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How It Works
The Peclet number measures whether bulk fluid motion (advection) or molecular diffusion is the dominant mechanism for transporting heat or mass. A large Pe means the flow carries heat downstream much faster than it can diffuse sideways, producing thin thermal boundary layers. A small Pe means diffusion spreads heat in all directions before the flow can carry it away.
Pe equals the product of the Reynolds and Prandtl numbers (Pe = Re × Pr), tying together fluid motion, viscosity, and thermal properties in a single parameter.
Example Problem
Water (ρ = 998 kg/m³, cₚ = 4,182 J/(kg·K), k = 0.6 W/(m·K)) flows at 0.5 m/s through a 0.01 m tube. What is the Peclet number?
- Pe = vρcₚD / k = 0.5 × 998 × 4,182 × 0.01 / 0.6
- Pe = 20,868.18 / 0.6 = 34,780
Pe ≫ 1 confirms that advection overwhelmingly dominates heat transport in this pipe, as expected for liquid water at moderate flow speeds.
Frequently Asked Questions
What does a high Peclet number mean physically?
A high Pe (much greater than 1) means the flow carries heat or mass downstream far faster than diffusion can spread it laterally. Thermal or concentration boundary layers are very thin, and upstream diffusion is negligible. Most industrial liquid flows have Pe in the thousands or higher.
When is the Peclet number small?
Pe is small in very slow flows, highly conductive fluids (like liquid metals), or very short length scales (microfluidics). In these situations, diffusion dominates and you can sometimes neglect the advective term entirely in the energy equation.
How is the Peclet number related to Re and Pr?
Pe = Re × Pr for heat transfer, or Pe = Re × Sc for mass transfer (where Sc is the Schmidt number). This decomposition is useful because Re and Pr (or Sc) are often available from standard property tables.
Related Calculators
- Nusselt Number Calculator — convective vs. conductive heat transfer at a surface.
- Prandtl Number Calculator — momentum vs. thermal diffusivity, one half of Pe = Re × Pr.
- Fourier Number Calculator — dimensionless time for transient heat conduction.
- Reynolds Number Calculator — determine flow regime, since Pe = Re × Pr.
- Thermal Diffusivity Calculator — find the diffusivity used in Peclet number calculations.