After the kiln's first run, it was found that it wasn't getting near as hot as I had hoped - not near as hot as the optimistic model had predicted either! In this log, we tweak the model parameters so that the time-dependent thermal model outputs a curve that is (somewhat) close to the experimental data from the kiln's first run. The script used for this is kiln_model_mathcing.py.

Here's the end result in graphical format:

The important model parameters are the following:

rho = 2000.0 # density of wall material in kg / m^3
k = 1.3 # thermal conductivity of wall material in W / (m*K)
c = 400.0 # specific heat capacity in J / (kg*K)
h = 12.0 # convective heat transfer coefficient in W / (m^2 * K)
Q_dot_in = 1500.0 # heater power in watts
T_inf = 291.0 # ambient temperature in Kelvin

A couple things to note...

1. These values are arrived at manually - I tweaked 'em around until the graphs looked about right.
2. The simulated inside temperature matches the data OK, but the simulation of the outside temperature has it heating up much faster than the experimental data showed. I'm not sure why.
3. The value of k is much higher than I had initially guessed. This might be due in part to the large gaps between bricks. Sealing the gaps might improve (reduce) this value.
4. The values of h and c are somewhat lower than I had initially guessed.

So how hot will this thing get if we add a second heater? Here are the traces using the above parameters for a heater of Q_dot = 3000 watts:

This gets up to about 1160 Kelvin, or 1628 degrees F, or 887 degrees C. Still not quite as high as I had wanted, but let's try it and see how high we get!