Fundamentals of Heat and Mass Transfer
7th Edition
ISBN: 9780470917855
Author: Bergman, Theodore L./
Publisher: John Wiley & Sons Inc
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Chapter 12, Problem 12.114P
A contractor must select a roof covering material from the two diffuse, opaque coatings with
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The last portion asks you for "net radiant heat flux to the surface", meaning that positive net radiative heat flux means in and negative net radiative heat flux means out. This is opposite the typical sign convention - be aware of this
as fast as.
The spectral, hemispherical absorptivity of an opaque surface and the spectral distribution of radiation incident on the surface are as
shown.
Assume that a₁ = 0.8.
xx
α
0
0
2
4
6
λ (μm)
What is the total, hemispherical absorptivity of the surface?
α =
i
G₂(W/m².μm)
5000
2
4
6
λ (um)
If it is assumed that ε = α and that the surface is at 900 K, what is its total, hemispherical emissivity?
8 = i
What is the net radiant heat flux to the surface, in W/m²?
qad.net =
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Chapter 12 Solutions
Fundamentals of Heat and Mass Transfer
Ch. 12 - Consider an opaque horizontal plate that is well...Ch. 12 - A horizontal, opaque surface at a steady-state...Ch. 12 - The top surface of an L=5mmthick anodized aluminum...Ch. 12 - A horizontal semitransparent plate is uniformly...Ch. 12 - What is the irradiation at surfaces A2 , A3 , and...Ch. 12 - According to its directional distribution, solar...Ch. 12 - Solar radiation incident on the earth’s surface...Ch. 12 - On an overcast day the directional distribution of...Ch. 12 - During radiant heat treatment of a thin-film...Ch. 12 - A small radiant heat source of area A1=2x104m2...
Ch. 12 - Determine the fraction of the total, hemispherical...Ch. 12 - The spectral distribution of the radiation emitted...Ch. 12 - Consider a 5-mm-square, diffuse surface A0 having...Ch. 12 - Assuming blackbody behavior, determine the...Ch. 12 - The dark surface of a ceramic stove top may be...Ch. 12 - The energy flux associated with solar radiation...Ch. 12 - A small flat plate is positioned just beyond the...Ch. 12 - A spherical aluminum shell of inside diameter D=2m...Ch. 12 - The extremely high temperatures needed to trigger...Ch. 12 - An enclosure has an inside area of 100m2 , and its...Ch. 12 - Assuming the earth’s surface is black, estimate...Ch. 12 - A proposed method for generating electricity from...Ch. 12 - Approximations to Planck’s law for the spectral...Ch. 12 - Estimate the wavelength corresponding to maximum...Ch. 12 - A furnace with a long, isothermal, graphite tube...Ch. 12 - Isothermal furnaces with small apertures...Ch. 12 - For materials A and B, whose spectral...Ch. 12 - A small metal object, initially at Ti=1000K ,is...Ch. 12 - The directional total emissivity of nonmetallic...Ch. 12 - Consider the metallic surface of Example 12.7....Ch. 12 - The spectral, directional emissivity of a diffuse...Ch. 12 - Consider the directionally selective surface...Ch. 12 - A sphere is suspended in air in a dark room and...Ch. 12 - Estimate the total, hemispherical emissivity for...Ch. 12 - Sheet steel emerging from the hot roll section of...Ch. 12 - A large body of nonluminous gas at a temperature...Ch. 12 - An opaque surface with the prescribed spectral,...Ch. 12 - The spectral reflectivity distribution for white...Ch. 12 - A diffuse, opaque surface at 700 K has spectral...Ch. 12 - The spectral, hemispherical absorptivity of an...Ch. 12 - The spectral, hemispherical absorptivity of an...Ch. 12 - Consider an opaque, diffuse surface for which the...Ch. 12 - Radiation leaves a furnace of inside surface...Ch. 12 - The spectral transmissivity of a 1-mm-thick layer...Ch. 12 - The spectral transmissivity of plain and tinted...Ch. 12 - Referring to the distribution of the spectral...Ch. 12 - The spectral absorptivity and spectral...Ch. 12 - Consider a large furnace with opaque, diffuse,...Ch. 12 - Four diffuse surfaces having the spectral...Ch. 12 - The spectral transmissivity of a 50m -thick...Ch. 12 - An opaque, horizontal plate has a thickness of...Ch. 