Discussion Closed This discussion was created more than 6 months ago and has been closed. To start a new discussion with a link back to this one, click here.

Formulating correct ODE, heat balance

Michael Rembe Certified Consultant

Please login with a confirmed email address before reporting spam

I have a subdomain with a volume V, that changes versus time. For the subdomain I have to formulate a ODE calculating heat balance. Can me anybody give a hint for the right formulation?

It is correct (?):

V*rho*cp*dT/dt+T*rho*cp*dV/dt=qss

with:
qss heat sinks and sources [J/s]
V Volume [m³]
rho density [kg/m³]
cp specific heat capacity [J/kg/K]
T temperature [K]
t time [s]

It seems, that the units are correct.

Thank you very much!
Michael Rembe

2 Replies Last Post Aug 6, 2009, 9:12 a.m. EDT
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)

Please login with a confirmed email address before reporting spam

Posted: 2 decades ago Aug 5, 2009, 4:04 p.m. EDT
Hi

I would propose that you state explicitely which variables are time dependent and which are not (COMSOL documents assumes that you know, this is often misleading for me) so if I assume you have rho, cp and qss as constants I would rewrite this as:

rho*cp*( V(t)*dT(t)/dt+T(t)*dV(t) ) = qss

or

d( V(t)*T(t) )/dt = qss/rho/cp = cte

which by integration is

V(t)*T(t) = qss/rho/cp*(t-t0)

no ?

So if the volume and the temperature are changing with time, but not the density, nor cp you should be talking about an incompressible fluid I believe, then I do not see what you are missing (for a constant power exchange), except if you are talking about chemistry (for which I'm not using COMSOL regularly), but then you should express this as several volumes mixing, no ?

There are so many "physics" that can be solved with COMSOL, so perhaps you should be more explicit on the physics and the boundary conditions ?

Good luck
Ivar
Hi I would propose that you state explicitely which variables are time dependent and which are not (COMSOL documents assumes that you know, this is often misleading for me) so if I assume you have rho, cp and qss as constants I would rewrite this as: rho*cp*( V(t)*dT(t)/dt+T(t)*dV(t) ) = qss or d( V(t)*T(t) )/dt = qss/rho/cp = cte which by integration is V(t)*T(t) = qss/rho/cp*(t-t0) no ? So if the volume and the temperature are changing with time, but not the density, nor cp you should be talking about an incompressible fluid I believe, then I do not see what you are missing (for a constant power exchange), except if you are talking about chemistry (for which I'm not using COMSOL regularly), but then you should express this as several volumes mixing, no ? There are so many "physics" that can be solved with COMSOL, so perhaps you should be more explicit on the physics and the boundary conditions ? Good luck Ivar

Michael Rembe Certified Consultant

Please login with a confirmed email address before reporting spam

Posted: 2 decades ago Aug 6, 2009, 9:12 a.m. EDT
Hi Ivar,

it seems, d( V(t)*T(t) )/dt = qss/rho/cp = cte helps and V*Tst+Ts*V_t-cte=0 is the correct formulation of the ODE.

Thanks for your hint!

Best regards
Michael
Hi Ivar, it seems, d( V(t)*T(t) )/dt = qss/rho/cp = cte helps and V*Tst+Ts*V_t-cte=0 is the correct formulation of the ODE. Thanks for your hint! Best regards Michael

Note that while COMSOL employees may participate in the discussion forum, COMSOL® software users who are on-subscription should submit their questions via the Support Center for a more comprehensive response from the Technical Support team.