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TRANSIENT HEAT CONDUCTION TEST 1
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Question 1 of 20
1. Question
1 pointsIn areas where the air temperature remains below 0°C for prolonged periods of time, the freezing of water in underground pipes is a major concern. Fortunately, the soil remains relatively warm during those periods, and it takes weeks for the subfreezing temperatures to reach the water mains in the ground. Thus, the soil effectively serves as an insulation to protect the water from subfreezing temperatures in winter. The ground at a particular location is covered with snow pack at 10°C for a continuous period of three months, and the average soil properties at that location are k= 0.4 W/m · °C and ∝= 0.15 x 10^6 m²/s (Fig.). Assuming an initial uniform temperature of 15°C for the ground, determine the minimum burial depth to prevent the water pipes from freezing.
Assumptions 1 The temperature in the soil is affected by the thermal conditions at one surface only, and thus the soil can be considered to be a semiinfinite medium with a specified surface temperature of 10°C. 2 The thermal properties of the soil are constant
Properties The properties of the soil are as given in the problem statement.(ANSWER UPTO TWO DECIMAL)
Correct
SOLUTION The water pipes are buried in the ground to prevent freezing. The minimum burial depth at a particular location is to be determined.
Analysis The temperature of the soil surrounding the pipes will be 0°C after three months in the case of minimum burial depth. Therefore, from( Fig.,) we have
Incorrect
SOLUTION The water pipes are buried in the ground to prevent freezing. The minimum burial depth at a particular location is to be determined.
Analysis The temperature of the soil surrounding the pipes will be 0°C after three months in the case of minimum burial depth. Therefore, from( Fig.,) we have

Question 2 of 20
2. Question
1 pointsThe temperature of a gas stream is to be measured by a thermocouple whose junction can be approximated as a 1.2mmdiameter sphere. The properties of the junction are k =35 W/m · °C, P=8500 kg/m³, and Cp= 320 J/kg · °C, and the heat transfer coefficient between the junction and the gas is h =65 W/m² · °C. Determine how long it will take for the thermocouple to read 99 percent of the initial temperature difference
Correct
38.5 s
Incorrect
38.5 s

Question 3 of 20
3. Question
1 pointsTo warm up some milk for a baby, a mother pours milk into a thinwalled glass whose diameter is 6 cm. The height of the milk in the glass is 7 cm. She then places the glass into a large pan filled with hot water at 60°C. The milk is stirred constantly, so that its temperature is uniform at all times. If the heat transfer coefficient between the water and the glass is 120 W/m² · °C, determine how long it will take for the milk to warm up from 3°C to 38°C. Take the properties of the milk to be the same as those of water. Can the milk in this case be treated as a lumped system?(ANSWER I ONE DECIMAL)
Correct
5.8 min
Incorrect
5.8 min

Question 4 of 20
4. Question
1 pointsStainless steel ball bearings (P= 8085 kg/m³ , k =15.1W/m · °C, Cp =0.480 kJ/kg · °C, and ∝= 3.91 x 10^6 m²/s) having a diameter of 1.2 cm are to be quenched in water. The balls leave the oven at a uniform temperature of 900°C and are exposed to air at 30°C for a while before they are dropped into the water. If the temperature of the balls is not to fall below 850°C prior to quenching and the heat transfer coefficient in the air is 125 W/m² · °C, determine how long they can stand in the air before being dropped into the water(answer in one decimal)
Correct
3.7 s
Incorrect
3.7 s

Question 5 of 20
5. Question
1 pointsA long 35cmdiameter cylindrical shaft made of stainless steel 304 (k= 14.9 W/m · °C, p= 7900 kg/m³ , Cp= 477 J/kg · °C, and ∝= 3.95 x 10^6 m²/s) comes out of an oven at a uniform temperature of 400°C. The shaft is then allowed to cool slowly in a chamber at 150°C with an average convection heat transfer coefficient of h =60 W/m²· °C. Determine the temperature at the center of the shaft 20 min after the start of the cooling process
Correct
390°C,
Incorrect
390°C,

