This chapter delves into radiation heat transfer, exploring electromagnetic wave-based heat exchange. It covers fundamental laws like Stefan-Boltzmann, Planck, and Wien's Displacement Laws. The importance of emissivity, absorptivity, and Kirchhoff's Law is highlighted. Practical applications in com...
Forsberg Heat Transfer
Chapter 9
Radiation Heat Transfer
Electromagnetic Radiation
Electromagnetic radiation wavelengths:
Thermal radiation 0.1 to 100m (microns)
Visible light 0.4 to 0.8m
X-rays 10 −11 to 2 x 10 −8 m
Microwaves 1 mm to 10 m
Radio waves 10 m to 30 km
co =
co = speed of light in vacuum = 2.9979 x 10 8 m / s
= wavelength of radiation, m
= frequency of radiation, / s
1
, Blackbody Emission
A "blackbody" emits radiation at the maximum
possible rate. The emission is given by Planck's Law:
2 hco2 −5
Eb ( ,T ) =
hc
exp o − 1
kT
Eb = spectral emissive power of a blackbody, W / (m2 m)
h = Planck's constant k = Boltzmann's constant
C1 −5
Eb ( ,T ) =
exp ( C2 / T ) − 1
C1 = 3.7417 x 108 (W/m2 ) (m)4
C2 = 1.4388 x 10 4 m K
Blackbody Spectral Emissive Power
9
Spectral E
8
5800
10
7
6
10
534
1000
10
2 K K
1−10
10300
0−12
−3
0.1
K 1 10 100
10
10Wavele 2
, Stefan-Boltzmann Law
Integrating the Spectral Emissive Power over all
wavelengths, we get the Stefan-Boltzmann Law:
Eb (T ) = 0 E b ( ,T ) d = T 4
= Stefan-Boltzmann constant = 5.670 x 10 −8 W / m2 K4
Terminology:
"Spectral" = parameter depends on wavelength
"Total" = parameter is independent of wavelength
Wien’s Displacement Law
Looking at the spectral-emissive-power figure,
it is seen that the curves have maximums. As the
temperature increases, the maximums move to
a higher wavelength. This is Wien's Displacement
Law: maxT = 2898 m K
max = wavelength of maximum emission
T = absolute temperature of blackbody, K
3
, For a 5800 K blackbody, max = = 0.500 m
For a 1000 K blackbody, max = = 2.90 m
For a 300 K blackbody, max = = 9.66 m
The sun can be approximated as a blackbody at 5800 K.
The space inside a car or in a room is about 300 K.
Glass has a high transmission at low wavelengths,
but a low transmission at higher wavelengths.
Solar radiation enters the space, but radiation in the
space has difficulty leaving. The greenhouse effect.
Blackbody Radiation Function
Let's say we want the total emissive power for a
blackbody at temperature T for a wavelength
range of 1 to 2 . We want
Eb (1 → 2 ,T ) = 12 E b ( ,T ) d
The fraction of radiation emitted by a blackbody
in wavelength range 1 to 2 is
Eb ( ,T ) d 1 E b ( ,T ) d
2 2
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller AhmedKnight. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $7.49. You're not tied to anything after your purchase.
