# Can thermal mass cause an increase in temp. after heat source is removed?

In class, I built a Bang-bang control system that used a light bulb to generate heat which we measured with a thermocouple, a FX3U Mitsubishi PLC and a FX3U-4AD-TC-ADP. One of the topics we were investigating was overshoot. I thought that the fact that the temperature continued to increase after the bulb was turned off was an artifact of our measuring system. I thought that the conservation of energy would prohibit any energy increase in the system we are measuring after the light bulb went off. The professor wrote a note advising that I look up thermal mass. As I understand it, (and I'm checking to see if this is correct): Thermal mass slows the change of temperature. I didn't think thermal mass would cause the temperature to continue to rise after the heat source is removed. Can anyone clarify? Thanks

• Are we talking about heat traveling through a vacuum? Or through a material? In either case the travel takes time. It has a speed. Even if the source turns off, the heat that is already on its way but hasn't arrived yet will still continue. Sep 30, 2017 at 15:57

## 2 Answers

It depends on where you are measuring the temperature. If your heat source heats one part of the system A, and you are measuring another part of the system B, it is indeed possible that heat continues to flow from A to B after you stop heating A - because there will be thermal gradients in the object, and diffusion of heat takes time.

So if the part of the system that is heated has thermal mass, it is indeed possible that it will continue to give off heat to another part of the system that was initially cooler. On the other hand if you were measuring the temperature of A close to the point where you applied the heat, you would find that it cools down somewhat after removing the heat, as A continues to give heat to (cooler) B.

In my own real experiment I heat a thermal mass and then observe the thermal response. What I notice is a couple of things. 1.) There is a thermal delay between the application of heat and the sensor response, this is due to thermal gradients, thermal resistance, ect. 2.) Beyond the thermal delay I notice that the temperature of the system continues to increase even though the power has been removed. I know this is true because I model the system using a first order differential response curve. My simulated model follows the empirical exactly (along with the time delay) up until the point where, theoretically the temperature should begin its exponential decline back to ambient. However, although my simulated data shows a temperature decline within the thermal delay time, immediately after the power is removed, my empirical data shows an increase in temperature long after the calculated delay time. This, in essence is a thermal equivalent of a second order response. Now, thermally speaking, this should not be possible, but as we look into thermal expansion, atomic vibrations, and other physical energy storage components, we find that in fact (and real empirical data proves this to be true) a thermal system can and does increase in temperature after the heat source has been removed. Sorry to say that Google search will unlikely be of help here because very few people are asking the question or doing the research at that level. Most will say that thermal response is simply a first order response with a delay, but mathematical simulation of closed loop proportional control will fail to match that of real world response without consideration of second order components.