a. the 16-cm dimension verticalb. the 10-cm dimension vertical
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19.2 A 2-in. copper cylinder, 6 in. in length, at a uniform temperature of 200°F, is plunged vertically into a large tank of water at 50°F.
a. How long will it take for the outside surface of the cylinder to reach 100°F?
b. How long will it take for the center of the cylinder to reach 100°F?
c. What is the surface temperature when the center temperature is 100°F? Heat transfer from ends of the cylinder may be neglected.
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19.3 A fluorescent light bulb, rated at 100 W, is illuminated in air at 25°C and atmospheric pressure. Under these conditions the surface temperature of the glass is 140°C.Determine the rate of heat transfer from the bulb by natural convection. The bulb is cylindrical, having a diameter of 35 mm and a length of 0.8 m, and is oriented horizontally.
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19.4 Determine the steady-state surface temperature of an electric cable, 25 cm in diameter, which is suspended horizon- tally in still air in which heat is dissipated by the cable at a rate of 27 W per meter of length. The air temperature is 30°C.
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19.5 A copper cylinder 20.3 cm long with a diameter of 2.54 cm is being used to evaluate the surface coefficient in a laboratory experiment. When heated to a uniform temperature of 32.5°C and then plunged into a –1°C liquid bath, the center temperature of the cylinder reaches a value of 4.8°C in 3 min. Assuming the heat exchange between the cylinder and water bath to be purely by convection, what value for the surface coefficient is indicated?
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19.6 Rubber balls are molded into spheres and cured at 360 K. Following this operation they are allowed to cool in room air. What will be the elapsed time for the surface temperature of a solid rubber ball to reach 320 K when the surrounding air temperature is 295 K? Consider balls with diameters of 7.5, 5, and 1.5 cm. Properties of rubber that may be used are k = 0.24 W/m · K, ρ = 1120 kg/m3, cp = 1020 J/kg · K.
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19.7 A 1-in., 16-BWG copper tube has its outside surface maintained at 240°F. If this tube is located in still air at 60°F, what heat flux will be achieved if the tube is oriented
a. horizontally?The tube length is 10 ft.
b. vertically?
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19.8 A 0.6-m-diameter spherical tank contains liquid oxygen at 78 K. This tank is covered with 5 cm of glass wool. Determine the rate of heat gain if the tank is surrounded by air at 278 K. The tank is constructed of stainless steel 0.32 cm thick.
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19.9 A solar energy collector measuring 20 × 20 ft is installed on a roof in a horizontal position. The incident solar energy flux is 200 Btu/h ft2, and the collector surface temperature is 150°F. What fraction of incident solar energy is lost by convection to the stagnant surrounding air at a temperature of 50°F? What effect on the convective losses would result if the collector were criss- crossed with ridges spaced 1 ft apart?
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19.10 Copper wire with a diameter of 0.5 cm is covered with a 0.65-cm layer of insulating material having a thermal conductivity of 0.242 W/m · K. The air adjacent to the insula- tion is at 290 K. If the wire carries a current of 400 A, determine
a. the convective heat-transfer coefficient between the insulation surface and the surrounding air
b. the temperatures at the insulation-copper interface and at the outside surface of the insulation
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19.11 A cooking oven has a top surface temperature of 45°C when exposed to still air. At this condition the inside oven temperature and room air temperature are 180°C and 20°C, respectively, and heat is transferred from the top surface at 40 W.To reduce the surface temperature, as required by safety regulations, room air is blown across the top with a velocity of 20 m/s. Conditions inside the oven may be considered unchanged.
a. What will be the rate of heat loss under this new operating condition?
b. What will be the top surface temperature?
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19.12 A “hot stage” for a manufacturing process is shown in the accompanying figure, where a slab of stainless steel is mounted on top of an electrical resistance heater. The stainless steel slab is 20 cm wide, 60 cm long, and 2 cm thick. A load material, which is placed on top of the stainless steel hot plate, requires a power input of 600 W. The dimensions of the load material are 20 cm in width, 60 cm in length (in the direction of air flow), and 0.5 cm thick. The surface temperature of the load material exposed to the air is measured to be Ts = 207°C (480 K). The air flow has a bulk velocity of 3 m/s, and the ambient temperature of the air is
a. Estimate the heat loss from the surface of load material, in Watts....
b. What is the total power output, in Watts, required for the heater, assuming there are no heat-transfer losses from the sides of the plate?
c. What is the temperature at the interface between the stainless steel hot stage and the load material?
d. What is the estimated temperature at the base of the hot stage in contact with the electrical resistance heater (T2)?
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19.13 Saturated steam at 0.1 bar condenses on the outside of a copper tube having inner and outer diameters of 16.5 and 19 mm, respectively. The surface coefficients on the inner (water) sur- face and outer (steam) surface are 5200 and 6800 W/m2 · K, respectively.When the mean water temperature is 28 K, estimate the rate of steam condensed per meter of tube length. The latent heat of condensation of steam may be taken as 2.390 kJ/kg.
