More Measurements

After doing more measurements with power settings up to about $P = 226\,\mathrm{W}$ ($18/64$ of the total power), I came up with this set of steady states:

That's not very linear, so the simple $P=\dot{Q}=K(T_A-T_\infty)$ with a constant $K$ won't work well. Here $K=k \cdot A$ where $k$ is the overall heat transfer coefficient. $K$ needs to include a non-linear term that takes the temperature difference into account. Here is one: $$K=K_0 + K_T\left( \frac{T_A - T_\infty}{T_\infty} \right)^{E_K}$$ Let's fit that to the data (although the underlying physical model is quite coarse...). I used Matlab's cftool and a custom function, yielding the coefficients $$K_0 = 0.2072\,\mathrm{\frac{W}{K}},~K_T = 1.04\,\mathrm{\frac{W}{K}},~E_K = 0.5219$$

While this looks good, it is by far not an accurate model of the oven. The $K$ calculated above is just one temperature-dependent factor for the following phenomena:

• natural convection between the heaters and the air in the oven,
• natural convection between the air and the oven's inner wall,
• radiation between the heaters and the oven's inner wall,
• heat conduction in the insulation,
• natural convection between the oven's outer wall and the surrounding air,
• radiation between the oven's outer wall and any surrounding walls of the building it is in (this can be neglected I think).

No transient phenomena are modeled, but they will be important for controlling the oven. I'll try to come up with a model in OpenModelica or even write one with boost.Odeint.