Lewis Number Equations Formulas Calculator

Fluid Mechanics Heat Mass Transfer Dimensionless Value

Problem:

Solve for Lewis number.

Enter Calculator Inputs:

Can you share this page? Because, it could help others.

Solution:

Enter input values and press Calculate.

Solution In Other Units:

Enter input values and press Calculate.

Input Unit Conversions:

Enter input values and press Calculate.

Change Equation or Formulas:

Tap or click to solve for a different unknown or equation

	Lewis number
	thermal diffusivity
	mass diffusivity

Reference - Books:

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

Background

The Lewis Number (Le) is a crucial dimensionless value in fluid mechanics, specifically in heat and mass transfer analysis. Named after Warren K. Lewis, a pioneer in chemical engineering, the Lewis Number represents the ratio of thermal diffusivity to mass diffusivity. It provides insights into a fluid's relative rates of heat and mass transfer processes. Understanding the Lewis Number is vital in designing efficient thermal systems and improving heat and mass exchange mechanisms in various engineering applications.

Equation

The following equation defines the Lewis Number:

Le = α / D_c

where:

α = thermal diffusivity (m²/s)
D_c = mass diffusivity (m²/s)

Thermal diffusivity (α) is a measure of how quickly heat spreads through a material, while mass diffusivity (D_c) measures the rate of mass transfer.

How to Solve

To solve for the Lewis Number, follow these steps:

Determine Thermal Diffusivity (α): Obtain the thermal diffusivity of the substance, which may be provided or can be calculated using the formula, α = k/ (ρ x c_p), where k is thermal conductivity, ρ is density, and c_p is specific heat capacity.
Determine Mass Diffusivity (D_c): Obtain the mass diffusivity of the substance, which is often provided in tables or can be determined experimentally.
Apply the Lewis Number Equation: Substitute the values of α and D_c into the Lewis Number equation, Le = α / D_c.

Example

Consider a gas with the following properties:

Thermal diffusivity (α) = 0.01 m²/s

Mass diffusivity (D_c) = 0.005 m²/s

To find the Lewis Number:

Le = 0.01 / 0.005 = 2

Thus, the Lewis Number for this gas is 2.

Fields/Degrees it is Used In

Chemical Engineering: For heat and mass transfer processes, such as distillation and absorption.
Mechanical Engineering: In the design of heat exchangers and thermal systems.
Environmental Engineering: To model the dispersion of pollutants in the atmosphere.
Aerospace Engineering: In the study of heat transfer in high-speed flight conditions.
Materials Science: For analyzing new materials' thermal and mass diffusion properties.

Real-Life Applications

Heat Exchangers: Designing efficient heat exchangers that optimize heat transfer between fluids.
Air Conditioning Systems: Enhancing the heat and mass transfer processes for improved cooling and heating efficiency.
Pollution Control: Understanding the dispersion of pollutants for better environmental protection measures.
Food Processing: Optimizing drying and cooling processes to maintain food quality.
Combustion Engines: Improving the efficiency of engines by optimizing the heat and mass transfer in combustion processes.

Common Mistakes

Incorrect Units: Failing to use units for thermal and mass diffusivity consistently can lead to incorrect calculations.
Misidentifying Properties: Confusing thermal conductivity with thermal diffusivity.
Neglecting Temperature Dependence: Not accounting for the temperature dependence of diffusivities.
Simplifying Assumptions: Overlooking assumptions that may not hold in real-world scenarios.
Input Errors: Entering incorrect values into calculators or formulas.

Frequently Asked Questions (FAQs)

Q1. What is the significance of the Lewis Number?
A1. The Lewis Number indicates the relative importance of heat transport versus mass transport in a fluid. A high Lewis number means heat transport is more dominant than mass transport.
Q2. How do thermal diffusivity and mass diffusivity differ?
A2. Thermal diffusivity measures how quickly heat spreads through a material, whereas mass diffusivity measures the rate at which particles or substances spread.
Q3. In which scenarios is the Lewis Number beneficial?
A3. The Lewis Number is critical in chemical processes concerning heat and mass transfer, such as drying, humidification, and absorption.
Q4. Can the Lewis Number be dimensionless?
A4. Yes, the Lewis Number is a dimensionless quantity, which means it has no units. It is a ratio of two diffusivities.
Q5. How can I find reliable data for thermal diffusivity and mass diffusivity (D_c)?
A5. Reliable data for thermal and mass diffusivity (D_c) can typically be found in engineering handbooks, scientific literature, and specialized databases. Experimental measurements can also provide accurate values.