What is the best way to heat up a thermal liquid ?

Hello everyone,

In your opininon what is the best way to heat up a thermal liquid knowing the heat flow (in W). I am currently using a pipe with a controlled heat flow source but the fluid is not heating up correctly. Thank you in advance.

[Andres Adam]

Hi Karim, could you clarify what you mean by "not heating up correctly"? How do you know that the result is not correct?

[Karim Darwich]

@Andres Adam

I calculated the mdot*Cp*DT with DT the temperature difference between port A and B of the pipe and it's not equal to the value I entered in the heat flow component. I don't know if this clears it up. Thank you in advance

[Andres Adam]

Using a controlled heat flow source is a good way to ensure that the liquid in a pipe (TL) is heated or cooled. Whether it is the best way or not will depend on the physical setup you want to model.

You will not get an exact match using mdot*Cp*DT mostly because Simscape uses temperature-dependent values for density and Cp, but you can get very close. The temperature will also be affected by the viscous dissipation due to the pipe walls. You can check the documentation for the formulas used in the pipe block, and the source code for the foundation library Pipe (TL) is also open.

https://www.mathworks.com/help/simscape/ref/pipetl.html

If you still suspect something is wrong, do you mind sharing your model?

[Karim Darwich]

@Andres Adam

Of course here is the model with the data. Thank you for your response!

[Andres Adam]

Got it. A couple of notes first:

• You do not need two mass flow rate sources. One mass flow rate will ensure the specified mass flow through its line, and there is only one flow entry and one flow exit, so the second source is redundant and discrepancies will cause errors.
• You have an algebraic loop in your system. The temperature at the pipe exit will depend on the heat flux added, but the heat flux added depends on the pipe exit temperature. This can make the simulation unstable or slower. You can solve this by simply adding a unit delay in the sensor reading or the specification of heat flux. This will also help model real-world delays/latencies in your heating process.

I got your model and compared the Q added to mass flow * Cp * (Tin-Tout). The result is very close, but it is not exact - and it should not be! is valid for stationary processes, neglecting conductive heat transfer and viscous dissipation.

Your pipe is 2km long, that means there can be considerable heat dissipation, non-stationary effects, and conductive heat transfer. The Q you are specifiying with the "Controlled heat flow source" is the sum of conductive and convective heat transfer.

I will write an answer with a plot and another suggestion. Let me know if you have any more questions!

[Karim Darwich]

@Andres Adam

Thank you very much, I really appreciate your help Andres. Till now I have no further questions.

Have a nice day!

Answer 1

[Andres Adam]

Using a "Heat flow rate source" block is usually my go-to for adding heat to a Pipe (TL) and many other fluid blocks with a thermal port.

You mentioned the result was suspicious because the heat added to the pipe does not match the equation . While the right-hand side is a term for heat transfer, it is not the only factor for fluid energy change between inlet and outlet. The documentation for Pipe (TL) shows that term, adjusted by a factor dependent on the Nusselt number, plus non-stationary effects and conductive heat transfer. The heat flow specified by theat flow rate source will be the combination of conductive and convective heat transfers.

https://www.mathworks.com/help/simscape/ref/pipetl.html

Here is the comparison from your model. The difference is close to zero compared to the value of Q, but not exactly zero. See that the yellow line is slightly above zero while the system is almost stationary. That should be the combined effects of conductive heat transfer and heating through viscous effects.

However, directly connecting a heat flow rate source to the thermal port of a pipe may not be the most realistic solution. Between the pipe and the heat flow blocks, Simscape will put whatever temperature value can achieve the specified flow rate - no matter how unrealistic. In real-world applications, we often apply heat to the pipe from the outside and the pipe walls have thermal inertia. That's why we often add a "Thermal mass" block between the pipe and the heat flow source, like in this example:

https://www.mathworks.com/help/simscape/ug/engine-cooling-system.html