Fundamentals of Heat and Mass Transfer
7th Edition
ISBN: 9780470501979
Author: Frank P. Incropera, David P. DeWitt, Theodore L. Bergman, Adrienne S. Lavine
Publisher: Wiley, John & Sons, Incorporated
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Chapter 12, Problem 12.24P
An enclosure has an inside area of
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An enclosure has an inside area of 50 m², and its inside surface is black and is maintained at a constant temperature. A small opening in
the enclosure has an area of 0.03 m². The radiant power emitted from this opening is 52 W. What is the temperature of the interior
enclosure wall, in K? If the interior surface is maintained at this temperature, but is now polished so that its emissivity is 0.15, what will
be the value of the radiant power emitted from the opening, in W?
T, =
grad =
i
K
W
Earth absorbs solar energy and radiates infrared energy. The intensity of the solar radiation incident on earth is J = 1350 Wm-2, also known as the solar constant. Assume earth’s surface (ground) temperature to be uniform at Ts, and that the ground and atmosphere are black (emissivity = 1) for infrared radiation. The radius of the earth is 6.378 x 106 m. The diagram shows the ground at the surface temperature Ts and the atmosphere, represented as a thin black layer, at temperature Ta . Suppose the atmosphere absorbs 100% of the infrared radiation emitted by the ground. Assume that the ground absorbs 47.5% of the incident solar energy, and that the atmosphere absorbs 17.5% of the incident solar energy (for a total of 65% absorbed by the planet).
Calculate the "steady state” numerical values of the earth’s ground temperature Ts and the atmospheric temperature Ta taking into account the “greenhouse effect” of atmospheric infrared absorption and emission described above.
3. Two parallel plates with a diameter of 60
cm, separated at a distance of 15 cm. The
temperature on the top surface is 4 oC and
the temperature on the bottom surface is
300 K. If all the surfaces are black, what is
the rate of heat transfer?
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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- 1.28 The sun has a radius of and approximates a blackbody with a surface temperature of about 5800 K. Calculate the total rate of radiation from the sun and the emitted radiation flux per square meter of surface area.arrow_forwardTwo large parallel plates with surface conditions approximating those of a blackbody are maintained at 816C and 260C, respectively. Determine the rate of heat transfer by radiation between the plates in W/m2 and the radiative heat transfer coefficient in W/m2K.arrow_forward11.41 Determine the steady-state temperatures of two radiation shields placed in the evacuated space between two infinite planes at temperatures of 555 K and 278 K. The emissivity of all surfaces is 0.8.arrow_forward
- 1.26 Repeat Problem 1.25 but assume that the surface of the storage vessel has an absorbance (equal to the emittance) of 0.1. Then determine the rate of evaporation of the liquid oxygen in kilograms per second and pounds per hour, assuming that convection can be neglected. The heat of vaporization of oxygen at –183°C is .arrow_forwardDetermine the rate of radiant heat emission in watts per square meter from a blackbody at (a) 15C, (b) 600C, and (c) 5700C.arrow_forward1.25 A spherical vessel, 0.3 m in diameter, is located in a large room whose walls are at 27°C (see sketch). If the vessel is used to store liquid oxygen at –183°C and both the surface of the storage vessel and the walls of the room are black, calculate the rate of heat transfer by radiation to the liquid oxygen in watts and in Btu/h.arrow_forward
- Determine 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_forwardA long wire 0.7 mm in diameter with an emissivity of 0.9 is placed in a large quiescent air space at 270 K. If the wire is at 800 K, calculate the net rate of heat loss. Discuss your assumptions.arrow_forwardThree thin sheets of polished aluminum are placed parallel to each other so that the distance between them is very small compared to the size of the sheets. If one of the outer sheets is at 280C and the other outer sheet is at 60C, calculate the temperature of the intermediate sheet and the net rate of heat flow by radiation. Convection can be ignored.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_forwardThe peak wavelength of radiation emitted by a black body at a temperature of 2000 K is 1.45 µm. If the peak wavelength of emitted radiation changes to 2.90 pm, then the temperature (in K) of the black body isarrow_forwardAn electric hot plate is placed in a room which is maintained at a temperature of 297 K. The plate is maintained at a temperature of 403 K and has an emissivity of 0.8. If the plate surface resembles a circular disc of diameter 250 mm, electrical power consumed by the hot plate will be?arrow_forward
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