Thermal physics of cooking with an electric stove I'm wondering why stoves have a 1-9 scale of the amount of heat and a not temperature scale.
My understanding is that for each of the modes corresponding to a number, a certain amount of heat is being produced inside the stove that is being transferred to the surface. And then depending on how cold it is outside the surface of the stove and a thermal conductivity coefficient, the temperature might change. Is it correct?
My second question is what does the temperature on the surface depend on? Does it depend on just two parameters - thermal conductivity and temperature of the surface adjacent to the stove? ( adjacent to the stove surface of the pan, air or anything else)?
My third question is - is the equation for finding the temperature of the surface of the stove 
$$\frac{∂ \Delta T}{∂t}=\frac{E}{A}-k\Delta T,$$
where $\Delta T=T_1-T_2$, $T_1$ is the temperature of the surface of the stove we want to find, $T_2$ is the temperature of the outside layer, $E$ is the amount of energy being produced per amount of time by an electric component inside the stove, $k$ is the coefficient of thermal conductivity between the surface and the outside layer of adjacent material, $A$ is the area of the surface of the stove? 
"The rate of change of $\Delta T$ is equal to the difference between influx $\frac{E}{A}$ and outflux $k\Delta T$ of heat to the surface" is my understanding of the above equation. Is this understanding correct? Is this equation physically correct? 
Should it be correct (perhaps under certain assumptions of the physical model), how to actually find $T_1$ from it? I was thinking that not only does the temperature of the surface of the stove change with time, but also the temperature of the adjacent material (air, pan, etc.) changes, so  both unknown functions $T_1$ and $T_2$ should be present in the equation, and they both depend on $T_2$ and $T_1$ respectively, and change with time. 
Say in the model of electric stove-surface-pan, is it only possible to find $T_1$ at a state of equilibrium, when we assume both $\frac{∂T_1}{∂t}$ and $\frac{∂T_2}{∂t}$ to be zero? 
Thanks!
 A: This is a partial answer, but perhaps it will motivate reformulating the question.
Electric stoves come nowadays in at least three kinds:

*

*The traditional one - with a heated plate that acts via direct contact with dishes, i.e. via the heat conductivity

*The radiation stoves, where the dishes are placed in a ceramic plate irradiated from the bottom

*The induction stoves, where pulsed magnetic field induces currents in metallic dishes and thus heats them

None of these controls the temperature of the heated dish, but only the energy spent by the stove. Moreover, neither does a gas stove nor a fireplace: the temperature is controlled by changing the power of the heating element and/or controlling its proximity to the dish, i.e. via regulating the heat loss.
Note also that in my list the heating efficiency is higher in every new generation.
Finally, there is no reason why we should not include here microwave stoves - it is technically a different piece of equipment, but it does the same job. These have an interesting feature that one typically controls not only the power of the stove, but also the total amount of energy spent, via controlling time during which the power is generated.