12 - Two small surfaces, A and B, are placed inside an...Ch. 12 - Consider an opaque, diffuse surface whose spectral...Ch. 12 - The 50-mm peephole of a large furnace operating at...Ch. 12 - The window of a large vacuum chamber is fabricated...Ch. 12 - A thermograph is a device responding to the...Ch. 12 - A radiation thermometer is a radiometer calibrated...Ch. 12 - A radiation detector has an aperture of area...Ch. 12 - A small anodized aluminum block at 35C is heated...Ch. 12 - Consider the diffuse, gray opaque disk A1 , which...Ch. 12 - A two-color pyrometer is a device that is used to...Ch. 12 - An apparatus commonly used for measuring the...Ch. 12 - A procedure for measuring the thermal conductivity...Ch. 12 - One scheme for extending the operation of gas...Ch. 12 - The equipment for heating a wafer during a...Ch. 12 - Neglecting the effects of radiation absorption,...Ch. 12 - Consider the evacuated tube solar collector...Ch. 12 - Solar flux of 900W/m2 is incident on the top side...Ch. 12 - Consider an opaque, gray surface whose directional...Ch. 12 - A contractor must select a roof covering material...Ch. 12 - It is not uncommon for the night sky temperature...Ch. 12 - Plant leaves possess small channels that connect...Ch. 12 - In the central receiver concept of solar energy...Ch. 12 - Radiation from the atmosphere or sky can be...Ch. 12 - A thin sheet of glass is used on the roof of a...Ch. 12 - Growers use giant fans to prevent grapes from...Ch. 12 - A circular metal disk having a diameter of 0.4 m...Ch. 12 - The neighborhood cat likes to sleep on the roof of...Ch. 12 - The exposed surface of a power amplifier for an...Ch. 12 - Consider a thin opaque, horizontal plate with an...Ch. 12 - The oxidized-aluminum wing of an aircraft has a...Ch. 12 - Two plates, one with a black painted surface and...Ch. 12 - A radiator on a proposed satellite solar power...Ch. 12 - A radiator on a proposed satellite solar power...Ch. 12 - A spherical satellite in near-earth orbit is...Ch. 12 - An annular fin of thickness t is used as a...Ch. 12 - The directional absorptivity of a gray surface...Ch. 12 - Two special coatings are available for application...Ch. 12 - Consider the spherical satellite of Problem...Ch. 12 - A spherical capsule of 3-m radius is fired from a...Ch. 12 - Consider the spherical satellite of Problem...Ch. 12 - A solar panel mounted on a spacecraft has an area...Ch. 12 - It is known that on clear nights a thin layer of...Ch. 12 - A shallow layer of water is exposed to the natural...Ch. 12 - A roof-cooling system, which operates by...Ch. 12 - A wet towel hangs on a clothes line under...Ch. 12 - Our students perform a laboratory experiment to...
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- A tungsten filament is heated to 2700 K. At what wavelength is the maximum amount of radiation emitted? What fraction of the total energy is in the visible range (0.4to0.75m)? Assume that the filament radiates as a graybody.arrow_forward11.31 A large slab of steel 0.1 m thick contains a 0.1 -m-di- ameter circular hole whose axis is normal to the surface. Considering the sides of the hole to be black, specify the rate of radiative heat loss from the hole. The plate is at 811 K, and the surroundings are at 300 K.arrow_forwardDetermine the total average hemispherical emissivity and the emissive power of a surface that has a spectral hemispherical emissivity of 0.8 at wavelengths less than 1.5m, 0.6 at wavelengths from 1.5to2.5m, and 0.4 at wavelengths longer than 2.5m. The surface temperature is 1111 K.arrow_forward
- 11.68 Two infinitely large, black, plane surfaces are 0.3 m apart, and the space between them is filled by an isothermal gas mixture at 811 K and atmospheric pressure. The gas mixture consists of by volume. If one of the surfaces is maintained at 278 K and the other at 1390 K, calculate (a) the effective emissivity of the gas at its temperature, (b) the effective absorptivity of the gas to radiation from the 1390 K surface, (c) the effective absorptivity of the gas to radiation from the 278 K surface, and (d) the net rate of heat transfer to the gas per square meter of surface area.arrow_forwardDetermine the following: a. Average emissivity of both surfaces b. Absorptivity of both surfaces c. reflectivity of both surfaces d. which surface is more suitable to serve as a solar absorber?arrow_forward13.41 Consider two very large parallel plates with diffuse, gray surfaces. - T, = 1000 K, ɛ, = 1 T, = 500 K, ez = 0.8 Determine the irradiation and radiosity for the upper plate. What is the radiosity for the lower plate? What is the net radiation exchange between the plates per unit area of the plates?arrow_forward
