# Peclet Number

Written by Jerry Ratzlaff. Posted in Dimensionless Numbers

Péclet Number is a dimensionless number defined as a ratio of a flow rate of momentum diffusivity to thermal diffusivity.

## FORMULA

$$Pe = \frac { \nu} { \alpha }$$

$$Pe = \frac { v \rho c l } { k }$$

Where:

$$Pe$$ = Peclet Number

$$\nu$$ = kinematic viscosity

$$\alpha$$ = thermal diffusivity

$$v$$ = velocity

$$\rho$$ = density

$$c$$ = heat capacity

$$l$$ = characteristic length

$$k$$ = thermal conductivity

Solve for:

$$v = \frac {Pe k} { \rho c l }$$

$$\rho = \frac {Pe k} { v c l }$$

$$c = \frac {Pe k} { v \rho l }$$

$$l = \frac {Pe k} { v \rho c }$$

$$k = \frac { v \rho c l } { Pe }$$