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21.2 A black solar collector, with a surface area of 60 m2, is placed on the roof of a house. Incident solar energy reaches the collector with a flux of 800 W/m2. The surroundings are considered black with an effective temperature of 30°C. The convective heat-transfer coefficient between the collector and the surrounding air, at 30°C, is 35 W/m · K. Neglecting any conductive loss from the collector, determine
a. The net radiant exchange between the collector and its surroundings
b. The equilibrium temperature of the collector
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21.3 A tungsten filament, radiating as a gray body, is heated to a temperature of 4000°R. At what wavelength is the emissive power maximum? What portion of the total emission lies within the visible-light range, 0.3 to 0.75 μm?
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21.4 The filament of an ordinary 100 W light bulb is at 2910 K and it is presumed to be a black body. Determine (a) the wavelength of maximum emission and (b) the fraction of emission in the visible region of the spectrum.
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21.5 The distribution of solar energy incident on Earth can be approximated as being from a black body at 5800 K.Two kinds of glass, plain and tinted, are being considered for use in windows. The spectral transmissivity for these two glasses is approximated as...Compare the fraction of incident solar energy transmitted through each material.Compare the fraction of visible radiant energy transmitted through each.
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21.6 The sun’s temperature is approximately 5800 K and the visible light range is taken to be between 0.4 and 0.7 mm. What fraction of solar emission is visible? What fraction of solar emission lies in the ultraviolet range? The infrared range? At what wavelength is solar emissive power a maximum?
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21.7 A furnace that has black interior walls maintained at 1500 K contains a peephole with a diameter of 10 cm. The glass in the peephole has a transmissivity of 0.78 between 0 and 3.2 μm and 0.08 between 3.2 μm and ∞. Determine the heat lost through the peephole.
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21.8 A large cavity with a small opening, 0.0025 m2 in area, emits 8 W. Determine the wall temperature of the cavity.
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21.9 A 7.5-cm-diameter hole is drilled in a 10-cm-thick iron plate. If the plate temperature is 700 K and the surroundings are at 310 K, determine the energy loss through the hole. The hole sides may be considered to be black.
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21.10 A cryogenic fluid flows in a 20-mm-diameter tube with an outer surface temperature of 75 K and an emissivity of 0.2. A larger tube, having a diameter of 50 mm, is concentric with the smaller one. This larger tube is gray, with ε = 0.05 and its surface temperature is 300 K. The intervening space between the two tubes is evacuated.Determine the heat gain by the cryogenic fluid, in watts per meter of tube length.Evaluate the heat gain per meter of length if there is a thin- walled radiation shield placed midway between the two tubes. The shield surfaces may be considered gray and diffuse with an emissivity of 0.04 on both sides.
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21.11 A heating element in the shape of a cylinder is maintained at 2000°F and placed at the center of a half-cylindrical reflector as shown. The rod diameter is 2 in. and that of the reflector is 18 in. The emissivity of the heater surface is 0.8, and the entire assembly is placed in a room maintained at 70°F. What is the radiantenergy loss from the heater per foot of length? How does this compare to the loss from the heater without the reflector present?...
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21.12 The circular base of the cylindrical enclosure shown may be considered a reradiating surface. The cylindrical walls have an effective emissivity of 0.80 and are maintained at 540°F. The top of the enclosure is open to the surroundings, which are maintained at 40°F. What is the net rate of radiant transfer to the surroundings?...
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21.13 A room measuring 12 ft by 20 ft by 8 ft high has its floor and ceiling temperatures maintained at 85°F and 65°F, respectively. Assuming the walls to be reradiating and all surfaces to have an emissivity of 0.8, determine the net-energy exchange between the floor and ceiling.
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21.14 A cylindrical cavity is closed at the bottom and has an opening centered in the top surface. A cross section of this configuration is shown in the sketch. For the conditions stated below, determine the rate of radiant energy passing through the 5-mm-diameter cavity opening. What will be effective emissivity of the opening?
a. All interior surfaces are black at 600 K....
b. The bottom surface is diffuse-gray with ε = 0.6, and has a temperature of 600 K. All other surfaces are reradiating.
c. All interior surfaces are diffuse-gray with ε = 0.6 and are at a uniform temperature of 600 K.
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21.15 Two parallel black rectangular surfaces, whose back sides are insulated, are oriented parallel to each other with a spacing of 5 m. They measure 5mby 10 m. The surroundings are black at 0 K. The two surfaces are maintained at 200 and 100 K, respectively. Determine the following:
a. The net radiant heat transfer between the two surfaces
b. The net heat supplied to each surface
c. The net heat transfer between each surface and the surroundings
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21.16 Two parallel rectangles have emissivities of 0.6 and 0.9, respectively. These rectangles are 1.2 m wide and 2.4 m high and are 0.6 m apart. The plate having ε = 0.6 is maintained at 1000 K and the other is at 420 K. The surroundings may be considered to absorb all energy that escapes the two-plate system. Determine
a. The total energy lost from the hot plate
b. The radiant-energy interchange between the two plates
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21.17 Two disks are oriented on parallel planes separated by a distance of 10 in., as shown in the accompanying figure. The disk to the right is 4 in. in diameter and is at a temperature of 500°F. The disk to the left has an inner ring cut out such that it is annular in shape with inner and outer diameters of 2.5 in. and 4 in., respectively. The disk surface temperature is 210°F. Find the heat exchange between these disks if
a. they are black...
b. they are gray e1 . 0.6, e2 . 0. 3
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21.18 A heavily oxidized aluminum surface at 755 K is the source of energy in an enclosure, which radiantly heats the side walls of a circular cylinder surface as shown, to 395 K. The side wall is made of polished stainless steel. The top of the enclosure is made of fire clay brick and is adiabatic. For purposes of calculation, assume that all three surfaces have uniform temperatures and that they are diffuse and gray. Evaluate the heat transfer to the stainless steel surface....
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21.19 A small (1/4-in.-diameter × 1 in. long) metal test specimen is suspended by very fine wires in a large evacuated tube. The metal is maintained at a temperature of 2500°F, at which temperature it has an emissivity of approximately 0.2. The watercooled walls and ends of the tube are maintained at 50°F. In the upper end is a small (1/4-in. diameter) silica glass viewing port. The inside surfaces of the steel tube are newly galvanized. Room temperature is 70°F. Estimate
a. The view factor from the specimen to the window...
b. The total net heat-transfer rate by radiation from the test specimen
c. The energy radiated through the viewing port
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21.20 A gas consisting of 20%CO2 and 80% oxygen and nitrogen leaves a lime kiln at 2000°F and enters a square duct measuring 6 in. by 6 in. in cross section. The specific heat of the gas is 0.28 Btu/lbm °F, and it is to be cooled to 1000°F in the duct, whose inside surface is maintained at 800°F, and whose walls have an emissivity of 0.9. The mass velocity of the kiln gas is 0.4 lbm/ft2 · s and the convective heat-transfer coefficient between the gas and duct walls is 1.5 Btu/h ft2 °F.
a. Determine the required length of duct to cool the gas to 1000°F.(Courtesy of the American Institute of Chemical Engineers.)Hint. As the response of the gas to emission and absorption of radiant energy differs, an approximation for the radiantenergy exchange between the enclosure and gas contained within an arbitrary control volume is given by AwFw−gσεw(εgTg4 − αgTw4).
b. Determine the ratio of radiant-energy transfer to that by convection.
c. At what temperature would the gas leave the duct if the length of the duct were twice the value determined in part (a)?
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