# What is Péclet Number – Definition

The Péclet number is a dimensionless number, named after the Jean C. E. Péclet. The Péclet number is defined as the ratio of the rate of advection to the rate of diffusion. Thermal Engineering

## What is Péclet Number

The Péclet number is a dimensionless number, named after the French physicist Jean Claude Eugène Péclet. The Péclet number is defined as the ratio of the rate of advection of a physical quantity by the flow to the rate of diffusion (matter or heat) of the same quantity driven by an appropriate gradient. Therefore we must distinguish between Peclet number for mass transfer and heat transfer.

## Peclet Number in Mass Transfer

In mass transfer problems, the Péclet number is the product of the Reynolds number, which describes the flow regime, and the Schmidt number, which is used to characterize fluid flows in which there are simultaneous momentum and mass diffusion convection processes.

where:

• u is the flow velocity,
• L is a characteristic linear dimension, (travelled length of the fluid; hydraulic diameter etc.)
• D is the mass diffusivity [m2/s]

## Peclet Number in Heat Transfer

In heat transfer problems, the Péclet number is the ratio of the thermal energy convected to the fluid to the thermal energy conducted within the fluid.  The Péclet number is simply defined as the product of the Reynolds number, which describes the flow regime, and the Prandtl number, which describes the relationship between momentum diffusivity and thermal diffusivity. If Pe is small, conduction is important.

where:

Thermal diffusivity represents how fast heat diffuses through a material and has units m2/s. In other words, it is the measure of thermal inertia of given material. Thermal diffusivity is usually denoted α and is given by:

As can be seen it measures the ability of a material to conduct thermal energy(represented by factor k) relative to its ability to store thermal energy (represented by factor ρ.cp). Materials of large α will respond quickly to changes in their thermal environment, whereas materials of small α will respond more slowly (heat is mostly absorbed), taking longer to reach a new equilibrium condition.

## Mass Diffusivity and Fick’s law

Diffusivity is encountered in Fick’s law, which states:

If the concentration of a solute in one region is greater than in another of a solution, the solute diffuses from the region of higher concentration to the region of lower concentration, with a magnitude that is proportional to the concentration gradient.

In one (spatial) dimension, the law is:

where:

• J is the diffusion flux,
• D is the diffusion coefficient,
• φ (for ideal mixtures) is the concentration.

The use of this law in nuclear reactor theory leads to the diffusion approximation.

References:
Heat Transfer:
1. Fundamentals of Heat and Mass Transfer, 7th Edition. Theodore L. Bergman, Adrienne S. Lavine, Frank P. Incropera. John Wiley & Sons, Incorporated, 2011. ISBN: 9781118137253.
2. Heat and Mass Transfer. Yunus A. Cengel. McGraw-Hill Education, 2011. ISBN: 9780071077866.
3. Fundamentals of Heat and Mass Transfer. C. P. Kothandaraman. New Age International, 2006, ISBN: 9788122417722.
4. U.S. Department of Energy, Thermodynamics, Heat Transfer and Fluid Flow. DOE Fundamentals Handbook, Volume 2 of 3. May 2016.

Nuclear and Reactor Physics:

1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
5. W.S.C. Williams. Nuclear and Particle Physics. Clarendon Press; 1 edition, 1991, ISBN: 978-0198520467
6. G.R.Keepin. Physics of Nuclear Kinetics. Addison-Wesley Pub. Co; 1st edition, 1965
7. Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988.
8. U.S. Department of Energy, Nuclear Physics and Reactor Theory. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.
9. Paul Reuss, Neutron Physics. EDP Sciences, 2008. ISBN: 978-2759800414.