- A large diffuse surface has spectral absorptivity of a -0.9 for à<1 jam and a=0.2 for 22 1 μm. The surface is insulated in the bottom, and exposed to two different conditions on the top: Insulated Insulated Case (2) Case (1) 6-1) Case 1): What is the value of the total hemispherical absorptivity of the large diffuse surface? Note that the sun emits approximately as a blackbody at 5800 K. Barkody Radiation Function AT AT 4000 S 051014 4.000 05720 100 000121 G40754 1.300 002134 6633767 BAY IND GOTIK 540 GA 1300 0.009341 0.700 BATZ 5.000 230 AND 0.140256 6754140 8180130 67234 280 0227697 AND 925010 AND 670129 3000 330 0316102 69217 1.400 7.40 6629927 0400607 7600 BA39102 AND 0441182 780 6-2) Case 1): The surface is exposed to the sun and G.-1200 W/m². Flowing air temperature Te is 300 K. Assuming the surface temperature of 7,- 320 K, what is the convective heat transfer coefficient? The answer should be given in the unit of W/(m²-K). 6-3) Case 2): The surface is shielded from the sun by a…arrow_forwardAn opaque surface at 1000 K if its spectral emissivity is = 0.4, 0.7, and 0.3 for 0 < < 2 µm, 2μm < 6 μm, and 6umarrow_forwardA large diffuse surface has spectral absorptivity of a=0.9 for 2 <1 jam and a=0.2 for 22 1 m. The surface is insulated in the bottom, and exposed to two different conditions on the top: sun Insulated Insulated Case (2) Case (1) 6-1) Case 1): What is the value of the total hemispherical absorptivity of the large diffuse surface? Note that the sun emits approximately as a blackbody at 5800 K. Blackbody Radiation Function AT AT 30 6.480677 63000 4300 0516014 600 0.000016 4000 0.379210 AND 6407554 0002134 6633747 140 5300 endy70 LND 001971 540 0.009341 5.400 0.301046 2000 5300 6.720178 230 0.066728 JOH 0.140256 ARD 6.737618 6.754140 8.180130 4227697 AND 6763199 925010 3.000 EXXION 330 0318302 6.819217 3,400 740 0.403607 7600 8.639102 7N0 6-2) Case 1): The surface is exposed to the sun and G. 1200 W/m². Flowing air temperature Te is 300 K. Assuming the surface temperature of 7,- 320 K, what is the convective heat transfer coefficient ? The answer should be given in the unit of W/(m²K). 9arrow_forward12.35 A small metal object, initially at T; = 1000 K, is cooled by radiation in a low-temperature vacuum chamber. One of two thin coatings can be applied to the object so that spectral hemispherical emissivities vary with wavelength as shown. For which coating will the object most rapidly reach a temperature of T, = 500 K? 1.0 Coating A Coating B టో 0.5 1 10 100 a (µm)arrow_forwardEat И 5000 6000 7000 2(A)arrow_forwardA proposed method for generating electricity from solar irradiation is to concentrate the irradiation into a cavity that is placed within a large container of a salt with a high melting temperature. If all heat losses are neglected, part of the solar irradiation entering the cavity is used to melt the salt while the remainder is used to power a Rankine cycle. (The salt is melted during the day and is resolidified at night in order to generate electricity around the clock.) 9R = Est-3.45 MW i Salt Tsalt = 1000°C Mirror MW qR Consider conditions for which the solar power entering the cavity is asol = 7.10 MW and the time rate of change of energy stored in the salt is Est = 3.45 MW. For a cavity opening of diameter D, = 1 m, determine the rate of heat transfer to the Rankine cycle, qr, in MW. The temperature of the salt is maintained at its melting point, Tsalt = Tm= 1000°C. Neglect heat loss by convection and irradiation from the surroundings. Sun Heliostatsarrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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