Fast Peclet estimates show when flow dominates over diffusion in systems today. Switch heat or mass modes, validate inputs, and download reports instantly here.
The Peclet number compares advective transport to diffusive transport.
| Case | Mode | U (m/s) | L (m) | Diffusivity (m²/s) | Pe | Typical interpretation |
|---|---|---|---|---|---|---|
| 1 | Heat | 0.20 | 0.05 | α = 1.4×10⁻⁷ | 7.14×10⁴ | Advection dominates |
| 2 | Heat | 0.005 | 0.01 | α = 1.4×10⁻⁷ | 357 | Advection-leaning mixed |
| 3 | Mass | 0.01 | 0.01 | D = 2.0×10⁻⁹ | 5.0×10⁴ | Advection dominates |
| 4 | Mass | 1.0×10⁻⁴ | 0.001 | D = 2.0×10⁻⁹ | 50 | Mixed transport |
The Peclet number, Pe, compares bulk advection with diffusion. Small Pe means diffusion rapidly smooths temperature or concentration gradients. Large Pe means flow transports features downstream faster than diffusion can erase them, creating sharper boundary layers and stronger spatial nonuniformity.
For heat transfer, Pe = U·L/α, with α as thermal diffusivity. For species transport, Pe = U·L/D, with D as mass diffusivity. Both are dimensionless, so the result depends on choosing U and L that represent your actual transport path and gradient scale.
Because Pe scales linearly with L, pick it carefully. In pipes, L is commonly diameter or hydraulic diameter. Over plates or cylinders, L may be body length or diameter. In porous media, grain size or pore length is often used. Select the distance across which diffusion must act to relax gradients.
Water near room temperature has α ≈ 1.4×10⁻⁷ m²/s, while air is roughly 2×10⁻⁵ m²/s. Molecular mass diffusivities are often 10⁻⁹ to 10⁻¹⁰ m²/s in liquids and near 10⁻⁵ m²/s in gases. Property realism is as important as geometry.
Pe ≪ 1 suggests diffusion-dominated behavior; Pe ≫ 1 suggests advection-dominated behavior. Many systems fall between these extremes. Microchannels can have moderate Pe because L is small, even at noticeable velocities. Large ducts, rivers, and atmospheric flows often produce very large Pe values.
This tool can also compute Pe from Pe = Re·Pr (heat) or Pe = Re·Sc (mass). For example, water around 20°C has Pr ≈ 7, so Re = 10,000 implies Pe ≈ 70,000. For dilute solutes in water, Sc commonly ranges from hundreds to thousands.
High Pe implies thin thermal or concentration boundary layers, strong axial transport, and increased sensitivity to entrance effects or poor mixing. Low Pe supports lumped models and faster cross-domain equilibration. In design, Pe helps decide whether you must resolve diffusion in simulations or can prioritize convection-dominated numerics.
Report U, L, diffusivity source, and units with Pe. Unit mistakes are common: converting cm²/s to m²/s multiplies by 10⁻⁴. Ensure α, D, ρ, μ, c_p, and k are positive. When using Re·Pr or Re·Sc, verify Re and Pr/Sc were computed from consistent properties.
With U = 0.2 m/s, L = 0.05 m, and α = 1.4×10⁻⁷ m²/s, Pe ≈ 7.1×10⁴. That usually indicates advection-dominated heat transport and thin thermal boundary layers.
Use the scale that matches the dominant gradient. For radial diffusion across the pipe, diameter is common. For axial diffusion along the flow, a streamwise length may be more appropriate.
In many correlations, Re and Pr or Sc are already known or tabulated. Using their product provides Pe consistently, and it helps connect transport behavior to flow regime and material properties.
You can compute α from α = k/(ρ c_p). Enter thermal conductivity, density, and specific heat using consistent units. The calculator converts to SI internally before computing α.
Pe ≈ 1 means advection and diffusion contribute comparably. You should expect neither mechanism to dominate, so models or simulations should represent both accurately.
Large U, large L, or very small diffusivity will increase Pe. Double-check units, especially cm²/s versus m²/s, and confirm L matches your physical gradient length rather than total device size.
Pe is typically reported as a magnitude. A negative value usually comes from a sign convention in velocity or coordinate choice. Use absolute velocity for transport strength, and document the convention if direction matters.
Use Peclet insights to refine models and experiments confidently.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.