---
title: "Lewis Number in Heat and Mass Transfer"
description: "Lewis Number is the ratio of thermal diffusivity to mass diffusivity in Heat and Mass Transfer, showing whether heat or species diffusion spreads faster."
canonical: "https://fiveable.me/heat-mass-transfer/key-terms/lewis-number"
type: "key-term"
subject: "Heat and Mass Transfer"
unit: "Unit 9"
---

# Lewis Number in Heat and Mass Transfer

## Definition

Lewis Number (Le) is a dimensionless ratio in Heat and Mass Transfer: thermal diffusivity divided by mass diffusivity. It tells you whether heat spreads faster than mass in a fluid.

## What It Is

Lewis Number is the dimensionless ratio that compares how fast heat diffuses to how fast mass diffuses in a fluid. In Heat and Mass Transfer, you usually write it as Le = α/D, where α is thermal diffusivity and D is mass diffusivity.

That ratio matters because heat and species do not always spread at the same rate. Thermal diffusivity tells you how quickly a temperature change moves through a material, while mass diffusivity tells you how quickly concentration differences smooth out. Lewis Number puts those two transport processes on the same scale.

If Le is greater than 1, heat diffuses faster than mass. If Le is less than 1, mass diffuses faster than heat. When Le is close to 1, the two processes move at similar speeds, which makes coupled heat and mass transfer problems easier to compare and sometimes easier to model.

This comes up a lot in fluid systems where both temperature and concentration gradients are present. For example, in a reacting flow, a cooling fluid may be carrying heat away while a dissolved species is also spreading through the same layer. Lewis Number helps you tell whether the temperature field or the concentration field will adjust more quickly.

A common mistake is to treat Lewis Number like a measure of total transfer rate. It is not that. It is a comparison of diffusivities, so it does not directly tell you how much heat or mass is moving, only how their spreading rates relate. That is why it belongs in dimensionless analysis alongside numbers like Prandtl, Reynolds, and Péclet, where the goal is to compare mechanisms rather than measure one quantity by itself.

## Why It Matters

Lewis Number gives you a fast way to judge whether thermal diffusion and mass diffusion are behaving on similar time scales. In Heat and Mass Transfer, that matters whenever a problem mixes temperature change with concentration change, such as drying, evaporation, combustion, absorption, or reacting boundary layers.

If you know Le is near 1, you can often use simpler analogies between heat transfer and mass transfer because the two fields develop in a similar way. If Le is far from 1, those shortcuts can break down, and the temperature boundary layer and concentration boundary layer will not look the same.

It also helps you interpret physical behavior. In combustion, Lewis Number can affect flame shape, flame stability, and whether diffusion of fuel or heat dominates the local process. In separation or cooling systems, it can point you toward which transport mechanism is limiting performance.

In problem sets, Lewis Number often appears as part of a dimensionless group comparison. You may be asked to calculate it from given diffusivities, classify the system, or use it to justify an approximation in a transport model. So it is not just a definition to memorize, it is a decision tool for choosing the right simplification.

## Connections

### [Thermal Diffusivity](/heat-mass-transfer/key-terms/thermal-diffusivity)

Lewis Number uses thermal diffusivity in the numerator, so you need to know how quickly temperature disturbances spread through a material. A higher thermal diffusivity pushes Le upward if mass diffusivity stays the same. That is why different fluids can have very different Lewis Numbers even when the temperature difference looks similar.

### Mass Diffusivity

Mass diffusivity is the other half of the ratio, and it controls how fast concentration gradients even out. If mass diffusivity is large, Lewis Number tends to drop because species transport is fast compared with heat transport. This is the part of the problem that links Le to diffusion of solutes, vapors, or reacting species.

### [Prandtl Number](/heat-mass-transfer/key-terms/prandtl-number)

Prandtl Number compares momentum diffusivity to thermal diffusivity, while Lewis Number compares thermal diffusivity to mass diffusivity. Both are dimensionless comparisons of transport rates, but they answer different questions. Seeing them side by side helps you keep straight whether the problem is about velocity, temperature, or concentration spreading.

### [Dimensionless Analysis](/heat-mass-transfer/key-terms/dimensionless-analysis)

Lewis Number is one of the standard dimensionless groups used to simplify transport problems. Instead of carrying units through every step, you compare ratios that reveal which process dominates. That makes it easier to scale from one system to another and to spot when two setups should behave similarly.

## On the AP Exam

A problem set question usually gives you thermal diffusivity and mass diffusivity and asks you to compute Le, then interpret what that means for heat and species transport. You might also see a short answer asking which mechanism spreads faster in a given fluid or whether a simplifying assumption is reasonable. In a transport analysis, you use Lewis Number to justify whether the thermal and concentration boundary layers should be treated as similar or very different. If the value is near 1, that is a cue to compare heat and mass transfer more directly. If it is far from 1, you should be cautious about using a heat-mass analogy without checking the assumptions.

## Key Takeaways

- Lewis Number is the ratio Le = α/D, so it compares thermal diffusivity with mass diffusivity.
- A Lewis Number greater than 1 means heat diffuses faster than mass, while a value less than 1 means mass diffuses faster than heat.
- Values near 1 suggest heat and mass spread at similar rates, which can make coupled transport problems easier to analyze.
- Lewis Number does not tell you the total amount of heat or mass transfer, only the relative speed of diffusion.
- In Heat and Mass Transfer, Le is useful in combustion, drying, reacting flows, and any problem where temperature and concentration change together.

## FAQs

### What is Lewis Number in Heat and Mass Transfer?

Lewis Number is a dimensionless ratio, Le = α/D, that compares thermal diffusivity to mass diffusivity. It tells you whether heat spreads faster than a species concentration spreads in a fluid. In transport problems, that comparison helps you judge which diffusion process will dominate.

### How do you interpret Lewis Number greater than 1 or less than 1?

If Le > 1, thermal diffusion is faster than mass diffusion, so temperature changes spread more quickly than concentration changes. If Le < 1, mass diffusion is faster. A value near 1 means the two processes are moving at roughly the same rate.

### Is Lewis Number the same as Prandtl Number?

No. Lewis Number compares thermal diffusivity to mass diffusivity, while Prandtl Number compares momentum diffusivity to thermal diffusivity. They are both dimensionless transport ratios, but they describe different pairs of mechanisms, so you should not swap them in a calculation.

### Where does Lewis Number show up in engineering problems?

You see it in combustion, drying, absorption, evaporation, and other problems where heat and mass transfer happen at the same time. It is also useful when you want to decide whether a heat and mass transfer analogy is reasonable or whether the two fields need separate treatment.

## Related Study Guides

- [9.2 Dimensionless Numbers in Mass Transfer](/heat-mass-transfer/unit-9/dimensionless-numbers-mass-transfer/study-guide/aQ3hHXoFgNsEMIuW)

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