Discussion Forum

Hi

I would say: in the Results add a domain integration of ht.Cp*T*ht.rho, but check it this varaible is not already defined by default by COMSOL ;)

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Good luck
Ivar

Hi

I would say: in the Results add a domain integration of ht.Cp*T*ht.rho, but check it this varaible is not already defined by default by COMSOL ;)

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Good luck
Ivar

Hi Ivar,

Thank you for your reply. Your suggestion would work just fine if Cp was constant. In my case Cp is a function of temperature. Therefore, in order to calculate the amount of heat stored, I think I need to calculate the area under the Cp versus Temperature curve (i.e. integrating Cp with respect to temperature) before I do a domain integration. This is the generalized form of enthalpy (H) definition.

H = integral (Cp . dT)

How can I do this in COMSOL?

Thanks again.

Ismail

Hi

if Cp is defined a Cp(T,p, ...) then COMSOl will map directly the Cp per element and per T corresponding to that elements, so I do not believe you need anything else than to write out the formula.

Now if you have defined Cp as a variable or an analytical function you need to integrate your_Cp(T)*T*ht.rho over the domain, all three of these are not truely varaibles but fields, with implicit Cp(T,p,x,y,z ...) variables, bit not shown in COMSOL notation convention

Test it out on a simple 2D example with "simple" known values to get convinced. The nice thing with COMSOl it's so easy to test the math underlaying by simple examples ;)

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Good luck
Ivar

Hi Ivar,

In my case Cp is a function of temperature and I define it via an interpolation (data source: table) under "Global Definitions" in COMSOL:

Cp(T)

And yes, at any given time point, there is a temperature distribution on my domain and we can calculate the corresponding Cp(T) distribution with no problem.

The question arises when we try to calculate the heat added into our domain:

heat added = (enthalpy at current time) - (enthalpy at time = 0)

Lets say temperature at time = 0 is T0 and the temperature at current time is T. Then,

heat added = integral of Cp(T)*dT (integrated from T0 to T)

Since Cp is not constant, the following is not true:

heat added = Cp(T)*T - Cp(T0)*T0

Yes, we can calculate Cp(T)*T in COMSOL for any given time point, but how can we take the following integral in COMSOL?

heat added = integral of Cp(T)*dT (integrated from T0 to T)

Thank you for your help.

Ismail

Hi

Ok now I understand you better ;) And you are perfectly right, it's not the same

then I would say define a global dependent variable via its time derivative and have COMSOL integrate it over your time dependent solver case t. I believe that is the closest you can get.

And if I remember right the KB (knowledge base) has some entries on this too, try a search on time derivatives

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Good luck
Ivar

Thanks Ivar. I will give it a thought. Another idea that came to my mind is to integrate Cp(T) with respect to T manually and enter it into COMSOL as another interpolation table. It would be really nice if COMSOL did this numerically for us though!

Thanks again!

Ismail

Hi

that is what I understand what COMSOl does if you define a global dependent variable as the integration of Cp(T)*T,
and write out the equations as a derivative. Then after a time "t" the resulting value is a time integation of the stored energy at each moment

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Good luck
Ivar

Hi Ivar,

We want to calculate:

integral of Cp(T)*dT

Per your suggestion, we can write the following by making use of the chain rule:

Cp(T)*dT = Cp(T)*(dT/dt)*dt

Then:

temperature integral of Cp(T) = time integral of Cp(T)*(dT/dt)

Great! Do you know the expression in COMSOL for the time derivative of temperature (i.e. dT/dt)?

Thanks!

Ismail

Hi Ivar,

It looks like Tt is the first time derivative of temperature in COMSOL.

Thanks again for all your help!

Ismail

Hi I am planing to write a partial PDE equation in comsol regarding heat transfer. Could you please help me to figure out how is possible?