Table 2.

Boundary conditions at unidirectional flow reactors.

Boundary condition	Expression	Details
I. inlet concentration is constant	${\frac{d{\mathit{C}}_{\mathit{A}}}{d\mathit{t}}|}_{\left(\mathit{z}=0\right)}=0$	Use for a single-pass of the fluid through the reactor, the solution plots the profile of ${\mathit{C}}_{\mathit{A}}$in z in the transient state.
II. External recirculation with a mixing tank	${\frac{d{\mathit{C}}_{\mathit{A}}}{d\mathit{t}}|}_{\left(\mathit{z}=0\right)}=\frac{1}{{\mathit{\tau }}_{\mathit{TK}}}\left({{\mathit{C}}_{\mathit{A}}}_{\left(\mathit{z}=1\right)}-{{\mathit{C}}_{\mathit{A}}}_{\left(\mathit{z}=0\right)}\right)$	External recirculation with a perfectly mixed tank without reaction and average residence time${\mathit{\tau }}_{\mathit{TK}}$. For ${\mathit{\tau }}_{\mathit{TK}}=1$the mean residence time of the external tank and reactor are equal. Multiple passes through the reactor can be analyzed.
III. Immediate recirculation	${\frac{d{\mathit{C}}_{\mathit{A}}}{d\mathit{t}}|}_{\left(\mathit{z}=0\right)}={\frac{d{\mathit{C}}_{\mathit{A}}}{d\mathit{t}}|}_{\left(\mathit{z}=1\right)}={-\frac{\partial {\mathit{C}}_{\mathit{A}}}{\partial \mathit{z}}|}_{\left(\mathit{z}=1\right)}-{Da|}_{\left(\mathit{z}=1\right)}$	The reactor outlet is connected to the reactor inlet. Mathematically, it is as if two reactors were joined, and the change in the output of one is equal to the change in the input of the next. Multiple passes through the reactor can be analyzed.