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Question: Using the ThermophysicalData package in a system of ODEs

Question:Using the ThermophysicalData package in a system of ODEs

mayzal 25 Maple 2024
dsolve differential-equations thermophysicaldata
December 10 2024
1

I'm trying to solve system of ODE (Temperature changing with time) which are going to use the heat capacity obtained from thermophysical package (heat capacity is changing with temperature).

In the support page there is an example in which they were able to integrate the heat capacity from the package. So I wondering if it is possible to include it in an ODE system.

I used their same approach, I tried defining the call to the package as a function but I'm getting an error:

"Error, (in dsolve/numeric/process_input) input system must be an ODE system, found {ThermophysicalData:-CoolProp:-PropsSI(C,P,101325,T,T1(t),"hydrogen"), T1(t), T2(t), T3(t)}"

Attached question.mw

restart:
with(ThermophysicalData):
with(CoolProp):
with(plots):

#I would like to get the heat capacity from this package. Heat capacity is a function of temperature and pressure.
CP:=T1->PropsSI(C, P, 101325, T, T1, "hydrogen")/10000:

#Parameters
UA:=10:T0:=20:TS:=250:W:=100:M:=1000:

#The temperature is changing in this system of ODE with time. I would like to have the heat capacity value changing with temperature using the values obtained from the package.
EQ1:=diff(T1(t),t)=(W*CP(T1(t))*(T0-T1(t))+UA*(TS-T1(t)))/M/CP(T1(t)):
EQ2:=diff(T2(t),t)=(W*CP(T1(t))*(T1(t)-T2(t))+UA*(TS-T2(t)))/M/CP(T1(t)):
EQ3:=diff(T3(t),t)=(W*CP(T1(t))*(T2(t)-T3(t))+UA*(TS-T3(t)))/M/CP(T1(t)):

sol:=dsolve({EQ1,EQ2,EQ3,T1(0)=25,T2(0)=25,T3(0)=25},[T1(t),T2(t),T3(t)],numeric):
odeplot(sol,[[t,T1(t)],[t,T2(t)],[t,T3(t)]],t=0..140,legend=[T1,T2,T3],labels = ["time [min]", "Ti [C]"],axes=boxed)
sol(57.7);
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