120°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.
Correct
7.1 W/m2 °C
Incorrect
7.1 W/m2 °C

Question 18 of 20
18. Question
1 pointsA simple solar collector is built by placing a 5cmdiameter 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°C,while the ambient air temperature is 26°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.(answer upto one decimal)
Correct
8.2 W
Incorrect
8.2 W

Question 19 of 20
19. Question
1 pointsConsider a 5mlong vertical plate at 85°C in air at 30°C. Determine the forced motion velocity above which natural convection heat transfer from this plate is negligible(answer upto one decimal)
Correct
9.04 m/s
Incorrect
9.04 m/s

Question 20 of 20
20. Question
1 pointsConsider a house in Atlanta, Georgia, that is maintained at 22°C and has a total of 20 m² of window area. The windows are doubledoortype with wood frames and metal spacers. The glazing consists of two layers of glass with 12.7 mm of air space with one of the inner surfaces coated with reflective film. The winter average temperature of Atlanta is 11.3°C. Determine the average rate of heat loss through the windows in winter.
Correct
456 W
Incorrect
456 W