The Lewis number (Le) is a

dimensionless number A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or 1) ...

defined as the ratio of

thermal diffusivity In heat transfer analysis, thermal diffusivity is the thermal conductivity divided by density and specific heat capacity at constant pressure. It measures the rate of transfer of heat of a material from the hot end to the cold end. It has the SI ...

to mass diffusivity. It is used to characterize fluid flows where there is simultaneous heat and mass transfer. The Lewis number puts the thickness of the thermal boundary layer in relation to the concentration boundary layer. The Lewis number is defined as :

\mathrm = \frac = \frac

. where

\alpha

is the

and

D

the mass diffusivity,

\lambda

the

thermal conductivity The thermal conductivity of a material is a measure of its ability to conduct heat. It is commonly denoted by k, \lambda, or \kappa. Heat transfer occurs at a lower rate in materials of low thermal conductivity than in materials of high thermal ...

\rho

the

density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematical ...

D_

the mixture-averaged diffusion coefficient, and

c_p

the

specific heat capacity In thermodynamics, the specific heat capacity (symbol ) of a substance is the heat capacity of a sample of the substance divided by the mass of the sample, also sometimes referred to as massic heat capacity. Informally, it is the amount of heat t ...

at constant pressure. In the field of fluid mechanics, many sources define the Lewis number to be the inverse of the above definition. The Lewis number can also be expressed in terms of the Prandtl number and the

Schmidt number Schmidt number (Sc) is a dimensionless number defined as the ratio of momentum diffusivity ( kinematic viscosity) and mass diffusivity, and it is used to characterize fluid flows in which there are simultaneous momentum and mass diffusion convec ...

: :

\mathrm = \frac

. It is named after

Warren K. Lewis Warren Kendall Lewis (21 August 1882 – 9 March 1975) was an MIT professor who has been called the father of modern chemical engineering. He co-authored an early major textbook on the subject which essentially introduced the concept of unit opera ...

(1882–1975), who was the first head of the Chemical Engineering Department at

MIT The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the m ...

. Some workers in the field of combustion assume (incorrectly) that the Lewis number was named for

Bernard Lewis Bernard Lewis, (31 May 1916 – 19 May 2018) was a British American historian specialized in Oriental studies. He was also known as a public intellectual and political commentator. Lewis was the Cleveland E. Dodge Professor Emeritus of Near ...

(1899–1993), who for many years was a major figure in the field of combustion research.

Literature

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References

{{NonDimFluMech Dimensionless numbers Fluid dynamics Dimensionless numbers of fluid mechanics Combustion