# Heat transfer through layered wall

An electrical heater is placed between two layers of insulation. The three layers (the heater and the two layers of insulation) have the same thickness. The figure below shows different temperature profiles at steady-state. The air temperature at the front- and backside of the heater is $$\ce{T_{front}}$$ resp. $$\ce{T_{rear}}$$. Heat transfer in the air film adjacent to the heater is negligible.

a) Which profile corresponds to that of a turned on heater?

b) Which profile corresponds to that of a turned off heater?

c) Which profile is impossible?

d) Which of the three layers has the lowest thermal conductivity? Which layer has the highest?

I have no answer for a) or b).

c) My reasoning is that since a heater is a conductor, the k-value needs to be high, resulting in a fairly straight line in the temp. profile. Hence, (C) is impossible. Is this correct thinking?

However, I don't know what it means when a temperature profile has that kind of curvature for one of the layers, such as in (A) and (B), so if someone could please explain that, I would appreciate it.

d) Based on the fact that low k-values give a steeper line, I would say that layer 3 has the lowest thermal conductivity. And because the heater is a conductor it should have the highest thermal conductivity.

Also, how can you tell if the heater is turned on or off from looking at different temperature profiles? I am having a very difficult time understanding this and would appreciate if someone could make this a bit clearer.

I apologize if these types of questions are considered off-topic, but I really want to know how to determine these things and we have not been provided with any answers nor explanations.

• This is maybe more on-topic for Physics SE Jul 29 '20 at 8:32