Question 6 of 20
6. Question
1 pointsA long 35cmdiameter cylindrical shaft made of stainless steel 304 (k= 14.9 W/m · °C, P=7900 kg/m³, Cp =477 J/kg · °C, and ∝= 3.95 x 10^6 m²/s) comes out of an oven at a uniform temperature of 400°C. The shaft is then allowed to cool slowly in a chamber at 150°C with an average convection heat transfer coefficient of h 60 W/m² · °C determine the heat transfer per unit length of the shaft during this time period.
Correct
16,015 kJ/m
Incorrect
16,015 kJ/m

Question 7 of 20
7. Question
1 pointsIn Betty Crocker’s Cookbook, it is stated that it takes 2 h 45 min to roast a 3.2kg rib initially at 4.5°C “rare” in an oven maintained at 163°C. It is recommended that a meat thermometer be used to monitor the cooking, and the rib is considered rare done when the thermometer inserted into the center of the thickest part of the meat registers 60°C. The rib can be treated as a homogeneous spherical object with the properties P= 1200 kg/m³ , Cp =4.1 kJ/kg · °C, k =0.45 W/m · °C, and ∝= 0.91 10^7 m²/s. Determine the heat transfer coefficient at the surface of the rib, (answer upto one decimal)
Correct
156.9 W/m² · °C
Incorrect
156.9 W/m² · °C

Question 8 of 20
8. Question
1 pointsIn Betty Crocker’s Cookbook, it is stated that it takes 2 h 45 min to roast a 3.2kg rib initially at 4.5°C “rare” in an oven maintained at 163°C. It is recommended that a meat thermometer be used to monitor the cooking, and the rib is considered rare done when the thermometer inserted into the center of the thickest part of the meat registers 60°C. The rib can be treated as a homogeneous spherical object with the properties P= 1200 kg/m³ , Cp =4.1 kJ/kg · °C, k =0.45 W/m · °C, and ∝= 0.91 10^7 m²/s. Determine the temperature of the outer surface of the rib when it is done, (answer upto one decimal)
Correct
159.5°C,
Incorrect
159.5°C,

Question 9 of 20
9. Question
1 pointsIn Betty Crocker’s Cookbook, it is stated that it takes 2 h 45 min to roast a 3.2kg rib initially at 4.5°C “rare” in an oven maintained at 163°C. It is recommended that a meat thermometer be used to monitor the cooking, and the rib is considered rare done when the thermometer inserted into the center of the thickest part of the meat registers 60°C. The rib can be treated as a homogeneous spherical object with the properties P= 1200 kg/m³ , Cp =4.1 kJ/kg · °C, k =0.45 W/m · °C, and ∝= 0.91 10^7 m²/s. Determine the the amount of heat transferred to the rib. ,
Correct
1629 kJ,
Incorrect
1629 kJ,

Question 10 of 20
10. Question
1 pointsIn Betty Crocker’s Cookbook, it is stated that it takes 2 h 45 min to roast a 3.2kg rib initially at 4.5°C “rare” in an oven maintained at 163°C. It is recommended that a meat thermometer be used to monitor the cooking, and the rib is considered rare done when the thermometer inserted into the center of the thickest part of the meat registers 60°C. The rib can be treated as a homogeneous spherical object with the properties P= 1200 kg/m³ , Cp =4.1 kJ/kg · °C, k =0.45 W/m · °C, and ∝= 0.91 10^7 m²/s. Determine Using the values obtained, predict how long it will take to roast this rib to “medium” level, which occurs when the innermost temperature of the rib reaches 71°C
Correct
3.0 h
Incorrect
3.0 h

