Fundamentals of Momentum, Heat and Mass Transfer, 6th Edition International Student Version - Chapter 17

17.1 An electrical system employs fuses that are cylindrical in shape and have lengths of 0.5 cm and diameters of 0.1 mm. Air, at 30°C, surrounds a fuse with a surface coefficient of 10 W/m2 · K. The fuse material melts at 900°C.Assuming all heat transfer to be from the fuse surface, estimate the time it will take for the fuse to blow after a current of 3 A flows through it.Pertinent properties of the fuse material are
Resistance = 0.2 Ωk = 20 W = m · Kα = 5 × 10–5 m2/s

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17.2 Cast-iron cannonballs used in the War of 1812 were occasionally heated for some extended time so that, when fired at houses or ships, they would set them afire. If one of these, the so-called “hot shot,” were at a uniform temperature of 2000°F, how long after being exposed to air at 0°F with an outside convective heat-transfer coefficient of 16 Btu/h ft2 °F, would be required for the surface temperature to drop to 600°F? What would be the center temperature at this time? The ball diameter is 6 in. The following properties of cast iron may be used:
k = 23 Btu/h ft °Fcp = 0.10 Btu/lbm °Fρ = 460 lbm/ft3.

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17.3 A copper cylinder with a diameter of 3 in. is initially at a uniform temperature of 70°F. How long after being placed in a medium at 1000°F with an associated convective heat-transfer coefficient of 4 Btu/h ft2 °F will the temperature at the center of the cylinder reach 500°F, if the height of the cylinder is (a) 3 in.? (b) 6 in.? (c) 12 in.? (d) 24 in.? (e) 5 ft?
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17.4 Water, initially at 40°F, is contained within a thin-walled cylindrical vessel having a diameter of 18 in. Plot the temperature of the water vs. time up to 1 h if the water and container are immersed in an oil bath at a constant temperature of 300°F. Assume that the water is well stirred and that the convective heat-transfer coefficient between the oil and cylindrical surface is 40 Btu/h ft2 °F. The cylinder is immersed to a depth of 2 ft.
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17.5 Buckshot, 0.2 in. in diameter, is quenched in 90°F oil from an initial temperature of 400°F. The buckshot is made of lead and takes 15 s to fall from the oil surface to the bottom of the quenching bath. If the convective heat-transfer coefficient between the lead and oil is 40 Btu/h ft2 °F, what will be the temperature of the shot as it reaches the bottom of the bath?
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17.6 A type-304 stainless steel billet, 6 in. in diameter, is passing through a 20-ft-long heat-treating furnace. The initial billet temperature is 200°F, and it must be raised to a minimum temperature of 1500°F before working. The heat-transfer coefficient between the furnace gases and the billet surface is 15 Btu/h ft2 °F, and the furnace gases are at 2300°F. At what minimum velocity must the billet travel through the furnace to satisfy these conditions?
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17.7 It is common practice to treat wooden telephone poles with tar-like materials to prevent damage by water and insects. These tars are cured into the wood at elevated temperatures and pressures.Consider the case of a 0.3-m-diameter pole, originally at 25°C, placed in a pressurized oven. It will be removed when the tar has penetrated to a depth of 10 cm. It is known that a 10-cm depth of penetration will occur when a temperature of 100°C is achieved. For an oven temperature of 380°C and h = 140 W/m2 · K, determine the time required for the pole to remain in the oven. Properties of the wooden pole arek = 0.20 W/m · Kα= 1.1 × 10–7 m2/s
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17.8 A copper bus bar is initially at 400°F. The bar measures 0.2 ft by 0.5 ft and is 10 ft long. If the edges are suddenly all reduced to 100°F, how long will it take for the center to reach a temperature of 250°F?
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17.9 Consider a hot dog to have the following dimensions and properties: diameter = 20 mm, cp = 3.35 kJ/kg · K, r = 880 kg/ m3, and k = 0.5 W/m · K. For the hot dog initially at 5°C, exposed to boiling water at 100°C, with a surface coefficient of 90 W/m2 · K, what will be the cooking time if the required condition is for the center temperature to reach 80°C?
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17.10 This problem involves using heat-transfer principles as a guide for cooking a pork roast.The roast is to be modeled as a cylinder, having its length and diameter equal to each other, with properties being those of water. The roast weighs 2.25 kg.Properly cooked, every portion of the meat should attain a minimum temperature of 95°C. If the meat is initially at 5°C and the oven temperature is 190°C, with a surface coefficient of 15 W/m2 · K, what is the minimum cooking time required?
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17.11 In the canning process, sealed cans of food are sterilized with pressurized steam in order to kill any microorganisms initially present in the food and thereby prolong the shelf life of the food. A cylindrical can of food has a diameter of 4 cm and length of 10 cm. The food material has a heat capacity of 4000 J/kg · K, a density of 1500 kg/m3, and thermal conductivity of 0.6 W/m · K. In the present process, steam, at 120°C, is used to sterilize the can. The convective heat-transfer coefficient is 60 W/m2 · K. Initially, the can and its contents are at a uniform temperature of 20°C.
a. If the heat-transfer resistance offered by the can itself is neglected, and the can ends are thermally insulated, how long will it take for the center of the can to reach a temperature of 100°C, which is sufficient to kill all microorganisms?
b. What is the required time if the ends of the can are not sealed?
c. What will be the center temperature of the can and contents after 2500 seconds have elapsed?

