How to calculate the radiation heat transfer

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 ft^{2 o}R⁴))

       =  0.119 10-10 (Btu/(h in^{2 o}R⁴))

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

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