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19.14 A 1-in., 16-BWG copper tube, 10 ft long, has its outside surface maintained at 240°F. Air at 60°F and atmospheric pressure is forced past this tube with a velocity of 40 fps. Determine the heat flux from the tube to the air if the flow of air is
a. parallel to the tubeb. normal to the tube axis
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19.15 An electric light bulb rated at 60 W has a surface temperature of 145°C when cooled by atmospheric air at 25°C. The air flows past the bulb with a velocity of 0.5 m/s. The bulb can be modeled as a sphere with a diameter of 7.5 cm. Determine the heat transfer from the bulb by the mechanism of forced convection.
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19.16 We are interested in predicting the time it will take for popcorn kernels to pop in a fluidized bed. The superficial air velocity inside the bed is 3 m/s, which is above the minimum fluidization velocity for popcorn kernels. The air temperature is maintained constant at 520 K (247°C) by heating coils placed around the fluidization vessel. The average diameter of the popcorn kernels is 0.5 cm. When the temperature of a kernel reaches 175°C, it will pop. At 25°C, the thermal conductivity of popcorn is 0.2 W/m · K, the specific heat is 2000 J/kg · K, and the density is 1300 kg/m3.
a. What is the convective heat-transfer coefficient for air flow around each popcorn kernel?
b. What is the Biot number for a popcorn kernel? Is a lumped- parameter model valid?
c. If we assume that the popcorn kernel pops when its center- line temperature reaches 175°C, how long after entering the bed will it take for the popcorn kernel to pop? Initially, the popcorn kernels are at 25°C.
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19.17 A hot-wire anemometer is a common instrument used to measure the velocity of a flowing gas. A typical probe tip is shown below.Electrical current is passed through a very thin wire of platinum or tungsten. The electrical resistance of the wire generates heat as the current passes through it, making the wire hot. This “hot wire” is placed normal to the flowing gas stream and the heat generated by the wire is dissipated to the gas stream flowing around the wire by convective heat transfer. The current passing through the wire and temperature of the wire are measured, and, from this information, the velocity of the gas flowing over the wire is estimated.In the current set of measurements, the hot-wire anemometer is mounted inside a tube containing flowing N2 gas at 20°C. During one test, the power load on the wire was 13 mW, and the temperature of the wire was 200°C. The diameter of the platinum wire is 4 μm, and its length is 1.2 mm.
a. What is the Prandtl number for the N2 gas flowing around the hot wire?Thermophysical properties of N2 gas
b. What is the measured Nusselt number (Nu) for the N2 gas flowing around the hot wire?
c. What is the estimated velocity of the flowing N2 gas inside the tube at the point where the hot-wire anemometer probe tip is located?
| Temperature (°C) | Density, ρ (kg/m3) | Viscosity, μ (kg/m-sec) | Heat Capacity, Cp(J/kg · K) | Thermal Conductivity, k(W/m•K) |
| 350 | 0.9754 | 2.0000 × 10–5 | 1042.1 | 0.029691 |
| 400 | 0.8533 | 2.19950 × 10–5 | 1049.9 | 0.033186 |
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19.18 An industrial heater is composed of a tube bundle consisting of horizontal 3/8-in.-OD tubes in a staggered array with tubes arranged in equilateral triangle fashion having a pitchto- diameter ratio of 1.5. If water at 160°F flows at 20 ft/s past the tubes with constant surface temperature of 212°F, what will be the effective heat-transfer coefficient?
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19.19 A tube bank employs an in-line arrangement with ST=SL =3.2 cm and tubes that are 1.8 cm in outside diameter. There are 10 rows of tubes, which are held at a surface temperature of 85°C. Air at atmospheric pressure and 20°C flows normal to the tubes with a free-stream velocity of 6 m/s. The tube bank is 10 rows deep, and the tubes are 1.8 m long. Determine the amount of heat transferred.
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19.20 A tube bank employs tubes that are 1.30 cm in outside diameter at ST = SL = 1.625 cm. There are eight rows of tubes, which are held at a surface temperature of 90°C. Air, at atmo- spheric pressure and a bulk temperature 27°C, flows normal to the tubes with a free-stream velocity of 1.25 m/s. The tube bank is eight rows deep, and the tubes are 1.8 m long. Estimate the heat-transfer coefficient.
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19.21 Air at 60°F and atmospheric pressure flows inside a 1-in., 16-BWG copper tube whose surface is maintained at 240°F by condensing steam. Find the temperature of the air after passing through 20 ft of tubing if its entering velocity is 40 fps.
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19.22 When the valve on the water line in Problem 20.38 is opened wide, the water velocity is 35 fps. What is the heat loss per 5 ft of water line in this case if the water and pipe temperatures are the same as specified in Problem 20.38?Problem 20.38A tube bank employs tubes that are 1.30 cm in outside diameter at ST = SL = 1.625 cm. There are eight rows of tubes, which are held at a surface temperature of 90°C. Air, at atmo- spheric pressure and a bulk temperature 27°C, flows normal to the tubes with a free-stream velocity of 1.25 m/s. The tube bank is eight rows deep, and the tubes are 1.8 m long. Estimate the heat-transfer coefficient.
