Peclet Number Calculator

What is the Peclet Number?

The Peclet number ($Pe$) is a dimensionless parameter used in physics and engineering transport equations. It defines the ratio of transport by advection (bulk fluid flow movement) to the transport by diffusion (spontaneous molecular spreading). Understanding the Peclet number is crucial for analyzing heat exchangers, chemical reactors, environmental pollutant dispersions, and chromatography columns.

Mathematical Formulations

Depending on whether you are studying the transport of heat or the transport of mass (species), the Peclet number is defined using different parameters:

1. Thermal Peclet Number

For heat transfer, the Peclet number represents the ratio of thermal advection to thermal diffusion:

$$Pe = \frac{v \cdot \rho \cdot c_p \cdot L}{k}$$

Where:

• $v$ is the fluid flow velocity (m/s)
• $\rho$ is the fluid density (kg/m³)
• $c_p$ is the specific heat capacity (J/(kg·K))
• $L$ is the characteristic length (m)
• $k$ is the thermal conductivity (W/(m·K))

It can also be written in terms of the thermal diffusivity ($\alpha = k / (\rho \cdot c_p)$):

$$Pe = \frac{v \cdot L}{\alpha}$$

2. Mass Peclet Number

For mass transfer, the Peclet number describes species transport:

$$Pe = \frac{v \cdot L}{D}$$

Where:

• $v$ is the flow velocity (m/s)
• $L$ is the characteristic length (m)
• $D$ is the mass diffusion coefficient (m²/s)

Interpreting Peclet Number Values

The magnitude of the Peclet number tells us which mechanism governs transport in the fluid:

• Low Peclet Number ($Pe \ll 1$): Diffusion dominates. Fluid motion is slow or characteristic distances are tiny. Heat or mass spreads outwards in all directions, regardless of flow direction (for example, in microfluidic channels or capillary flows).
• High Peclet Number ($Pe \gg 1$): Advection dominates. Heat or mass is carried downstream by bulk fluid movement much faster than it spreads outwards by molecular diffusion.