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 12.22P
A spherical aluminum shell of inside diameter
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Irradiation on a semi-transparent medium is at a rate of 640 W/m². If 160
W/m² of the irradiation is reflected from the medium and 130 W/m² is
transmitted through the medium,
Determine the absorptivity of the medium.
The absorptivity of the medium is
0.75
X
Two parallel gray planes that are very large have emissivities of ε1 = 0.8 and ε2 = 0.7; surface 1 is at 1100°F (866.5 K) and surface 2 is at 600°F (588.8 K). Use SI units for the following:
(a) What is the net radiation from 1 to 2?
(b) If the surfaces are both black, what is the net radiation?
as fast as.
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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- 11.31 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_forward1. For an opaque surface, the absorptivity (a) , transmissivity (T) and reflectivity (p) are related by the equation : (A) a + p= T (B) α +ρ +t+ 1 (C) a + p = 1 (D) α +ρ = 0arrow_forwardTwo concentric spheres of diameter D = 0.8 m and D2 = 1.2 m are separated by an air space and have surface temperatures of T = 400 K and T2 = 300 K. (a) If the surfaces are black, what is the net rate of radiation exchange between the spheres, in W? 912 = (b) What is the net rate of radiation exchange between the surfaces if they are diffuse and gray with e = 0.5 and e2 = 0.05, in W? 912 = W (c) What is the net rate of radiation exchange if D2 is increased to 20 m, with ɛz = 0.05, ɛ1 = 0.5, and D = 0.8 m, in W? 912 = w (d) What is the net rate of radiation exchange if the larger sphere behaves as a black body (82 = 1.0) and with & = 0.5, D2 = 20 m, and D = 0.8 m, in W? 912 = Warrow_forward
- An opaque surface with the prescribed spectral, hemispherical reflectivity distribution is subject to the spectral irradiation shown. Find: 1.0 600 0.5 0 05 10 15 λ (μm) G₂(W/m²•μm) 300 0 0 5 10 15 20 20 λ (μm) (1) Find the spectral absorptivity distribution (αλ). (2) Determine the total irradiation G on the surface (3) Determine the radiant flux that is absorbed by the surface. (4) The total absorptivity a.arrow_forwardA thin, disk-shaped silicon wafer of diameter D=20 cm on a production line must be maintained at a temperature of 100 deg C. The wafer loses heat to the room by convection and radiation from its upper surface, while heat is supplied at a constant flux from below. The surrounding air is at 20 deg C, while all surrounding surfaces (which can be treated as blackbodies) can be approximated to be isothermal at a temperature of 15 deg C. The wafer-to-air heat transfer coefficient is 30 W/m2-K and the emissivity of the wafer’s surface (which can be approximated to be gray) is 0.85. How much heat (in W) must be supplied to the wafer?arrow_forwardA typical car's exterior consists of a thin layer of silica (SiO2) over an opaque painted metal panel. Silica is transparent in the visible wavelengths but offers high reflectance in the near- to mid- infrared wavelengths. The plot on the next page depicts the diffuse spectral reflectivity (pa) of the car's surface: Spectral reflectivity, P₂ 0.8 0.6 0.4 ལ 0.2 0 0.1 1 1 10 Wavelength, λ(μm) 100 If the car's exterior temperature is T₁ = 77°C, determine both the total absorptivity (a) and the total emissivity (a) of the silica-covered panel. Assume that the Sun's temperature is Tsun = 5800 K.arrow_forward
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- Calculate the radiation in watts per square centimeter from a block of copper at 200°C and at 1000°C. The oxidized copper surface radiates at 0.60 the rate of a black body.arrow_forwardSpectral hemispherical reflectivity distribution of an opaque surface is shown below. Surface is subjected to the spectral irradiation as shown. 1.0 400 a 0.4 200 5 10 15 20 a (um) 5 10 15 2 (um) Calculate the total irradiation on the surface in W/m2 Calculate the irradiation absorbed by the surface in W/m2 3250 || 3750 || 4250|| 5000 || 5750|| 6250|| 7500 1050 || 1200 1400|| 1600|| 1750| 1850 || 2000arrow_forwardHeat Transfer Question is imagearrow_forward
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