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 $\Omega(1) = 0$.

• what does Ω(x) equal? – Dan Jan 31 '15 at 20:05

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