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17.12 Drug formulations contain an active drug dissolved in a nontoxic solution to facilitate its delivery into the body. They are often packaged into sterile syringes so that the patient can inject the drug formulation directly into the body and then throw the syringe away. Often the drug-loaded syringes are shipped by air freight to customers. There is a concern that the low temperatures associated with air freight cargo holds might promote the precipitation of the drug from solution. A certain monoclonal antibody is known to precipitate from its delivery solution at 2°C. The cargo hold in the airplane used by the air freight company is maintained at 0°C. Initially, the syringe is at a uniform temperature of 25°C. Within the current packaging environment of the syringe, the convective heat-transfer coefficient of air surrounding the syringe is 0.86 W=m2 · K. The barrel of the syringe containing the liquid is 0.70 cm inner diameter and 8 cm in length. The thermal conductivity of the solution is 0.3 W/m · K, the density is 1 g/cm3 and heat capacity is 2000 J/kg · K. The syringe wall is very thin.If the air flight is 3.5 hr in length, will the drug completely precipitate and ruin the product?
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17.13 A rocket-engine nozzle is coated with a ceramic material having the following properties: k = 1.73 Btu/h ft °F, α = 0.35 ft2 /h. The convective heat-transfer coefficient between the nozzle and the gases, which are at 3000°F, is 200 Btu/h ft2 °F. How long after start-up will it take for the temperature at the ceramic surface to reach 2700°F? What will be the temperature at a point 1/2 in. from the surface at this time? The nozzle is initially at 0°F.
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17.14 After a fire starts in a room, the walls are exposed to combustion products at 950°C. If the interior wall surface is made of oak, how long after exposure to the fire will the wood surface reach its combustion temperature of 400°C? Pertinent data are the following:...
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17.15 Soil, having a thermal diffusivity of 5.16 × 107 m2/s, has its surface temperature suddenly raised and maintained at 1100 K from its initial uniform value of 280 K. Determine the temperature at a depth of 0.25 m after a period of 5 h has elapsed at this surface condition.
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17.16 A thick wall of oak, initially at a uniform temperature of 25°C, is suddenly exposed to combustion exhaust at 800°C. Determine the time of exposure required for the surface to reach its ignition temperature of 400°C, when the surface coefficient between the wall and combustion gas is 20 W/ m2 · K.
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17.17 How long will a 1-ft-thick concrete wall subject to a surface temperature of 1500°F on one side maintain the other side below 130°F? The wall is initially at 70°F.
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17.18 A thick plate made of stainless steel is initially at a uniform temperature of 300°C. The surface is suddenly exposed to a coolant at 20°C with a convective surface coefficient of 110 W/m2 · K. Evaluate the temperature after 3 min of elapsed time at
a. the surface
b. a depth of 50 mm
Work this problem both analytically and numerically.
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17.19 One way to treat tumors that exist near the skin surface is to heat the tumor tissue, as the cellular viability of some tumor tissues is more sensitive to higher temperatures than the surrounding skin tissue. In the simplest method, a directed heat source is put in contact with the skin surface as shown in the figure. In the present treatment process shown, the tumor is approximately 3 mm (0.003 m) below the skin surface and begins to respond to thermal treatment when its temperature reaches 45°C. The surface temperature is maintained at 55.5°C (132°F). After 2 min, the patient feels discomfort, and the device is turned off. Independent measurements showed that both the skin tissue and the tumor tissue had the following thermo- physical properties: thermal conductivity, k = 0.35 W/m · K, heat capacity, = 3.8 kJ/kg · K, and density ρ = 1005 kg/m3. The body temperature before treatment was uniform at 37°C.
a. What is the thermal diffusivity of the tissue?
b. How long was the active treatment time of the tumor—i.e., how long was the tumor at a minimum of 45°C within the 2.0 min treatment time?
...
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17.20 If the temperature profile through the ground is linear, increasing from 35°F at the surface by 0.5°F per foot of depth, how long will it take for a pipe buried 10 ft below the surface to reach 32°F if the outside air temperature is suddenly dropped to 0°F. The thermal diffusivity of soil may be taken as 0.02 ft2/h, its thermal conductivity is 0.8 Btu/h ft °F, and the convective heat- transfer coefficient between the soil and the surrounding air is 1.5 Btu/h ft2 °F.
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17.21 A masonry brick wall 0.45 m thick has a temperature distribution at time, t = 0 which may be approximated by the expression T (K) = 520 + 330 sinp (x/L) where L is the wall width and x is the distance from either surface. How long after both surfaces of this wall are exposed to air at 280 K will the center temperature of the wall be 360 K? The convective coefficient at both surface of the wall may be taken as 14 W/m2 · K. What will the surface temperature be at this time?
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