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I am trying to solve a system of 3 equations and 3 unknown variables that change in time (Tw(t), Tcor(t), Texit(t)).

Clear[Tw];
Clear[Tcor];
Clear[Texit];
hb = 159.96;
hl = 45.90;
tf = 1400;
hfg = 2257.1*1000;
cpw = 4.2*1000;
ab = 0.0022765;
al = 0.030615;
Tf = 1450;
qm = 0.4474;
T0 = 298;
cpm = 4.01005*1000;

eq1 = Derivative[1][Tw][
    t] == (hb*ab*(((Tf - Tcor[t])/2) - Tw[t]) + 
      hl*al*(((Tcor[t] - Texit[t])/2) - Tw[t]) + 0.08*hfg - 
      cpw*Tw[t]*0.08)/(cpw*0.08*t);
eq2 = Derivative[1][Tcor][t] == 
   2*(-hb*ab*(((Tf - Tcor[t])/2) - Tw[t]) + qm*cpm*(Tf - T0) - 
       qm*cpm*(Tcor[t] - T0))/(cpm*qm);
eq3 = Derivative[1][Texit][t] == 
   2*(-hl*al*(((Tcor[t] - Texit[t])/2) - Tw[t]) + 
       qm*cpm*(Tcor[t] - T0) - qm*cpm*(Texit[t] - T0))/(cpm*qm);

sol = NDSolve[{eq1, eq2, eq3, Tw[0.000001] == 300, 
    Tcor[0.000001] == 750, Texit[0.000001] == 300}, 
   Tw, {t, 0.000001, 6000}, Tcor, {t, 0.000001, 6000}, 
   Texit, {t, 0.000001, 6000}];
Plot[Evaluate[Tw[t] /. sol], {t, 0.000001, 6000}] 

It is not working because 2 messages appear... a) Duplicate variable t found in the expression b) The expression is neither a list of replacement rules nor a valid dispatch table, and so cannot be used for replacing.

Although there are already a few answers about similar questions, I have no idea to solve this whatsoever.

Plus, it should also be imposed the condition of maximum Tw < 375 kelvin. As it simulates water boiling.

Thanks in advanced!

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    – bbgodfrey
    Commented Oct 11, 2021 at 17:26

1 Answer 1

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Change the two last commands by

sol = NDSolve[{eq1, eq2, eq3, Tw[0.000001] == 300, Tcor[0.000001] == 750, Texit[0.000001] == 300}, {Tw, Tcor, Texit}, {t, 0.000001, 6000}]
Plot[Evaluate[Tw[t] /. sol], {t, 0.000001, 6000}]
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  • $\begingroup$ I was not expecting that it was a syntax problem, thanks a lot! $\endgroup$
    – Eduardo
    Commented Oct 12, 2021 at 9:24
  • $\begingroup$ By any chance, do you have any idea how to impose a horizontal asymptode at Tw = 375? $\endgroup$
    – Eduardo
    Commented Oct 12, 2021 at 9:25

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