In a previous screencast, I showed you how
to calculate the heat flux between two, infinite,
parallel plates with and without radiation
shields. Here, we're going to look at the
same system, but we're going to calculate
the temperature of the radiation shield. We
have these two infinite, parallel plates with
a radiation shield between them and Surface
One has a temperature of 800 kelvin and an emissivity
of 0.6. Surface Two has a temperature of 500
kelvin and an emissivity of 0.7. Finally, our radiation
shield, which we don't know the temperature
of, has a very low emissivity of 0.02. Like
we did before, we're going to use a circuit
system, but this time instead of calculating
the heat flux, which we already did for this
system, we're going to use the same approach
to calculate the temperature of the radiation
shield. Note that the flux stays constant
throughout the system, so we can look at any
part of the system. So in this case, what
we're going to do here is look at the system
between Surface One and the first surface
of the radiation shield. So let's draw the
circuit between them. So note we go from Surface
One here, acting as a blackbody, to Surface
Three, which we're going to call the radiation
shield, and then we have resistances based
on the emissivity of material one (or Surface
One), the view factor between the two surfaces
(which is equal to one) and the resistance
due to the emissivity of the first side of
the radiation shield. So now we can write
this as our flux is equal to our Stefan-Boltsmann
constant, T one to the fourth minus T three
to the fourth, divided by the sum of the resistances.
So here we know what our heat flux is and
what we're trying to find is this temperature
here. So let's put in our numbers. And so
if we solve for T three, we find that the
temperature of the radiation shield is equal
to 696.5 kelvin. Now let's take a look at
it from the other side - in other words, the
system between the other side of the radiation
shield and the second surface. So let's see
what that circuit looks like. So here we start
at temperature three, which we're going to
solve for and see if it's similar to the temperature
we calculated by doing the first half of the
circuit, going to temperature two, which is
the temperature of the second surface, or
500 K. And if you note these resistances,
this is the emissivity on the second half
of the radiation shield, here's our view factor
between the shield and the second surface
which is one, and here is our resistance based
on the emissivity of the second surface. If
we put the numbers in here, and if we solve
for our T three, this is going to be equal
to 697.1 kelvin, almost identical to the T
3 that we calculated here.
