Lewis Number Calculator
Calculate the Lewis number, ratio of thermal to mass diffusivity.
Understanding Lewis Number Calculator
The Lewis number compares thermal diffusivity to mass diffusivity. Le = 1 means heat and mass transfer occur at the same rate (Lewis analogy).
$$Le = \frac{\alpha}{D} = \frac{Sc}{Pr}$$
How to use this calculator
- Enter the thermal diffusivity \(\alpha\) and the mass diffusivity \(D\), using matching units.
- If you have the Prandtl number \(Pr\) and Schmidt number \(Sc\), you can use those instead.
- Check that the values are positive, since diffusivities and dimensionless numbers used here should be greater than zero.
- Read the Lewis number \(Le\), which is the ratio of thermal diffusivity to mass diffusivity.
The formula explained
The Lewis number is computed by \(Le=\frac{\alpha}{D}=\frac{Sc}{Pr}\). It tells you how thermal diffusion compares with molecular mass diffusion in the same system.
- Le = Lewis number, a dimensionless ratio of thermal to mass diffusivity
- \(\alpha\) = Thermal diffusivity, how quickly heat spreads, typically in \(\mathrm{m^2/s}\)
- D = Mass diffusivity, how quickly a species spreads, typically in \(\mathrm{m^2/s}\)
- Sc = Schmidt number, a dimensionless ratio related to momentum and mass diffusion
- Pr = Prandtl number, a dimensionless ratio related to momentum and thermal diffusion
Step by step method
- Find the thermal diffusivity \(\alpha\) and the mass diffusivity \(D\), or the pair \(Sc\) and \(Pr\).
- Compute the ratio \(Le=\frac{\alpha}{D}\), or equivalently \(Le=\frac{Sc}{Pr}\).
- Simplify the quotient to get the Lewis number.
- Interpret the result, where \(Le>1\) means heat diffuses faster than mass and \(Le<1\) means mass diffuses faster than heat.
Worked example
Problem. A fluid has thermal diffusivity \(\alpha=1.8\times 10^{-5}\,\mathrm{m^2/s}\) and mass diffusivity \(D=2.4\times 10^{-5}\,\mathrm{m^2/s}\). Find the Lewis number.
- Use the formula \(Le=\frac{\alpha}{D}\).
- Substitute the values, \(Le=\frac{1.8\times 10^{-5}}{2.4\times 10^{-5}}\).
- Divide to get \(Le=0.75\).
Answer. \(Le=0.75\)
Tips and common mistakes
- Make sure \(\alpha\) and \(D\) are in the same units before dividing, otherwise the ratio will be wrong.
- Do not confuse the Lewis number with the Schmidt or Prandtl number, because \(Le\) is specifically their ratio, \(Le=\frac{Sc}{Pr}\).
Frequently asked questions
How do I calculate the Lewis number from thermal diffusivity and mass diffusivity?+
Use Le = α / D, where α is thermal diffusivity and D is mass diffusivity. If both values are in consistent units such as m²/s, the result is a unitless number.
What does the Lewis number tell me in heat and mass transfer?+
The Lewis number compares how quickly heat spreads to how quickly mass spreads in a fluid. A Lewis number near 1 means thermal and mass diffusivities are similar, while a larger or smaller value shows one process dominates the other.
Can I compute Lewis number from Prandtl number and Schmidt number?+
Yes, if you know the Prandtl number and Schmidt number, use Le = Sc / Pr. This form is useful when you have fluid property data instead of diffusivities.
What units should I use in the Lewis number calculator?+
Enter thermal diffusivity and mass diffusivity in matching units, typically m²/s. The Lewis number itself has no units because it is a ratio of two diffusivities.
What happens if the mass diffusivity is very small or zero?+
A very small mass diffusivity makes the Lewis number very large, because heat diffuses much faster than mass. If D is zero, the Lewis number is undefined since division by zero is not possible.
More Physics Tools
Explore related calculators in this category
Euler Number Calculator
Calculate the Euler number, dimensionless pressure drop in fluid flow.
Fourier Number Calculator
Calculate the Fourier number for transient heat conduction analysis.
Froude Number Calculator
Froude Number Calculator. Compute Fr = v/√(gL) for open channel flow analysis.
Knudsen Number Calculator
Calculate the Knudsen number to determine flow regime (continuum vs molecular).
You Might Also Like
Popular tools from other categories
Avogadro's Number Calculator
Convert between moles and number of particles. Free calculator with instant calculations, the underlying formula, and an easy-to-follow example.
Complex Number Calculator
Perform operations on complex numbers.
Number Base Converter
Convert between any two number bases (2-36).
Number Sequence Calculator
Identify and extend number sequences.
Can't Find the Right Calculator?
Try our AI Math Solver, type any problem in plain English and get instant step-by-step solutions.