Peclet Number Calculator
Find the Peclet number Pe = LV/alpha (heat) or Pe = LV/D (mass), the ratio of advective to diffusive transport.
🌀 What is the Peclet Number Calculator?
This Peclet number calculator finds Pe, the dimensionless ratio of advective transport to diffusive transport in a moving fluid. Switch between Heat Transfer mode, which computes Pe = LV/alpha using thermal diffusivity, and Mass Transfer mode, which computes Pe = LV/D using a mass diffusion coefficient, both from the same characteristic length L and flow velocity V.
Engineers and students use the Peclet number to design heat exchangers, size chemical reactors, analyze groundwater contaminant transport, and evaluate microfluidic devices. A large Peclet number tells you that bulk fluid motion is carrying heat or a dissolved species far faster than molecular diffusion can spread it, so plug-flow behavior dominates. A small Peclet number tells you the opposite, diffusion smooths out gradients faster than the flow can carry them, so the system behaves more like a well-mixed reactor.
A common point of confusion is mixing up the Peclet number with the Reynolds or Prandtl numbers. For heat transfer specifically, Pe is not independent of those two: Pe = Re x Pr exactly, so the Peclet number is really a shortcut that combines flow inertia effects and fluid property effects into a single advection-versus-diffusion comparison.
This calculator is useful for anyone studying convective heat transfer, mass transfer operations, chemical reaction engineering, or environmental transport who needs Pe quickly without manually multiplying and dividing three separate quantities by hand.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 - Water flowing through a small pipe (heat mode)
Example 2 - Slow micro-scale heat conduction in a copper chip (heat mode)
Example 3 - Small solute diffusing in a water channel (mass mode)
❓ Frequently Asked Questions
🔗 Related Calculators
What is the Peclet number?
The Peclet number, Pe, is a dimensionless quantity that compares the rate of advective transport (heat or mass carried by bulk fluid motion) to the rate of diffusive transport (molecular spreading). A large Pe means advection dominates, a small Pe means diffusion dominates.
What is the formula for the Peclet number?
For heat transfer, Pe = LV/alpha, where L is a characteristic length in metres, V is flow velocity in m/s, and alpha is thermal diffusivity in m squared per second. For mass transfer, Pe = LV/D, where D is the mass diffusion coefficient in m squared per second, in place of alpha.
How is the Peclet number related to Reynolds and Prandtl numbers?
For heat transfer, the Peclet number equals the product of the Reynolds number and the Prandtl number, Pe = Re x Pr. This identity is useful when you already know Re and Pr from a separate calculation and want Pe without re-entering length, velocity, and diffusivity.
What does a large Peclet number mean?
A large Peclet number (Pe much greater than 1) means advection dominates the transport process: bulk fluid motion carries heat or a dissolved species far faster than molecular diffusion can spread it. Most everyday pipe flows and heat exchangers have Pe in the thousands or higher.
What does a small Peclet number mean?
A small Peclet number (Pe much less than 1) means diffusion dominates: molecular spreading moves heat or mass faster than the slow bulk flow does. This regime shows up in microfluidic devices, groundwater seepage, and very small-scale heat conduction problems.
What is the difference between the thermal and mass transfer Peclet number?
Both use the same LV numerator (length times velocity) but divide by a different diffusivity: thermal diffusivity alpha for heat transfer, or the mass diffusion coefficient D for a dissolved or suspended species. The physical meaning, advection versus diffusion, is identical in both cases.
What is a typical thermal diffusivity value for water?
Water has a thermal diffusivity of about 0.143 mm squared per second (1.43 x 10 to the -7 m squared per second) at room temperature, much lower than most gases because liquids conduct heat comparatively slowly relative to their heat capacity.
What is a typical thermal diffusivity value for air?
Air has a thermal diffusivity of about 22 mm squared per second (2.2 x 10 to the -5 m squared per second) at room temperature, roughly 150 times higher than water, which is why heat spreads through still air by conduction much faster than through still water.
What is a typical mass diffusion coefficient for a small molecule in water?
A small solute dissolved in water typically has a mass diffusion coefficient around 0.001 mm squared per second (1 x 10 to the -9 m squared per second) at room temperature. Gas-phase diffusion coefficients are usually four to five orders of magnitude larger.
Why does the Peclet number matter for reactor and heat exchanger design?
The Peclet number tells engineers whether a flow behaves more like plug flow (high Pe, minimal back-mixing) or a well-mixed reactor (low Pe, diffusion smooths out concentration or temperature gradients). It directly affects reactor sizing, residence time distribution, and heat exchanger effectiveness calculations.
Can the Peclet number be calculated without a chemistry or heat transfer background?
Yes. You only need three numbers: a characteristic length (such as a pipe diameter or particle size), a flow velocity, and either the thermal diffusivity or mass diffusion coefficient of the fluid, which are widely tabulated for common substances like water and air.