Fundamentals of Momentum, Heat and Mass Transfer, 6th Edition International Student Version - Chapter 14

14.1 An asbestos pad is square in cross section, measuring 5 cm on a side at its small end, increasing linearly to 10 cm on a side at the large end. The pad is 15 cm high. If the small end is held at 600 K and the large end at 300 K, what heat-flow rate will be obtained if the four sides are insulated? Assume one-dimensional heat conduction. The thermal conductivity of asbestos may be taken as 0.0173 W/m · K.
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14.2 A sheet of insulating material, with thermal conductivity of 0.22 W/m · K, is 2 cm thick and has a surface area of 2.97 m2. If 4 kW of heat are conducted through this sheet and the outer (cooler) surface temperature is measured at 55°C (328 K), what will be the temperature on the inner (hot) surface?
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14.3 Plate glass, k = 1.35 W/m · K, initially at 850 K, is cooled by blowing air past both surfaces with an effective surface coefficient of 5 W/m2 · K. It is necessary, in order that the glass not crack, to limit the maximum temperature gradient in the glass to 15 K/cm during the cooling process. At the start of the cooling process, what is the lowest temperature of the cooling air that can be used?
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14.4 The heat loss from a boiler is to be held at a maximum of 900 Btu/h ft2 of wall area. What thickness of asbestos (k = 0.10 Btu/h ft °F) is required if the inner and outer surfaces of the insulation are to be 1600 and 500°F, respectively?
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14.5 A composite wall is to be constructed of 1/4-in. stainless steel (k = 10 Btu/h ft °F), 3 in. of corkboard (k = 0.025 Btu/h ft °F) and 1/2 in. of plastic (k = 1.5 Btu/h ft °F).
a. Draw the thermal circuit for the steady-state conduction through this wall.
b. Evaluate the individual thermal resistance of each material layer.
c. Determine the heat flux if the steel surface is maintained at 250°F and the plastic surface held at 80°F.
d. What are the temperatures on each surface of the corkboard under these conditions?

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14.6 A 1-in.-thick steel plate measuring 10 in. in diameter is heated from below by a hot plate, its upper surface exposed to air at 80°F. The heat-transfer coefficient on the upper surface is 5 Btu/h ft °F and k for steel is 25 Btu/h ft °F.
a. How much heat must be supplied to the lower surface of the steel if its upper surface remains at 160°F? (Include radiation.)
b. What are the relative amounts of energy dissipated from the upper surface of the steel by convection and radiation?

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14.7 A 0.20-m-thick brick wall (k = 3W/m · K) separates the combustion zone of a furnace from its surroundings at 25°C. For an outside wall surface temperature of 100°C, with a convective heat-transfer coefficient of 18 W/m2 · K, what will be the inside wall surface temperature at steady-state conditions?
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14.8 The solar radiation incident on a steel plate 2 ft square is 400 Btu/h. The plate is 1.4 in. thick and lying horizontally on an insulating surface, its upper surface being exposed to air at 90°F. If the convective heat-transfer coefficient between the top surface and the surrounding air is 4 Btu/h ft °F, what will be the steady-state temperature of the plate?
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14.9 The freezer compartment in a conventional refrigerator can be modeled as a rectangular cavity 0.3mhigh and 0.25mwide with a depth of 0.5 m. Determine the thickness of styrofoam insulation (k = 0.30 W/m · K) needed to limit the heat loss to 400 W if the inner and outer surface temperatures are –10 and 33°C, respectively.
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14.10 The cross section of a storm window is shown in the sketch. How much heat will be lost through a window measuring 1.83 m by 3.66 m on a cold day when the inside and outside air temperatures are, respectively, 295 and 250 K? Convective coefficients on the inside and outside surfaces of the window are 20 and 15 W/m2 · K, respectively. What temperature drop will exist across each of the glass panes? What will be the average temperature of the air between the glass panes?...
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14.11 The outside walls of a house are constructed of a 4-in. layer of brick, 1/2 in. of celotex, an air space ... in: thick, and 1/4 in. of wood panelling. If the outside surface of the brick is at 30°F and the inner surface of the panelling at 75°F, what is the heat flux if
a. the air space is assumed to transfer heat by conduction only?
b. the equivalent conductance of the air space is 1.8 Btu/h ft2 °F?
c. the air space is filled with glass wool?
kbrick = 0:38 Btu/h ft °Fkcelotex = 0.028 Btu/h ft °Fkair = 0.015 Btu/h ft °Fkwood = 0.12 Btu/h ft °Fkwool = 0.025 Btu/h ft °F
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14.12 Determine the heat-transfer rate per square meter of wall area for the case of a furnace with inside air at 1340 K. The furnace wall is composed of a 0.106-m layer of fireclay brick and a 0.635-cm thickness of mild steel on its outside surface. Heat transfer coefficients on inside and outside wall surfaces are 5110 and 45 W/m2 · K, respectively; outside air is at 295 K. What will be the temperatures at each surface and at the brick-steel interface?
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14.13 A 4-in.-OD pipe is to be used to transport liquid metals and will have an outside surface temperature of 1400°F under operating conditions. Insulation is 6 in. thick and has a thermal conductivity expressed as...where k is in Btu/h ft °F and T is in °F, is applied to the outside surface of the pipe.
a. What thickness of insulation would be required for the outside insulation temperature to be no higher than 300°F?
b. What heat-flow rate will occur under these conditions?

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14.14 A 1-in.-nominal-diameter steel pipe with its outside surface at 400°F is located in air at 90°F with the convective heat-transfer coefficient between the surface of the pipe and the air equal to 1.5 Btu/h ft °F. It is proposed to add insulation having a thermal conductivity of 0.06 Btu/h ft °F to the pipe to reduce the heat loss to one-half that for the bare pipe. What thickness of insulation is necessary if the surface temperature of the steel pipe and ho remain constant?
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14.15 Liquid nitrogen at 77 K is stored in a cylindrical container having an inside diameter of 25 cm. The cylinder is made of stainless steel and has a wall thickness of 1.2 cm. Insulation is to be added to the outside surface of the cylinder to reduce the nitrogen boil-off rate to 25% of its value without insulation. The insulation to be used has a thermal conductivity of 0.13 W/m · K. Energy loss through the top and bottom ends of the cylinder may be presumed negligible.Neglecting radiation effects, determine the thickness of insulation when the inner surface of the cylinder is at 77 K, the convective heat-transfer coefficient at the insulation surface has a value of 12 W/m2 · K, and the surrounding air is at 25°C.
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