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Did you know that any object that has a temperature greater than absolute zero is constantly emitting
electromagnetic waves that travel through space at the speed of light.
It's these electromagnetic waves that produce thermal radiation.
Along with conduction and convection, thermal radiation is one of three ways in which heat
transfer can occur between different objects.
Whether it's to design photo-voltaic cells, heat exchangers or energy efficient structures,
engineers need to be able to model the effects of thermal radiation.
And a good way to start is by taking a closer look at the electromagnetic waves themselves.
A first observation we can make is that these waves travel in a straight line from the emitter.
They can also travel through a vacuum, which gives thermal radiation one of its unique
properties - unlike conduction and convection, it can occur in the absence of a medium.
An electromagnetic wave is characterised by its wavelength Lambda.
Radio waves for instance are just electromagnetic waves with very long wavelengths, and Gamma
rays and X-rays are electromagnetic waves with short wavelengths.
Visible light has a wavelength between around 0.4 and 0.7 microns.
The thermal radiation emitted by an object due to its temperature has a wavelength between
0.1 and 100 microns.
It overlaps with the UV, visible, and infrared parts of the spectrum.
The total energy radiated by a body each second, per unit area, is called the emissive power E.
It has units of Watts per square meter.
To study thermal radiation it's useful to define a perfect emitter, that emits the maximum
possible amount of thermal radiation at a given temperature.
This theoretical object is called a black body.
No real object can emit more thermal radiation than a black body can.
The emissive power of a black body can be calculated using a surprisingly simple law
called the Stefan-Boltzmann law.
T is the absolute temperature in Kelvin, and Sigma is a constant, called the Stefan-Boltzmann
constant.
Multiplying the emissive power by the surface area of the body gives us the heat transfer
rate.
A spherical black body with a radius of 30cm at 300 Kelvin for example will emit heat at
a rate of 520 Watts, or 520 Joules per second.
Temperature in the Stefan-Boltzmann law is raised to the fourth power.
This means that bodies at high temperatures emit far more energy by radiation than those
at lower temperatures.
Increasing the temperature of the sphere to 600 Kelvin will cause it to radiate 16 times
more energy each second.
The electromagnetic waves emitted due to thermal radiation don't all have the same wavelengths.
For the black body with a temperature of 300 Kelvin the radiated energy is in the form
of electromagnetic waves with wavelengths mainly between 2 and 50 microns.
The total emissive power, which we saw earlier can be calculated by the Stefan-Boltzmann
law, can be obtained from this graph by summing up all of the contributions from each wavelength,
which is just integrating to obtain the area under the curve.
At 300 Kelvin none of the emitted energy is in the visible part of the spectrum.
As the temperature of the black body increases the total emissive power increases very quickly,
so we'll need to switch to a log scale graph to be able to compare distributions for different
temperatures.
As temperature increases the distribution shifts to the left, meaning that the emissive
power is made up of shorter and shorter wavelengths.
Starting at around 700 Kelvin we reach the visible part of the spectrum, which is why
objects begin to glow when they reach high enough temperatures.
The surface of the sun can be modelled as a black body with a temperature of 5800 Kelvin,
and the wavelengths that emit the most radiation fall within the visible range of the spectrum,
although it emits a lot of energy in the UV and infrared wavelengths too.
The wavelength at which most of the power is emitted is often of interest.
It varies with temperature, and is given by a relation called Wien's displacement law.
Wien's law is often applied in astronomy.
If we measure the light emitted by a distant star, for example, we can determine the wavelength
at which the maximum power is emitted, and so by assuming the star behaves as a black
body we can determine its surface temperature.
The distributions we've looked at so far only apply to black bodies - they're defined by
Planck's Law.
But it's important to remember that a black body is an idealisation.
Some real bodies do behave similarly to black bodies, but for most, the spectral emissive
power profile will look something like this.
Since the black body's an idealisation of the perfect emitter, the total emissive power
of the real body is less than that of the black body.
We can still use the Stefan-Boltzmann law to calculate the emissive power of a real
body, we just need to include an additional term, the emissivity Epsilon, that defines
how much the real body emits relative to a black body.
It's defined more formally as the emissive power of the real body divided by the emissive
power of a black body at the same temperature.
Emissivity values, which tend to vary with temperature and wavelength, can be found in
reference texts or can be determined experimentally.
A body is said to be a grey body if the emissivity is constant for all wavelengths.
This is a simplification that makes it easier to analyse real bodies.
For an opaque body, thermal radiation is very much governed by the properties of its surface,
so coating type and surface roughness significantly affect emissivity.
In fact surface emissivity is often an important consideration when making design decisions.
