Hi

I want to solve a system of equation with one PDE which is heat-diffusion equation and one ODE which is Arrhenius equation:

```
eq = [ρ*Cp*Dt(T(t,x,y)) ~ kx*Dxx(T(t,x,y)) + ky*Dyy(T(t,x,y)) - H*W*Dt(c(t,x,y)),
-Dt(c(t,x,y)) ~ A*c(t,x,y)*exp(-E/(Rc*T(t,x,y)))]
```

I want to determine T and c.

for this system, The Temperature in the ODE is the average temperature in the whole domain and c is a function of time only.

My problems are:

- How can I implement or define the average Temperature for the second equation (instead of T which is computed for each node)?
- When I write c(t) I get error and the error vanishes when I define it as c(t,x,y)
- I got a boundary condition which is conduction-convection balance:

` -kx*Dx(T(t,Le,y)) ~ h * (T(t,Le,y)- T_ext)`

Le is the length of the domain which is on the right boundary.

Is defining the boundary condition like this ok since there is Temperature in it?

ps: Every parameter in the equation is constant except T and c.

Thanks