Heat
transfer through radiation takes place in the form of electromagnetic waves mainly
in the infrared region. Radiation emitted by a body is a consequence of thermal
agitation of its composing molecules. Radiation heat transfer can be described
by a reference to the so-called 'black body'.
The Black Body
A
black body is defined as a body that absorbs all radiation that falls on its
surface. Actual black bodies don't exist in nature - though its characteristics
are approximated by a hole in a box filled with highly absortive material. The
emission spectrum of such a black body was first fully described by Max Planck.
A black body is a hypothetical body that completely absorbs all wavelengths of
thermal radiation incident on it. Such bodies do not reflect light, and
therefore appear black if their temperatures are low enough so as not to be
self-luminous. All blackbodies heated to a given temperature emit thermal
radiation. The radiation energy per unit time from a black body is proportional
to the fourth power of the absolute temperature and can be expressed with
Stefan-Boltzmann Law as:
q = σ
T4 A (1)
where
q
= heat transfer per unit time (W)
σ = 5.6703 10-8 (W/m2K4) - The
Stefan-Boltzmann Constant
T
= absolute temperature Kelvin (K)
A
= area of the emitting body (m2)
The
Stefan-Boltzmann Constant in Imperial Units
σ = 5.6703 10-8 (W/m2K4)
= 0.1714 10-8 (Btu/(h ft2 oR4))
=
0.119 10-10 (Btu/(h in2 oR4))
Example
- Radiation from the surface of the Sun
If the surface temperature of the sun
is 6700 K and if we assume that the sun can be regarded as a black body the
radiation energy per unit time can be expressed by modifying (1) like
q / A =
σ T4
= (5.6703 10-8 W/m2K4) (6700K)4
= 11.43 x 107 (W/m2)
Gray
Bodies and Emissivity Coefficients
For objects other than ideal
blackbodies ('gray bodies') the Stefan-Boltzmann Law can be expressed as
q = ε
σ
T4 A (2)
where
ε = emissivity of the
object (one for a black body)
For the gray body the incident
radiation (also called irradiation) is partly reflected, absorbed or
transmitted.
For the gray body the incident
radiation (also called irradiation) is partly reflected, absorbed or
transmitted.
The emissivity coefficient lies in
the range 0 < ε < 1 depending on
the type of material and the temperature of the surface. The emissivity of some
common materials
- Oxidized Iron at 390 oF (199 oC) > ε = 0.64
- Polished Copper at 100 oF (38 oC) > ε = 0.03
The emissivity coefficient -ε-
for some common materials can be found in the table below. Note that the
emissivity coefficients for some products varies with the temperature. As a
guideline the emmisivities below are based on
temperature 300 K.
Surface Material
|
Emissivity Coefficient
ε |
Alloy 24ST Polished
|
0.09
|
Alumina, Flame
sprayed
|
0.8
|
Aluminum Commercial
sheet
|
0.09
|
Aluminum Foil
|
0.04
|
Aluminum Commercial
Sheet
|
0.09
|
Aluminum Heavily
Oxidized
|
0.2 - 0.31
|
Aluminum Highly
Polished
|
0.039 - 0.057
|
Aluminum Anodized
