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Formulating correct ODE, heat balance
Posted Aug 5, 2009, 5:04 a.m. EDT 2 Replies
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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
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
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Posted:
1 decade ago
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
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
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Posted:
1 decade ago
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
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