# Changes

## Péclet number (Pe) - Nishanth Saldanha

, 21 January
m
Derivation [3]
$\frac{dC}{dt} = \frac{\partial J}{\partial x}\rightarrow \frac{\partial C}{\partial t} =\triangledown nabla J$
This equation is also described in three dimensions.
$\frac{\partial x}{\partial t} = u$
$\frac{\partial C}{\partial t} = D\frac{\partial^{2} C}{\partial x^{2}} - u \frac{\partial C}{\partial x}\rightarrow \frac{\partial C}{\partial t} + u \frac{\partial C}{\partial x}= D\frac{\partial^{2} C}{\partial x^{2}} \rightarrow \frac{\partial C}{\partial t} + u \triangledown nabla C= D \triangledownnabla^{2} C$
Dimensionless numbers, as shown below can be used to restate the mass balance. $U$ equals the convective linear flow rate.
278
edits