|
0.77
|
Aluminum Rough
|
0.07
|
Aluminum
paint
|
0.27 - 0.67
|
Antimony, polished
|
0.28 - 0.31
|
Asbestos
board
|
0.96
|
Asbestos paper
|
0.93 - 0.945
|
Asphalt
|
0.93
|
Basalt
|
0.72
|
Beryllium
|
0.18
|
Beryllium, Anodized
|
0.9
|
Bismuth, bright
|
0.34
|
Black Body Matt
|
1.00
|
Black lacquer on
iron
|
0.875
|
Black Parson
Optical
|
0.95
|
Black Silicone
Paint
|
0.93
|
Black Epoxy Paint
|
0.89
|
Black Enamel Paint
|
0.80
|
Brass Dull Plate
|
0.22
|
Brass Rolled Plate
Natural Surface
|
0.06
|
Brass Polished
|
0.03
|
Brass Oxidized 600oC
|
0.6
|
Brick, red rough
|
0.93
|
Brick, fireclay
|
0.75
|
Cadmium
|
0.02
|
Carbon, not
oxidized
|
0.81
|
Carbon filament
|
0.77
|
Carbon pressed
filled surface
|
0.98
|
Cast Iron, newly
turned
|
0.44
|
Cast Iron, turned
and heated
|
0.60 - 0.70
|
Chromium polished
|
0.058
|
Concrete
|
0.85
|
Concrete, rough
|
0.94
|
Concrete tiles
|
0.63
|
Cotton Cloth
|
0.77
|
Copper
electroplated
|
0.03
|
Copper heated and
covered with thick oxide layer
|
0.78
|
Copper Polished
|
0.023 - 0.052
|
Copper Nickel
Alloy, polished
|
0.059
|
Glass smooth
|
0.92 - 0.94
|
Glass, pyrex
|
0.85 - 0.95
|
Gold not polished
|
0.47
|
Gold polished
|
0.025
|
Granite
|
0.45
|
Gypsum
|
0.85
|
Ice smooth
|
0.966
|
Ice rough
|
0.985
|
Inconel X Oxidized
|
0.71
|
Iron polished
|
0.14 - 0.38
|
Iron, plate rusted
red
|
0.61
|
Iron, dark gray
surface
|
0.31
|
Iron, rough ingot
|
0.87 - 0.95
|
Lampblack paint
|
0.96
|
Lead pure
unoxidized
|
0.057 - 0.075
|
Lead Oxidized
|
0.43
|
Limestone
|
0.90 - 0.93
|
Lime wash
|
0.91
|
Magnesium Oxide
|
0.20 - 0.55
|
Magnesium Polished
|
0.07 - 0.13
|
Marble White
|
0.95
|
Masonry Plastered
|
0.93
|
Mercury liquid
|
0.1
|
Mild Steel
|
0.20 - 0.32
|
Molybdenum polished
|
0.05 - 0.18
|
Nickel,
elctroplated
|
0.03
|
Nickel, polished
|
0.072
|
Nickel, oxidized
|
0.59 - 0.86
|
Nichrome wire,
bright
|
0.65 - 0.79
|
Oak, planed
|
0.89
|
Oil paints, all
colors
|
0.92 - 0.96
|
Paper offset
|
0.55
|
Plaster
|
0.98
|
Platinum, polished
plate
|
0.054 - 0.104
|
Porcelain, glazed
|
0.92
|
Paint
|
0.96
|
Paper
|
0.93
|
Plaster, rough
|
0.91
|
Plastics
|
0.91
|
Porcelain glazed
|
0.93
|
Quartz glass
|
0.93
|
Roofing paper
|
0.91
|
Rubber, hard glossy
plate
|
0.94
|
Rubber Nat Hard
|
0.91
|
Rubber Nat Soft
|
0.86
|
Sand
|
0.76
|
Sawdust
|
0.75
|
Silicon Carbide
|
0.83 - 0.96
|
Silver Polished
|
0.02 - 0.03
|
Steel Oxidized
|
0.79
|
Steel Polished
|
0.07
|
Stainless Steel,
weathered
|
0.85
|
Stainless Steel,
polished
|
0.075
|
Stainless Steel,
type 301
|
0.54 - 0.63
|
Steel Galvanized
Old
|
0.88
|
Steel Galvanized
New
|
0.23
|
Tile
|
0.97
|
Tin unoxidized
|
0.04
|
Titanium polished
|
0.19
|
Tungsten polished
|
0.04
|
Tungsten aged
filament
|
0.032 - 0.35
|
Water
|
0.95 - 0.963
|
Wood Beech, planned
|
0.935
|
Wood Oak, planned
|
0.885
|
Wood, Pine
|
0.95
|
Wrought Iron
|
0.94
|
Zink Tarnished
|
0.25
|
Zink polished
|
0.045
|
To be continued
References:
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