Question 11 of 20
11. Question
1 pointsThe author and his 6yearold son have conducted the following experiment to determine the thermal conductivity of a hot dog. They first boiled water in a large pan and measured the temperature of the boiling water to be 94°C, which is not surprising, since they live at an elevation of about 1650 m in Reno, Nevada. They then took a hot dog that is 12.5 cm long and 2.2 cm in diameter and inserted a thermocouple into the midpoint of the hot dog and another thermocouple just under the skin. They waited until both thermocouples read 20°C, which is the ambient temperature. They then dropped the hot dog into boiling water and observed the changes in both temperatures. Exactly 2 min after the hot dog was dropped into the boiling water, they recorded the center and the surface temperatures to be 59°C and 88°C, respectively. The density of the hot dog can be taken to be 980 kg/m³ , which is slightly less than the density of water, since the hot dog was observed to be floating in water while being almost completely immersed. The specific heat of a hot dog can be taken to be 3900 J/kg · °C, which is slightly less than that of water, since a hot dog is mostly water. Using transient temperature charts, determine the thermal diffusivity of the hot dog
Correct
2.02 x 10^7 m²/s
Incorrect
2.02 x 10^7 m²/s

Question 12 of 20
12. Question
1 pointsThe author and his 6yearold son have conducted the following experiment to determine the thermal conductivity of a hot dog. They first boiled water in a large pan and measured the temperature of the boiling water to be 94°C, which is not surprising, since they live at an elevation of about 1650 m in Reno, Nevada. They then took a hot dog that is 12.5 cm long and 2.2 cm in diameter and inserted a thermocouple into the midpoint of the hot dog and another thermocouple just under the skin. They waited until both thermocouples read 20°C, which is the ambient temperature. They then dropped the hot dog into boiling water and observed the changes in both temperatures. Exactly 2 min after the hot dog was dropped into the boiling water, they recorded the center and the surface temperatures to be 59°C and 88°C, respectively. The density of the hot dog can be taken to be 980 kg/m³ , which is slightly less than the density of water, since the hot dog was observed to be floating in water while being almost completely immersed. The specific heat of a hot dog can be taken to be 3900 J/kg · °C, which is slightly less than that of water, since a hot dog is mostly water. Using transient temperature charts,determine the thermal conductivity of the hot dog,(answer upto three decimal)
Correct
0.771 W/m · °C,
Incorrect
0.771 W/m · °C,

Question 13 of 20
13. Question
1 pointsThe author and his 6yearold son have conducted the following experiment to determine the thermal conductivity of a hot dog. They first boiled water in a large pan and measured the temperature of the boiling water to be 94°C, which is not surprising, since they live at an elevation of about 1650 m in Reno, Nevada. They then took a hot dog that is 12.5 cm long and 2.2 cm in diameter and inserted a thermocouple into the midpoint of the hot dog and another thermocouple just under the skin. They waited until both thermocouples read 20°C, which is the ambient temperature. They then dropped the hot dog into boiling water and observed the changes in both temperatures. Exactly 2 min after the hot dog was dropped into the boiling water, they recorded the center and the surface temperatures to be 59°C and 88°C, respectively. The density of the hot dog can be taken to be 980 kg/m³ , which is slightly less than the density of water, since the hot dog was observed to be floating in water while being almost completely immersed. The specific heat of a hot dog can be taken to be 3900 J/kg · °C, which is slightly less than that of water, since a hot dog is mostly water. Using transient temperature charts,determine the convection heat transfer coefficient.
Correct
467 W/m² · °C
Incorrect
467 W/m² · °C

Question 14 of 20
14. Question
1 pointsLayers of 6in.thick meat slabs (k= 0.26 Btu/h · ft · °F and ∝= 1.4 x 10^6 ft2 /s) initially at a uniform temperature of 50°F are cooled by refrigerated air at 23°F to a temperature of 36°F at their center in 12 h. Estimate the average heat transfer coefficient during this cooling process.
Correct
1.5 Btu/h · ft² · °F
Incorrect
1.5 Btu/h · ft² · °F