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19.23 Oil at 300 K is heated by steam condensing at 372 K on the outside of steel pipes with ID = 2.09 cm, OD = 2.67 cm. The oil flow rate is 1.47 kg/s; six tubes, each 2.5 m long, are used. The properties of oil to be used are as follows:
| T, K | ρ, kg/m3 | cp, J/kg · K | k, W/m · K | μ, Pa · s |
| 300 | 910 | 1.84 × 103 | 0.133 | 0.0414 |
| 310 | 897 | 1.92 × 103 | 0.131 | 0.0228 |
| 340 | 870 | 2.00 × 103 | 0.130 | 7.89 10–3 |
| 370 | 865 | 2.13 × 103 | 0.128 | 3.72 10–3 |
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19.24 An apparatus, used in an operating room to cool blood, consists of a coiled tube that is immersed in an ice bath. Using this apparatus, blood, flowing at 0.006 m3/h, is to be cooled from 40°C to 30°C. The inside diameter of the tube is 2.5 mm, and the surface coefficient between the ice bath and outer tube surface is 500 W/m2 · K. The thermal resistance of the tube wall may be neglected.Determine the required length of tubing to accomplish the desired cooling. Properties of blood are the following:r = 1000 kg/m2k = 0.5 W=m · Kcp = 4.0 kJ=kg · Kv = 7 10–7 m2/sDetermine the total heat transfer to the oil and its temperature at the heater exit.
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19.25 A system for heating water with an inlet temperature of 25°C to an exiting temperature of 70°C involves passing the water through a thick-walled tube with inner and outer diameters of 25 and 45 mm, respectively. The outer tube surface is well insulated, and the electrical heating within the tube wall provides for a uniform generation of ... = 1.5 × 106 W/m3.
a. For a mass flow rate of water, ... = 0.12 kg/s, how long must the tube be to achieve the desired outlet temperature?
b. If the inner surface of the tube at the outlet is Ts = 110°C, what is the local convective coefficient at this location?
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19.26 Air is transported through a rectangular duct measuring 2 ft by 4 ft.The air enters at 120°Fandflows with amass velocity of 6 lbm/s · ft2. If the duct walls are at a temperature of 80°F, how much heat is lost by the air per foot of duct length? What is the corresponding temperature decrease of the air per foot?
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19.27 Air, at 322 K, enters a rectangular duct with a mass velocity of 29.4 kg/s · m2. The duct measures 0.61 m by 1.22 m and its walls are at 300 K.Determine the rate of heat loss by the air per meter of duct length and the corresponding decrease in air temperature per meter.
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19.28 Compressed natural gas is fed into a small underground pipeline having an inside diameter of 5.9 in. The gas enters at an initial temperature of 120°C and constant pressure of 132.3 psig. The metered volumetric flow rate at standard pressure of 14.7 psia and standard temperature of 25°C is 195.3 ft3/min. The ground temperature is constant at 15°C, as it serves as an “infinite sink” for heat transfer.
a. Show that the mass flow rate is 0.0604 kg/sec, volumetric flow rate is 0.01 m3/sec at 50°C and 10 atm, the total system pressure is 10 atm, and the gas density, assuming ideal gas behavior, is 6.04 kg/m3 at 50°C. Other properties (not dependent on pressure) for methane at 50°C are k = 0.035W/m · K, Cp =220 J/kg · K, and m = 1.2 10–5 kg/m-sec.
b. Develop an energy balance model to predict the steady-state temperature profile of the natural gas in the pipe.
c. Is the gas flow laminar, or turbulent?
d. What are the Prandtl, Nusselt, and Stanton numbers for methane in the pipe? What is a reasonable average temperature for estimation the thermophysical properties?
e. What is the heat-transfer coefficient for methane in the pipe?
f. Finally, how far from the pipe entrance will the methane gas reach a temperature of 50°C? How much heat is transferred at this point?
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19.29 Consider a continuous-flow device described below used to pasteurize liquid milk, whose properties approach those of water. Milk at 20°C enters a preheater tube at a volumetric flow rate of 6 L/min. The inner diameter of the tube is 1.5 cm. The tube winds through a steam chest, which heats the milk. The outer tube wall temperature is maintained at 115°C using pressurized steam. Since the thermal conductivity through the metal is high, the temperature difference across the wall is small, so it may be assumed that the inside wall temperature is also at 115°C. The heated milk then enters an adiabatic holding tube, which provides sufficient fluid residence time so that most of the microorganisms in the milk are destroyed at ∼70°C.
a. Develop an energy-balance model to predict the steady-state temperature profile of the milk as it moves down the pipe.
b. Is the milk in turbulent or laminar flow?
c. What are the Prandtl, Nusselt, and Stanton numbers for milk in the pipe? What is the film temperature to be used for estimating thermophysical properties? What is the average heat-transfer coefficient for the milk flowing inside the tube?
d. How long must the tube be to achieve the exit temperature of 70°C?
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