FOURIER_MASS

Overview

The FOURIER_MASS function calculates the Fourier number for mass transfer (Fo), a dimensionless number that characterizes transient mass diffusion. It is defined as the ratio of diffusive transport rate to the rate of storage of mass, and is widely used in chemical engineering, environmental engineering, and related fields. The Fourier number for mass transfer is given by:

where $D$ is the diffusivity (m²/s), $t$ is the time (s), and $L$ is the characteristic length (m).

For more information, see the fluids GitHub repository  and the official documentation .

This example function is provided as-is without any representation of accuracy.

Usage

To use the function in Excel:

=FOURIER_MASS(t, L, D)

• t (float, required): Time in seconds.
• L (float, required): Characteristic length in meters.
• D (float, required): Diffusivity in m²/s.

The function returns a single value (float): the Fourier number for mass transfer, or an error message (string) if the input is invalid or out-of-range.

Examples

Example 1: Basic Calculation

In Excel:

=FOURIER_MASS(1.5, 2, 1E-9)

Expected output:

Example 2: Shorter Time

In Excel:

=FOURIER_MASS(0.5, 2, 1E-9)

Expected output:

Example 3: Larger Length

In Excel:

=FOURIER_MASS(1.5, 4, 1E-9)

Expected output:

Example 4: Higher Diffusivity

In Excel:

=FOURIER_MASS(1.5, 2, 2E-9)

Expected output:

Python Code

import micropip
await micropip.install('fluids')
from fluids.core import Fourier_mass as fluids_fourier_mass
 
def fourier_mass(t, L, D):
    """
    Calculate the Fourier number for mass transfer (Fo).
 
    Args:
        t: Time in seconds.
        L: Characteristic length in meters.
        D: Diffusivity in m²/s.
 
    Returns:
        The Fourier number for mass transfer (float), or an error message (str) if the input is invalid or out-of-range.
 
    This example function is provided as-is without any representation of accuracy.
    """
    try:
        t_val = float(t)
        L_val = float(L)
        D_val = float(D)
    except Exception:
        return "Invalid input: could not convert arguments to float."
    if L_val == 0:
        return "Invalid input: L must not be zero."
    try:
        result = fluids_fourier_mass(t_val, L_val, D_val)
    except Exception as e:
        return f"Error: {str(e)}"
    return result

Live Notebook

Edit this function in a live notebook .

Live Demo