FOURIER_MASS

Calculates the mass-transfer Fourier number to quantify diffusive transport over time relative to characteristic length.

Excel Usage

=FOURIER_MASS(t, L, D)

t (float, required): Time (s)
L (float, required): Characteristic length (m)
D (float, required): Mass diffusivity (m²/s)

Returns (float): Fourier number for mass (float), or error message string.

Example 1: Mass Fourier number at moderate time and length

Inputs:

t	L	D
1.5	2	1e-9

Excel formula:

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

Expected output:

3.75e-10

Example 2: Shorter diffusion time lowers the Fourier number

Inputs:

t	L	D
0.5	2	1e-9

Excel formula:

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

Expected output:

1.25e-10

Example 3: Longer characteristic length lowers the Fourier number

Inputs:

t	L	D
1.5	4	1e-9

Excel formula:

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

Expected output:

9.375e-11

Example 4: Higher diffusivity raises the Fourier number

Inputs:

t	L	D
1.5	2	2e-9

Excel formula:

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

Expected output:

7.5e-10

Python Code

Show Code

from fluids.core import Fourier_mass as fluids_fourier_mass

def fourier_mass(t, L, D):
    """
    Calculate the Fourier number for mass transfer (Fo).

    See: https://fluids.readthedocs.io/fluids.core.html

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

    Args:
        t (float): Time (s)
        L (float): Characteristic length (m)
        D (float): Mass diffusivity (m²/s)

    Returns:
        float: Fourier number for mass (float), or error message string.
    """
    try:
        t_val = float(t)
        L_val = float(L)
        D_val = float(D)
    except Exception:
        return "Error: All parameters must be numeric values."
    if L_val == 0:
        return "Error: 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

Online Calculator

t *

Time (s)

L *

Characteristic length (m)

D *

Mass diffusivity (m²/s)