Question 15 of 20
15. Question
1 pointsA 65kg beef carcass (k =0.47 W/m · °C and ∝= 0.13 x 10^6 m² /s) initially at a uniform temperature of 37°C is to be cooled by refrigerated air at 6°C flowing at a velocity of 1.8 m/s. The average heat transfer coefficient between the carcass and the air is 22 W/m² · °C. Treating the carcass as a cylinder of diameter 24 cm and height 1.4 m and disregarding heat transfer from the base and top surfaces, determine how long it will take for the center temperature of the carcass to drop to 4°C. Also, determine if any part of the carcass will freeze during this process
Correct
14.0 h
Incorrect
14.0 h

Question 16 of 20
16. Question
1 pointsThe walls of a furnace are made of 1.5ftthick concrete (k =0.64 Btu/h · ft · °F and ∝=0.023 ft² /h). Initially, the furnace and the surrounding air are in thermal equilibrium at 70°F. The furnace is then fired, and the inner surfaces of the furnace are subjected to hot gases at 1800°F with a very large heat transfer coefficient. Determine how long it will take for the temperature of the outer surface of the furnace walls to rise to 70.1°F
Correct
181 min
Incorrect
181 min

Question 17 of 20
17. Question
1 pointsTurkeys with a water content of 64 percent that are initially at 1°C and have a mass of about 7 kg are to be frozen by submerging them into brine at 29°C. Using determine how long it will take to reduce the temperature of the turkey breast at a depth of 3.8 cm to 18°C. If the temperature at a depth of 3.8 cm in the breast represents the average temperature of the turkey, determine the amount of heat transfer per turkey assuming the entire water content of the turkey is frozen
Correct
1753 kJ,
Incorrect
1753 kJ,

Question 18 of 20
18. Question
1 pointsTurkeys with a water content of 64 percent that are initially at 1°C and have a mass of about 7 kg are to be frozen by submerging them into brine at 29°C. Using determine how long it will take to reduce the temperature of the turkey breast at a depth of 3.8 cm to 18°C. If the temperature at a depth of 3.8 cm in the breast represents the average temperature of the turkey, determine the amount of heat transfer per turkey assuming only 90 percent of the water content of the turkey is frozen at 18°C. Take the specific heats of turkey to be 2.98 and 1.65 kJ/kg · °C above and below the freezing point of 2.8°C, respectively, and the latent heat of fusion of turkey to be 214 kJ/kg.
Correct
1617 kJ
Incorrect
1617 kJ

Question 19 of 20
19. Question
1 pointsIn a meat processing plant, 10cmthick beef slabs (ρ =1090 kg/m³, Cp =3.54 kJ/kg · °C, k= 0.47 W/m · °C, and α= 0.13 x 10^–6 m² /s) initially at 15°C are to be cooled in the racks of a large freezer that is maintained at 12°C. The meat slabs are placed close to each other so that heat transfer from the 10cmthick edges is negligible. The entire slab is to be cooled below 5°C, but the temperature of the steak is not to drop below 1°C anywhere during refrigeration to avoid “frost bite.” The convection heat transfer coefficient and thus the rate of heat transfer from the steak can be controlled by varying the speed of a circulating fan inside. Determine the heat transfer coefficient h that will enable us to meet both temperature constraints while keeping the refrigeration time to a minimum.( answer upto one decimal)
Correct
9.9 W/m²· °C
Incorrect
9.9 W/m²· °C

Question 20 of 20
20. Question
1 pointsConsider two 2cmthick large steel plates (k =43 W/m · °C and ∝=1.17 x 10^5 m² /s) that were put on top of each other while wet and left outside during a cold winter night at 15°C. The next day, a worker needs one of the plates, but the plates are stuck together because the freezing of the water between the two plates has bonded them together. In an effort to melt the ice between the plates and separate them, the worker takes a large hairdryer and blows hot air at 50°C all over the exposed surface of the plate on the top. The convection heat transfer coefficient at the top surface is estimated to be 40 W/m² · °C. Determine how long the worker must keep blowing hot air before the two plates separate.
Correct
482 s
Incorrect
482 s