Fundamentals of Heat and Mass Transfer
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 12.125P

The neighborhood cat likes to sleep on the roof of our shed in the backyard. The roofing surface is weathered galvanized sheet metal ( ε =0 .65,  α s = 0.8 ) . Consider a cool spring day when the ambient air temperature is 10 C and the convection coefficient can be estimated from an empirical correlation of the form h ¯ = 1.0 Δ T 1 / 3 ,where Δ T is the difference between the surface and ambient temperatures. Assume the sky temperature is 40 C .

(a) Assuming the backside of the roof is well insulated, calculate the roof temperature when the solar irradiation is 600 W/m 2 . Will the cat enjoy sleeping under these conditions?

(b) Consider the case when the backside of the roof is not insulated,but is exposed to ambient air with the same convection coefficient relation and experiences radiation exchange with the ground, also at the ambient air temperature. Calculate the roof temperature and comment on whether the roof will be a comfortable place for the cat to snooze

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Chapter 12 Solutions

Fundamentals of Heat and Mass Transfer

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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