My MTK implementation of a DAE for doing Monte Carlo study of parameter uncertainty doesn’t work. I think it has to do with how MTK removes parameters that do not show up explicitly in the model equations.

Here is some code:

```
using ModelingToolkit
using DifferentialEquations
@register_symbolic u_If(t)
@register_symbolic u_It(t)
@register_symbolic u_Twc(t)
# Give the inputs some constant values, e.g.,
u_If(t) = 800
u_It(t) = 5e3
u_TWc(t) = 4
# Parameters with defaults
@parameters (UA_r2δ=2.7, UA_s2Fe=20, UA_Fe2a=14.3, UA_x=44.4, Q̇_Fe_σ=212, Q̇_f_σ=422.4,
m_r=9260, m_s=6827, m_Fe=71200, R_r=0.127e-3, R_s=1.95e-6, ṁ_a=49.2, ṁ_w=54.2,
ĉ_pCu=0.385, ĉ_pFe=0.465, ĉ_pa=1.15, ĉ_pw = 4.18,
N_St_a=UA_x/(ĉ_pa*ṁ_a), N_St_w=UA_x/(ĉ_pw*ṁ_w), N_St_Δ=N_St_w-N_St_a)
# Independent variable and differentiation operator
@variables t
Dt = Differential(t)
# Dependent variables
@variables (T_r(t)=28, T_s(t)=28, T_Fe(t)=28, T_ac(t)=14, T_aδ(t)=14, T_ah(t)=22, I_f(t), I_t(t), T_wc(t))
# Input equations/input system
eqs_i = [I_f ~ u_If(t), I_t ~ u_It(t), T_wc ~ u_Twc(t)]
@named sys_i = ODESystem(eqs_i)
# Model equations/system
eqs_p = [Dt(T_r) ~ (1.1*R_r*I_f^2 - UA_r2δ*(T_r-T_aδ))/(m_r*ĉ_pCu),
Dt(T_s) ~ (3*R_s*I_t^2 - UA_s2Fe*(T_s-T_Fe))/(m_s*ĉ_pCu),
Dt(T_Fe) ~ (UA_s2Fe*(T_s-T_Fe) - UA_Fe2a*(T_Fe-T_ah) + Q̇_Fe_σ)/(m_Fe*ĉ_pFe),
0 ~ ṁ_a*ĉ_pa*(T_ac-T_aδ) + UA_r2δ*(T_r-T_aδ) + Q̇_f_σ,
0 ~ ṁ_a*ĉ_pa*(T_aδ-T_ah) + UA_Fe2a*(T_Fe-T_ah),
0 ~ T_ac*(N_St_w-N_St_a*exp(-N_St_Δ)) - N_St_Δ*T_ah - N_St_a*(1-exp(-N_St_Δ))*T_wc]
@named sys_p = ODESystem(eqs_p)
# Total system
sys = extend(sys_i, sys_p)
sys_simp = structural_simplify(sys)
# Converting symbolic model to numeric model
tspan = (0, 600)
#
prob = ODEProblem(sys_simp, [], tspan)
```

The last statement crashes with error message:

```
ArgumentError: Any[UA_x / (ĉ_pw*ṁ_w), 0.017674089784376106UA_x, UA_x / (ĉ_pw*ṁ_w) - 0.017674089784376106UA_x] are either missing from the variable map or missing from the system's states/parameters list.
```

My *suspicion* is that MTK has *removed* parameters in the `@parameters`

list that do not *explicitly* appear in the model. This includes `UA_x`

, `ĉ_pw`

, `ṁ_w`

.

**Questions**:

- Is my suspicion correct?
- If so, how do I get around this?
- I
*could*of course remove the parameters`UA_x`

,`ĉ_pw`

,`ṁ_w`

and instead just specify the two*Stanton numbers*`N_St_a`

and`N_St_w`

. Then I think the model would work.*However*, I want to study uncertainty in the*heat transfer coefficient*`UA_x`

, which is a single parameter.