SB Chapter 12 Heat Transfer
The _____ for emitted radiation is defined as the rate at which radiation energy is emitted in the (θ, Φ) direction per unit area normal to this direction and per unit solid angle about this direction. Here, θ and Φ are zenith and azimuth angles, respectively.
radiation intensity
The spectral radiative property can be stated as the _____.
radiative property per unit wavelength
Identify the true statements about approximations utilized in radiation calculations.
-A surface is said to be diffuse if its properties are independent of direction. -A surface is said to be gray if its properties are independent of wavelength.
Identify the phenomena that are responsible for attenuation of solar radiation passing through the atmosphere.
-Absorption -Scattering
Identify the statements that best explain the nature of electromagnetic waves.
-Electromagnetic waves can be produced by accelerated charges. -Electromagnetic waves do not require a medium to transfer energy.
In the context of variation of the blackbody emissive power with wavelength, the wavelength at which the peak occurs for a specified temperature is given by _____.
Wien's displacement law
Direct solar radiation is the part of solar radiation that reaches the earth's surface _____.
Without being absorbed or scattered by the atmosphere
At a specified temperature, a ___________________ emits the highest amount of energy at a specified wavelength.
blackbody
The rate of thermal radiation emission increases with the _____.
increase in temperature of the radiating body
The radiation intensity for radiation emitted by a blackbody at an absolute temperature T is given by Ib(T) = _____, where σ is the Stefan-Boltzmann constant.
σT^4/π
Identify the true statements about spectral directional absorptivity.
-It varies with direction. -It varies with wavelength.
According to Max Planck, it is useful to view electromagnetic radiation as the propagation of a collection of discrete packets of energy. Identify the terms that are used to describe these packets of energy.
-Photons -Quanta
Identify the true statements about a gray, diffuse surface.
-The emissivity of a gray, diffuse surface is independent of direction. -The emissivity of a gray, diffuse surface is independent of wavelength.
The spectral blackbody emissive power is the amount of radiation energy emitted by a blackbody at a thermodynamic temperature (T) _____ about the wavelength (λ).
per unit time, per unit surface area, and per unit wavelength
Identify the expression that gives the net rate of radiation heat transfer (q˙net, rad) to a surface exposed to solar and atmospheric radiation. Here, αsαs is the absorptivity of the surface, Gsolar is the total solar energy incident on the surface, ε emissivity of the surface at room temperature, σ is the Stefan-Boltzmann constant, and Tsky and Ts represent the sky and the surface temperature, respectively.
q˙net, rad = αs Gsolar + ε σ (T4sky − T4s)
Heat transfer through an evacuated space can occur only by
radiation
The differential solid angle dω subtended by a differential area dS on a sphere of radius r can be expressed as dω = _____, where θ is the zenith angle and Φ is the azimuth angle.
sinθ dθ dΦ
The Stefan-Boltzmann law is expressed as _____, where T is the absolute temperature of the surface of a blackbody in kelvin, Eb is the energy emitted by the blackbody per unit time, and σ is the Stefan-Boltzmann constant.
Eb(T) = σT^4
Identify the true statement about radiation.
Energy transfer by radiation is the fastest of all the heat transfer processes.
True or false: A body that emits some radiation in the ultraviolet range is called a light source.
False
True or false: In humid places such as coastal areas, there is a large change between the daytime and nighttime temperatures.
False
Identify the correct equation to calculate irradiation (G) when the incident radiation is diffuse and Ii = constant.
G = π Ii
Identify a reason that causes greenhouse effect on earth.
Gases present in the atmosphere transmit the bulk of the solar radiation but absorb the infrared radiation emitted by the surface of the earth.
Identify the expression that gives the total solar energy Gsolar incident on earth's surface. Here, GD is the direct solar radiation, Gd is the diffuse solar radiation, and θ is the angle that the direct solar radiation makes with the normal to the surface.
Gsolar = GD cos θ + Gd
The radiation flux incident on a surface from all directions is called _____.
Irradiation
Identify the equation that relates radiosity (J) to the intensity of radiation (Ie+r) leaving a plane surface that is both a diffuse emitter and a diffuse reflector.
J = πIe+r
Match the wavelength ranges (in μm) (in the left column) with the types of waves (in the right column).
Less than 10^-10 matches Choice, Cosmic rays More than 10^10 matches Choice, Electrical power waves
The unit for spectral intensity of radiation emitted by a blackbody is _____.
W/m2⋅sr⋅μm
When can the expression G = πIi be used to express the irradiation for a surface? Here, G represents irradiation and Ii represents the intensity of incident radiation.
When the intensity of incident radiation is constant.
