0
$\begingroup$

I have the following ODE:

$\frac{dC(t)}{dt} = -\frac{3}{r_{p}}\cdot F\cdot k_{f}\cdot (C(t)-C_{p}(r,t))$

Where $C_{p}(r,t)$ is being solved by a PDE and $C_{p}(r,t=0) = 0$.

Is it correct to take $C_{p}(r,t)$ as a constant and write:

$C(t) = C_{p}(r,t) + C_{0}\cdot e^{(-\frac{3}{r_{p}}\cdot F\cdot k_{f}\cdot t)}$

?

This is the full problem:

Full problem

Thank you.

  • 0
    Well you can't write it as a constant since it varies with $t$. What is the PDE? – 2017-02-13
  • 0
    But if I solve the PDE corresponding to Cp(r,t) and I know its value at every time point, the above equation is not valid? – 2017-02-13
  • 0
    Well, if you've solved the PDE, just use the value $C_p(r,t)$ you found. Look, if you differentiate your solution with respect to $t$, you find the very first equation if and only if $\partial_t C_p(r,t) = -\frac{3}{r_p} k _f F C_p(r,t)$. – 2017-02-13

0 Answers 0