A metallic coating with a polished surface finish will have very low emissivity, and
so might be a good choice for the surfaces of a heat tank, as it will reduce the amount
of heat radiated to the environment.
But it probably won't be a good choice for an electronics enclosure that needs to be
able to radiate heat effectively.
Another idealisation assigned to a black body is that it's a diffuse emitter, meaning that
it emits radiation evenly in all directions.
But real surfaces tend to emit radiation unevenly.
The emissivity is then a function of the angles
Theta and Phi, although it varies mainly with the angle Theta.
Capturing this directional dependence in a heat transfer analysis can get quite complex,
but fortunately it's often reasonable to assume that objects act as diffuse emitters, and
to use either an average emissivity, or the emissivity in the direction normal to the
surface.
Of course when studying radiation we don't only care about how much power an object emits.
We mainly care about the interactions between different bodies, and emission is only one
part of that.
The total amount of thermal radiation that reaches a body per unit area, regardless of
where it originates from, is called irradiation, and it's denoted using the letter G.
When radiation reaches the surface of an object, three things can happen.
The waves can be absorbed, which increases the temperature of the body, they can be reflected,
or in the case of a body that isn't completely opaque they can also be transmitted through it.
The proportion of the total irradiation reaching a surface that is absorbed, reflected or transmitted
is described by the absorptivity Alpha, the reflectivity Rho and the transmissivity Tau.
Values for these parameters will differ depending on the surface material and finish, and like
the emissivity Epsilon they can be found in reference material or be determined experimentally.
Since all incident energy is either absorbed, reflected or transmitted, these three terms
must sum up to 1.
As well as being a perfect emitter, a black body also absorbs 100 percent of the radiation
incident upon it, so it has an absorptivity of 1, and the reflectivity and transmissivity
are zero.
This is where it gets its name - it absorbs all of the light that hits it, and so appears
to be black as long as it's not emitting radiation in the visible part of the spectrum.
Like for emissivity, a complication is that absorptivity, reflectivity and transmissivity
are typically functions of wavelength and direction.
We're getting closer to being able to model radiative heat transfer between different
objects, but there's one last thing we're missing.
The way radiation is exchanged between surfaces depends on how the surfaces are positioned
relative to one another.
Assuming that surface 1 is a diffuse emitter, and so emits thermal radiation evenly in all
directions, all of the radiation it emits will be in this area shown in orange.
But only a fixed portion of this radiation will ever reach surface 2.
We can define a parameter F that describes the fraction of energy radiated from surface
1 that reaches surface 2.
This is called a shape factor or view factor.
It's a purely geometric parameter that depends on the shape of the surfaces and how they
are oriented relative to one another.
A relation called the reciprocity rule gives us an equation relating the view factors and
areas for both surfaces.
This means that if we know the view factor in one direction, we can easily calculate
it in the reverse direction.
View factors can only really be calculated analytically for very basic cases.
Charts and tables are provided in reference texts for many simple configurations, but
specialist software needs to be used for more complex scenarios.
Once we have the view factor, we can calculate the heat exchange between the two surfaces.
If we assume both surfaces behave as black bodies, the total radiation that leaves surface
1 and reaches surface 2 is the product of the area of surface 1, the black body emissive
power of surface 1, and the view factor from surface 1 to surface 2.
We can then calculate the net heat transfer between the two surfaces by subtracting the
radiation that leaves surface 2 and reaches surface 1.
The emissive power Eb is defined by the Stefan-Boltzmann law, and applying the reciprocity relation
gives us this simple equation for the net rate of heat transfer between both surfaces.
Things get a bit more complicated if we assume the surfaces behave as grey bodies, because
it means we have to consider reflection.
To do this we can replace the black body emissive power Eb in the heat transfer equation with
a new parameter, the radiosity J. Radiosity is the total radiation that leaves a surface,
and is the sum of the emitted and the reflected portions.
Analysing radiation can get complicated very quickly, but we've covered the key concepts
that can be used as a starting point for dealing with more complex scenarios.
So far we've described radiation as electromagnetic waves, but the reality is much less straightforward.
Planck's law, that defines the distribution of the emissive power of a black body, was
derived by Max Planck at the beginning of the 20th Century.
Until then classical physics predicted distributions that looked vastly different to experimental
measurements at short wavelengths.
This unexplained discrepancy between the models and the data was called the "ultraviolet catastrophe".
Planck solved this by considering that radiation might not actually be emitted continuously,
as had been assumed by the classical models, but instead that it's emitted in discrete
packets of energy, that we now call photons.
This theory led to a much closer match with the experimental data, and the revolutionary
discovery that light is quantised opened the doors to the entire field of quantum mechanics.
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That's it for this look at thermal radiation.
Thanks for watching!