Peclet Number Equations Formulas Calculator

Heat Transfer Convection Conduction Dimensionless Value

Problem:

Solve for Peclet number.

Enter Calculator Inputs:

velocity (v)

density (ρ)

heat capacity (c_p)

characteristic length (D)

thermal conductivity (k)

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	Peclet number
	velocity
	density
	heat capacity
	characteristic length
	thermal conductivity

Background

In fluid dynamics and heat transfer, the Peclet number (Pe) is a dimensionless parameter that measures the relative importance of advection compared to diffusion. Named after the French physicist Jean Claude Eugène Péclet, it helps engineers and scientists predict how heat or mass moves through a flowing fluid. In processes where advection (bulk motion) dominates, transport is rapid and directional; when diffusion dominates, transport is slower and governed by molecular mixing.

Accurate evaluation of the Peclet number is essential for designing heat exchangers, chemical reactors, microfluidic devices, environmental models of pollutant dispersion, and electronics cooling systems. Pe guides decisions on geometry, flow rates, and material selection to achieve optimal thermal or concentration profiles by comparing advective and diffusive transport rates.

Equation

The Peclet number for heat transfer is defined as:

Pe = (ρ × v × cp × D) / k

Where:

Pe = Peclet number (dimensionless)
ρ = fluid density (kg/m³)
v = flow velocity (m/s)
cp = specific heat capacity at constant pressure (J/kg·K)
D = characteristic length or diameter (m)
k = thermal conductivity (W/m·K)

A high Pe indicates that advection (ρ·v·cp·D) dominates over conduction (k), whereas a low Pe means diffusion or conduction is the primary transport mechanism.

How to Solve

Determine fluid density (ρ): Obtain from material properties at the operating temperature.
Measure flow velocity (v): Use flow meters or calculate from volumetric flow rate and cross-sectional area.
Find specific heat (cp): Look up the fluid's heat capacity at the relevant temperature.
Select characteristic length (D): Choose a representative dimension, such as pipe diameter or channel width.
Obtain thermal conductivity (k): Use datasheets or handbooks for the fluid's conductivity.
Compute Pe: Substitute into Pe = (ρ·v·cp·D)/k.

Interpretation:

Pe ≫ 1: Advection dominates; heat or mass is carried rapidly downstream.
Pe ≪ 1: Diffusion dominates; transport is slow and spreads evenly.

Example

Problem:

Water (ρ = 1000 kg/m³, cp = 4184 J/kg·K, k = 0.6 W/m·K) flows through a pipe of diameter D = 0.01 m at velocity v = 0.2 m/s. Calculate the Peclet number.

Solution:

Numerator: ρ·v·cp·D = 1000 × 0.2 × 4184 × 0.01 = 8 368
Denominator: k = 0.6
Pe = 8 368 / 0.6 ≈ 13 947

Interpretation:

A Pe of ~1.4×10⁴ indicates advection overwhelmingly dominates conduction. Heat is carried downstream quickly, with minimal diffusive spread.

Five Fields or Degrees Where It's Used

Mechanical Engineering - Design of heat exchangers, boilers, and cooling jackets.
Chemical Engineering - Reactor design, separation processes, and mixing.
Environmental Engineering - Modeling pollutant transport in rivers and groundwater.
Biomedical Engineering - Microfluidic chip design for precise thermal control.
Electronics Cooling - Thermal management of CPUs, power electronics, and LED modules.

Five Real-Life Applications

Compact Heat Exchangers: Ensures efficient heat transfer in HVAC, power plants, and process industries.
Pollutant Dispersion Models: Predicts how contaminants travel in natural water bodies or air streams.
Lab-on-a-Chip Devices: Controls temperature gradients in microchannels for biochemical assays.
Food Pasteurization: Optimizes flow and heating to achieve uniform temperature without overprocessing.
Data Center Cooling: Guides coolant flow rates and channel dimensions for effective heat removal.

Five Common Mistakes

Wrong characteristic length: Using radius instead of diameter (or vice versa) without adjustment.
Assuming constant properties: Ignoring temperature dependence of ρ, cp, or k.
Mixing units: Failing to convert mm to m or J to W·s leads to erroneous Pe.
Neglecting flow regime: Overlooking turbulence effects that alter adequate mixing.
Ignoring wall effects: Not accounting for boundary layers that reduce effective transport.

Ignoring wall effects: Not accounting for boundary layers that reduce effective transport.Five Frequently Asked Questions (FAQs)

Q1: What does a very high Peclet number indicate?
A1: It means advection (bulk flow) dominates, so heat or mass is carried rapidly downstream with negligible diffusion.
Q2: When is diffusion more important than advection?
A2: When Pe is much less than 1, molecular diffusion (conduction) controls transport, leading to uniform spreading.
Q3: How do I choose the characteristic length (D)?
A3: Use a representative dimension where gradients develop—commonly pipe diameter, channel height, or plate thickness.
Q4: Can I apply this equation to gases and liquids alike?
A4: Yes. Use the appropriate ρ, cp, and k values for the fluid.
Q5: Is the Peclet number related to Reynolds and Prandtl numbers?
A5: For heat transfer, Pe = Re × Pr, linking inertial, viscous, and thermal diffusion effects in a single parameter.

References - Books:

Lindeburg, Michael R. 1992. Engineer In Training Reference Manual. Professional Publication, Inc. 8th Edition.