1
$\begingroup$

Governing equation:

$$\frac{\partial \Omega}{\partial t} = \frac{\partial^2 \Omega}{\partial x^2} -DH \frac{\partial \Omega}{\partial x} $$ Find the steady-state solution $\Omega(x)$ from the governing equation with boundary conditions $\Omega(0) = 1$ and $\Omega(1) = 0$.

$\endgroup$
  • $\begingroup$ what does Ω(x) equal? $\endgroup$ – Dan Jan 31 '15 at 20:05
1
$\begingroup$

The steady state solution occurs when $\Omega_t = 0$. The steady-state obeys the equation (assuming $DH$ is a constant)

$$\Omega''(x) - DH \Omega'(x) = 0$$

with BC's $\Omega(0) =1$ and $\Omega(1)=0$. The solution is

$$\Omega(x) = A+B e^{DH x}$$

where $A+B = 1$ and $A + B e^{DH} = 0$.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.