Peclet Number Calculator

Peclet Number, denoted as "Pe", is a dimensionless number representing the ratio of advective to diffusive transport rates within a fluid flow. It involves various physical parameters, such as velocity, density, heat capacity, and more, to assess the dominant transport mechanism.

Historical Background

The Peclet Number is named after the French physicist Jean Claude Eugene Peclet. It plays a crucial role in the field of transport phenomena, helping to predict the behavior of systems where both advection and diffusion are present.

Calculation Formula

The general formula to calculate the Peclet Number is:

\[ Pe = \frac{v \rho c_p D}{k} \]

where:

• \(v\) = Velocity (m/s)
• \(\rho\) = Density (kg/m³)
• \(c_p\) = Heat Capacity (J/kg-K)
• \(D\) = Characteristic Length (m)
• \(k\) = Thermal Conductivity (W/m-K)

Example Calculation

For instance, to calculate the Peclet Number with given values:

• Velocity (\(v\)) = 5 m/s
• Density (\(\rho\)) = 1000 kg/m³
• Heat Capacity (\(c_p\)) = 4182 J/kg-K
• Characteristic Length (\(D\)) = 0.01 m
• Thermal Conductivity (\(k\)) = 0.6 W/m-K

Applying the formula:

\[ Pe = \frac{5 \times 1000 \times 4182 \times 0.01}{0.6} \approx 348500 \]

This high Peclet Number indicates that advective transport dominates over diffusive transport in this scenario.

Importance and Usage Scenarios

Understanding the Peclet Number is essential for designing and optimizing processes in chemical and mechanical engineering, especially where heat and mass transfer play critical roles.

Common FAQs

1. What does a high Peclet Number indicate?

   • A high Pe indicates dominance of advective transport over diffusion.

2. Can the Peclet Number be negative?

   • No, since it's based on absolute physical quantities, it's always positive.

3. How does the Peclet Number affect process design?

   • It helps in scaling up processes from lab to industrial scale by understanding the transport phenomena involved.