According to Kirchhoff's law, the total hemispherical emissivity of a surface at temperature T is equal to its total hemispherical _____ for radiation coming from a blackbody at the same temperature.
absorptivity
A blackbody absorbs _____.
all incident radiation of all wavelengths in all directions
On the Ebλ-λ chart, the total blackbody emissive power Eb corresponds to the under the entire curve for a specified temperature.
area
In analogy to plane angle, we can say that the _____ is equivalent in magnitude to the solid angle it subtends.
area of a surface on a sphere of unit radius
The mathematical expression for the differential solid angle (dω) subtended by a differential surface area dA when viewed from a point at a distance r from dA is given by dω = _____, where α is the angle between the normal to the surface and the direction of viewing.
dAcosα/r2
Identify the expression for the radiation flux (dE) for emitted radiation. Consider dQ˙e to be the rate at which the radiation energy is emitted and dA to be the area of the differential element.
dE = dQ˙e/dA
The ratio of the radiation emitted by a surface at a given temperature to the radiation emitted by a blackbody at the same temperature is called the _____ of the surface.
emissivity
The radiation incident on any part of the surface of a small body at a temperature T in a large isothermal enclosure is _____ the radiation emitted by a blackbody at the same temperature.
equal to
Radiation emitted by bodies at room temperature falls into the _____ region of the electromagnetic spectrum.
infrared
When the variations of spectral radiation fluxes with wavelength λ are known, the total radiation fluxes can be determined by _____.
integration over the entire wavelength spectrum
The quantity that describes the magnitude of radiation emitted or incident in a specified direction in space is the radiation _____.
intensity
The given graph shows the variation of blackbody emissive power with wavelength for several temperatures. Here, the _____ represents the plot of Wien's displacement law.
locus of the peaks of the radiation emission curves
The total solar irradiance is the measure of the solar energy striking the _____.
outer edge of the atmosphere
The speed of propagation of electromagnetic waves in a medium (c) is related to the speed of light in a vacuum (c0) by c = c0/n, where n is the index of _____ of that medium.
refraction
The relationship between the frequency (ν) and the wavelength (λ) of electromagnetic waves in a medium is given by the equation λ = c/ν. Here, c represents the _____.
speed of the electromagnetic wave in that medium
The unit of solid angle is the _____.
steradian
Electromagnetic waves travel at a speed that is equal to _____ in a vacuum.
the speed of light
The spectral radiation intensity is the _____.
total radiation intensity per unit wavelength interval about a specific wavelength
The solar energy reaching the earth's atmosphere is called the _____.
total solar irradiance
The figure shows the radiation passing through a point in spherical coordinates. The angles θ and Φ denote the _____ and _____ angles, respectively.
θ zenith, Φ azimuth
Identify the expression for the relationship between the frequency (ν) and the wavelength (λ) of electromagnetic waves. The speed of propagation of the wave is represented by c.
λ = c/nu
Solar heat gain coefficient (SHGC) is expressed as _____. Here, αs is the absorptivity of the glass for solar energy, fi is the inward flowing fraction of the solar radiation absorbed by the glass, and τs is the fraction of the directly transmitted portion of solar radiation incident on the window.
τs + fiαs
If the solar heat gain coefficient (SHGC) is known, then the shading coefficient (SC) is expressed as _____.
SC = 1.15 × SHGC
The emission of thermal radiation from a blackbody is proportional to the _____ of the blackbody.
fourth power of absolute temperature
Identify the correct expression to calculate the emissive power (E) for a diffusely emitting surface, where Ie is the radiation intensity.
E = π Ie
Identify the radiation fluxes that are expressed in terms of intensity.
-Irradiation -Radiosity -Emissive power
Identify the true statements about Planck's law
-It gives the spectral emissive power of a blackbody. -It is valid for a surface in a vacuum or a gas.
Identify the true statements about blackbody radiation intensity.
-It is dependent on the temperature of the blackbody. -It is independent of zenith angle. -It is independent of azimuth angle.
The unit of spectral blackbody emissive power is _____.
watt/((meter)2×micro-meter)
The unit for radiation intensity is _____.
watt/meter^2 steradian
The given figure shows the variation of the spectral blackbody emissive power with wavelength for selected temperatures. Identify the correct observations that can be made from this figure.
-The emitted radiation is a continuous function of wavelength. -The amount of emitted radiation increases with increasing temperature.
When is a medium, that is filled with gases, treated as a vacuum in radiation analysis?
-The medium absorbs negligible radiation. -The medium emits negligible radiation.
Identify the types of electromagnetic waves present in solar radiation.
-Ultraviolet waves -Infrared waves -Visible light
The emissivity of a surface varies in the range of _____.
0 to 1
The blackbody radiation function fλ(T) is the fraction of radiation emitted from a blackbody at temperature T in the wavelength band that ranges from _____.
0 to λ
Thermal radiation is also defined as the portion of the electromagnetic spectrum that extends from about _____ μm.
