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How to know when the system reaches steady state?

Posted 2022年2月17日 GMT-5 03:00 Heat Transfer & Phase Change, Heat Transfer, Studies & Solvers Version 5.6 3 Replies

Orçun YILDIZ
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I am solving a "heat transfer in solids" problem (only conductive heat transfer) with time-dependent solver. Heat dissipation is pulsed and on/off periods are in microseconds.

I've solved the model with stationary solver by taking average of the heat dissipation. For instance, heat dissipation is 100W with a duty cycle of 40%, which makes 40W average heat dissipation. By solving the system with 40W heat dissipation by using stationary solver, I have the value for steady state.

However, when I try to solve the system with real on/off heat dissipation value, I need to use time dependent solver. However, temperature increase is extremely slow since pulse time is around 20 microsecs on/30 microsecs off. If the system reaches steady state after 10 seconds, for instance, it makes 10000000 microsecs which requires incredibly high number of timesteps to solve.

How do I determine or estimate total time for the system to reach steady state? Any suggestions? Thank you for reading and help.

Sincerely,

Orcun

3 Replies Last Post 2022年2月17日 GMT-5 08:50
Edgar J. Kaiser Certified Consultant
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Posted: 2 years ago 2022年2月17日 GMT-5 04:33

Orcun,

I would suggest to run a time dependent study with constant average heat dissipation.

Cheers Edgar

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Edgar J. Kaiser
emPhys Physical Technology
www.emphys.com
Orcun, I would suggest to run a time dependent study with constant average heat dissipation. Cheers Edgar
Orçun YILDIZ
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Posted: 2 years ago 2022年2月17日 GMT-5 06:02

Dear Edgar,

Thank you for your suggestion. I will be trying this to see when the model reaches S.S.

Best Regards,

Orcun

Dear Edgar, Thank you for your suggestion. I will be trying this to see when the model reaches S.S. Best Regards, Orcun
Jeff Hiller COMSOL Employee

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Posted: 2 years ago 2022年2月17日 GMT-5 08:50
Updated: 2 years ago 2022年2月17日 GMT-5 11:47

Hello Orcun,

You can also get a general feel for the order of magnitude of the time it will take for your system to reach steady state by considering that the penetration depth in a thermal conduction problem is proportional to sqrt(kt/(rhoCp)) and the time length scale is tau=rho * Cp * L^2 / k (See this old thread for details). For many problems where all the sinks and sources are on the boundaries, this provides a decent estimate, with steady state being reached -for practical purposes- in a few taus.

Best,

Jeff

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Jeff Hiller
Hello Orcun, You can also get a general feel for the order of magnitude of the time it will take for your system to reach steady state by considering that the penetration depth in a thermal conduction problem is proportional to sqrt(k*t/(rho*Cp)) and the time length scale is tau=rho * Cp * L^2 / k (See [this old thread](https://www.comsol.com/forum/thread/16808/weird-problem-in-comsol-tmeperature-measurment?last=2011-04-11T20:06:31Z) for details). For many problems where all the sinks and sources are on the boundaries, this provides a decent estimate, with steady state being reached -for practical purposes- in a few taus. Best, Jeff

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