Hi all,

I’m trying to get Julia’s NonlinearSolve to play well with CoolProp. I am very new at Julia, coming from many years of Python, so I am still learning the ropes.

This is the code that is giving me trouble:

```
using ModelingToolkit, NonlinearSolve, CoolProp
@variables dm ρ1
@parameters a1 T1 P1
# Define a nonlinear system
eqs = [
ρ1 ~ PropsSI("D","T",T1,"P",P1,"AIR"),
k1 ~ PropsSI("ISENTROPIC_EXPANSION_COEFFICIENT","T",T1,"P",P1,"AIR"),
dm ~ a1 * sqrt(k1*ρ1*P1*(2/(k1+1))^((k1+1)/(k1-1)))
]
@mtkbuild ns = NonlinearSystem(eqs, [dm, ρ1], [a1, T1, P1])
d1 = 0.15e-3
guess = [
dm => 0.5e-3,
ρ1 => 20
]
ps = [
P1 => 20e5,
a1 => (d1/2)^2 * pi,
T1 => 293.0
]
prob = NonlinearProblem(ns, guess, ps)
sol = solve(prob, NewtonRaphson())
```

And it returns this error:

```
MethodError: no method matching Float64(::Num)
Closest candidates are:
(::Type{T})(::Real, ::RoundingMode) where T<:AbstractFloat
@ Base rounding.jl:207
(::Type{T})(::T) where T<:Number
@ Core boot.jl:792
Float64(::IrrationalConstants.Logtwo)
@ IrrationalConstants ~/.julia/packages/IrrationalConstants/vp5v4/src/macro.jl:112
...
Stacktrace:
[1] convert(::Type{Float64}, x::Num)
@ Base ./number.jl:7
[2] cconvert(T::Type, x::Num)
@ Base ./essentials.jl:543
[3] PropsSI(output::String, name1::String, value1::Num, name2::String, value2::Num, fluid::String)
@ CoolProp ~/.julia/packages/CoolProp/RDEcq/src/CoolProp.jl:81
[4] top-level scope
@ In[81]:8
```

I would expect this to *just work* but clearly there’s something here that I misunderstand. I also know that I could solve this system analytically, but this is a baby step before building a bigger system.

I think I understand that it is the wrong type being passed to the PropsSI function, but I don’t understand how to troubleshoot this any further, and methoderror seems quite common for newbies with Julia. Can I simply convert the types?

I have based my example on the documentation for NonlinearSolve, and it seems clear to me that it’s CoolProp giving the issue.

I can pass variables to CoolProp and get meaningful returns, as I would in Python, just fine, but I don’t understand why it breaks when I try to use in in a system of equations here.