COMSOL Forums: apparent specific heat

Re: apparent specific heat

Tue, 09 Aug 2011 12:36:47 +0000

Hello Guys,

Thank you for the great help in this forum! I could understand the Cp defined here by Ivette, but I need some reading and training for using previously mentioned functions. Do you guys can refer me to a help source or a paper, etc which I can use them?

Thanks
Ehsan

Hello,

I have found this forum and it was so useful for me because I had the same problem about how type the apparent specific heat of phase change material in COMSOL.
But I've got interest in "sine" step or the function thay you metionated above, i don't know how to use it, but i understood that you can use it for check the function of cp, am I wrong??

I have a material that change phase from 313 to 316 K. The melting cp is 60.5 kJ/kgK and the cp from solid state is 2.5 kJ/kgK, and I type this into the program

Cp= 2500*(T<313)+(60500*(T>313)*(T<316))+2500*(T>316)

It works, but now i would like to plot the function in order to check the latent heat, if the integral of that cp function is the latent heat of my material i could validate the formula. My model is in 2D in COMSOL 3.5a.

I hope I've been clear,
thank you so much.

Ivette.

Re: apparent specific heat

Mon, 23 Aug 2010 19:44:12 +0000

Re: apparent specific heat

Tue, 10 Aug 2010 11:40:53 +0000

Hello,

I am working on a Phase Change Material simulation too. The specific heat capacity function is working very well with logical parameters. I want to compute the energy now. How do I integrate the specific heat capacity over the temperature to get the latent heat in my 3D model in COMSOL 3.5a

Thomas

Re: apparent specific heat

Tue, 09 Mar 2010 11:57:59 +0000

Hi

Thanks for the corrections, you are right I typed it out too quickly ;) I have corrected the "<"

The ice fraction is without units so I have a T[K] unit issue, I obviously need to revise my stuff ;)
I edited and added a "/DT" on my first reply, remains how to define correctly DT

furthermore if you need to express this as an energy there is a *rho [kg/m^3] missing and an implicit volume [m^3] from the integration (depending on how this is implemented in COMSOL) that is neither not explicitely writen out

Ivar

Re: apparent specific heat

Tue, 09 Mar 2010 11:20:41 +0000

This is a very interesting topic as I had the same issue when modelling a phase change material. Two small remarks concerning the equation proposed by Dr. KJELBERG:
1. condition for latent heat should be (T>Tm)*(T<Tf)
2. the unit of Cp is J/kg/K, hence to express Cp as a function of Latent Heat (J/kg), units must match. Please correct me if you have already considered it.

ps. for finely meshed model, I think the ice fraction term can be skipped, as this is already included in the temperature change of the considered control volume.
Best Regards

Re: apparent specific heat

Tue, 16 Feb 2010 05:41:23 +0000

Hi

good to hear that you found a way with smoothened functions, in V4 (soon there I have heard) the step standard function proposed are already "smoothened", still you must check that your time range does take a few point within the transition region, othervise it might skip over it (even fully I had the other day some short pulse with a low repetition cacle and the solvr just ignored several of them, so some hand tuning and a careful verification is mandatory.

Conserning heat exchanges over boundaries, when I do not want to use full fluidic models, induced convection fully simulated, I mostly set a Q heat loss factor (2W/K/m^2 for calme situations, 5W/K/m^2 and 2-4 times this for blow conditions, as "rule of thumb", but you must set a "true" external temperature, whatever that is).

Mostly this works quite OK but is rather empirical. For certain cases, such as small air gaps (mm and below)and "now blow", air behaves differently as convective exchange does manage to start up and you can get much lower heat exchange values, ar becomes a good isolator, I know you can use other tricks too and have larger air gaps while blocking the convective buildup, such as a "hairy surface" with fibres standing out, they do not even need to be very dense, finally it depends also on the direction of gravity w.r.t shell dimensions then I use only standfard convection of air with no "air" motion (just "bulk air as any bulk material).

Again all his depends on your experience and the details you want tu put in, not t sa the time you can spend simulatng ;)

Hope this helps on the way
Good luck
Ivar

Re: apparent specific heat

Mon, 15 Feb 2010 23:16:28 +0000

Thank you Dr. Ivar for your suggestion. When I tried to use the suggested expression with Heaviside function, the programme was not working properly. So currently I am using the apparent specific heat as

Cp_frozen+(Cp_unfrozen-Cp_frozen)*HS+D*(latent heat*Ice fraction)

where HS and D are Heaviside and Dirac functions.

If I use a constant temperature boundary condition for the freezing problem, I think its working. However, If i use a convention boundary condition (Suppose air with a heat transfer coefficient and temperature is blown to the boundary), the programme still doesn't give an accurate solution.

I am wondering whether you could help me in this regard.
Thanks,
Roopesh

Re: apparent specific heat

Sat, 06 Feb 2010 09:29:31 +0000

Hi

I would use something like:

Cp = Cp_frozen*(T<=Tf) +
Cp_latent heat*ice fraction/DT*(T-Tm')/(Tf-Tm')*(T>Tm’)*(T<Tf) +
Cp_unfrozen*(T>Tf)

Then you must combine, if you need to smoothen the "(T-Tm')/(Tf-Tm')", a "heaviside" or a "sine step" function. I prefere "sine" step as these are smooth up to to 2-3 derivatives without overshoots, but you must write them out first, a little agebra

PLS CHECK/PLOT this function out carefully, I might well have got the signs or the bolean wrong.

Often I define these expressions as functions in COMSOL as you can then easily check them with the "plot" button

Good luck
Ivar

apparent specific heat

Wed, 03 Feb 2010 16:00:34 +0000

I am using apparent specific heat during phase change.

The conditions are following. The apparent specific heat will be

Cp_unfrozen when T>Tf
Cp_frozen+(latent heat*ice fraction/temperature range) when Tm’<T<Tf
Cp_frozen when T<Tm’

How I can write the apparent heat expression in COMSOL using Heaviside and Dirac functions?

Thank you very much,
Roopesh