I want to solve some heat transfer problems with Mathematica. I am trying to run the heat transfer tutorial cases but I am always getting the error "NDSolveValue: Equation or list of equations expected instead of ..." I was reading into the HeatTransferPDEComponent documentation and tried running the example case, but the same problem appears. See the code below, I tried some stuff I found on the forum in the top 3 lines.

What is causing these errors and how can I fix it?

picture of code with error

Clear[vars, pars, \[CapitalOmega], eqn, Tfun]

ClearAll[vars, pars, \[CapitalOmega], eqn, Tfun]

vars = {\[CapitalTheta][x], {x}};

pars = <|"ThermalConductivity" -> 0.026, "HeatSource" -> 1|>;
\[CapitalOmega] = Line[{{0}, {1}}];

eqn = HeatTransferPDEComponent[vars, pars] == 0

Tfun = NDSolveValue[{eqn, 
    HeatTemperatureCondition[x == 0, vars, 
     pars, <|"SurfaceTemperature" -> 0|>]}, \[CapitalTheta], 
   x \[Element] \[CapitalOmega]];
Plot[Tfun[x], {x} \[Element] \[CapitalOmega]]

I want to add that I am new to Mathematica. Further I tried running some code snippets not using the HeatTransferPDEComponent stuff but defining the heat equation in the code, which worked just fine.

  • $\begingroup$ Indeed, I can't activate HeatTransferPDEComponent[{\[CapitalTheta][t, x], t, {x}}, <| "MassDensity" -> \[Rho], "SpecificHeatCapacity" -> Subscript[C, p], "ThermalConductivity" -> \[Kappa]|>] in 12.3. $\endgroup$
    – user64494
    Jul 15, 2021 at 9:02
  • $\begingroup$ I am running 12.1 by the way. $\endgroup$
    – Tobias
    Jul 15, 2021 at 9:13
  • $\begingroup$ @user64494, works just fine for me on 12.3 $\endgroup$
    – user21
    Jul 15, 2021 at 9:22
  • $\begingroup$ @user21: I obtain "Div::sclr: The scalar expression (-[Kappa]).{([CapitalTheta]^(0,1))[t,x]} does not have a divergence." $\endgroup$
    – user64494
    Jul 15, 2021 at 10:59
  • $\begingroup$ @user64494, what OS? $\endgroup$
    – user21
    Jul 15, 2021 at 11:17

1 Answer 1


The HeatTransferPDEComponent was introduced in version 12.2 so will need at least that version to run it. See how the function name is still blue - this means that symbol is not defined in the version you run.

  • $\begingroup$ Thanks a lot! I was going crazy on not being able to run the tutorial cases. $\endgroup$
    – Tobias
    Jul 15, 2021 at 9:26
  • $\begingroup$ @Tobias, but there is a heat transfer tutorial in 12.1, it just does not make use of the newly added functions. You could have a look at that. There are, of course, no reference pages in 12.1 as then the functions did not exist. But maybe this is an incentive to get the update. $\endgroup$
    – user21
    Jul 15, 2021 at 9:28
  • $\begingroup$ I can't update unfortunately as I am adding to some existing code that requires some older stuff. Any chance you know where I can find those old tutorials? I've been googling for quite a while and couldn't find anything useful. $\endgroup$
    – Tobias
    Jul 15, 2021 at 10:31
  • $\begingroup$ Paste PDEModels/tutorial/HeatTransfer/HeatTransfer into the help system $\endgroup$
    – user21
    Jul 15, 2021 at 10:34

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