0.1 to 100
Solar radiation falls into the wavelength band _____ μm.
0.3-3
When viewed from the center of the sphere, the angle between the normal to an elemental surface area on the sphere and the direction of viewing is α = _____.
0°
The shading coefficient of a single-pane clear glass window is SC = _____.
1
What is the value of the solar constant?
1373
The unit for the intensity of radiation emitted by a blackbody at absolute temperature is _____.
watt/meter^2 steradian
According to Max Planck, the energy of a photon is inversely proportional to its _____.
wavelength
The greenhouse effect is the consequence of the _____ dependence of radiation properties.
wavelength
The term "spectral" in the spectral blackbody emissive power relation given by Max Planck indicates dependence on _____.
wavelength
Absorptivity, reflectivity, and transmissivity are related by the equation α + ρ + τ = 1. How does this equation change for gases?
α + τ = 1
The angle of incidence of direct solar radiation falling on unit area of a horizontal surface on ground is 30°. The solar radiation consists of direct solar radiation GD = 600 W/m2 and diffuse solar radiation Gd = 300 W/m2. Determine the total solar energy incident on this surface.
819.6 Wm2
Match the types of material (in the left column) with the types of radiation phenomena (in the right column) associated with it.
Nonopaque (transparent) solids matches Choice, Volumetric phenomenon Opaque (nontransparent) solids matches Choice, Surface phenomenon
The conservation of energy principle requires that the sum of transmissivity, reflectivity, and absorptivity of the glass for solar energy be equal to _____.
One
The first law of thermodynamics states that the sum of the absorptivity, reflectivity, and transmissivity is equal to _____.
One
Which of the following statements is true about radiation?
Radiation does not require the presence of a material medium to take place.
Calculate the transmissivity of a surface whose absorptivity and reflectivity are 0.5 and 0.1, respectively.
Reason: Absorptivity + Reflectivity + Transmissivity = 1 α + ρ + τ = 1 0.5 + 0.1 + τ = 1 τ = 1 - 0.5 - 0.1 τ = 0.4
Calculate the radiation emission from the atmosphere to the earth's surface if the effective sky temperature (Tsky) is given as 270 K. Assume the Stefan-Boltzmann constant to be σ = 5.67 x 10-8 W/m2⋅K4.
Reason: The radiation emission from the atmosphere to the earth's surface can be calculated as follows: Gsky = σTsky4 Gsky = (5.67x10-8) × (2704) Gsky = 301.3 W/m
Calculate the solid angle ω for a surface of area A = 10 cm2, when viewed from a point at a relatively large distance r = 160 cm from A. The angle between the normal to the surface and the direction of viewing is α = 60ο.
Reason: The solid angle can be calculated using the following relations: An = Acosα An = 10cos60° = 5 cm2 ω ≈ An/r2 = 5/1602 ω ≈ 1.95 × 10^-4 sr
Determine the fraction of radiation energy emitted by a blackbody at temperature T over a finite wavelength band from λ1 to λ2, if the blackbody radiation functions are fλ1(T) = 0.564 and fλ2(T) = 0.744.
Reason: fλ1-λ2(T) = fλ2(T) - fλ1(T) fλ1-λ2(T) = 0.744 - 0.564 fλ1-λ2(T) = 0.18
When the solar heat gain coefficient (SHGC) of a window is known, the total solar heat gain Q˙solar, gain through that window is determined from ____. Here, Aglazing is the glazing area of the window and q˙solar, incident is the solar heat flux incident on the outer surface of the window.
SHGC x Aglazing x q˙solar, incident
Integration of Planck's law over all wavelengths gives the _____ law.
Stefan-Boltzmann
Identify the condition under which Kirchhoff's law is derived.
The surface temperature should be equal to the temperature of the source of irradiation.
Identify the true statements about microwave radiation.
They are transmitted by glass and plastics. They are reflected by metals.
True or false: According to Max Planck's theory of electromagnetic radiation, shorter-wavelength radiation possesses larger photon energies.
True
True or false: Radiation reaching a surface, in general, consists of direct radiation, diffuse radiation, and reflected radiation.
True
True or false: Scattering is mainly governed by the size of the particle relative to the wavelength of the radiation.
True
True or false: The electrons, atoms, and molecules of all solids, liquids, and gases above absolute zero temperature are constantly in motion, and thus radiation is constantly emitted, as well as being absorbed or transmitted throughout the entire volume of matter. That is, radiation is a volumetric phenomenon.
True
Identify the steps that are used in calculating the solid angle ω for a small surface of area A, when viewed from a point at a relatively large distance r from A, with its normal making an angle α with the direction of viewing.
Use the expression An/r2 to calculate the solid angle. Use the expression A cosα to find the projected area An.
