BEJAN

Overview

The BEJAN function computes the Bejan number, a dimensionless number used in heat transfer and fluid mechanics to characterize the relative importance of pressure drop to thermal diffusion. There are two common forms:

• Bejan number (Length-based, $Be_L$):

  $$Be_L = \frac{\Delta P L^2}{\mu \alpha}$$

  where $\Delta P$ is the pressure drop (Pa), $L$ is the characteristic length (m), $\mu$ is the dynamic viscosity (Pa·s), and $\alpha$ is the thermal diffusivity (m²/s).

• Bejan number (Permeability-based, $Be_p$):

  $$Be_p = \frac{\Delta P K}{\mu \alpha}$$

  where $K$ is the permeability (m²).

The Bejan number is useful in analyzing forced convection and porous media flows. For more information, see the fluids.core documentation  and the fluids GitHub repository .

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

Usage

To use the function in Excel:

=BEJAN(type, dP, L_or_K, mu, alpha)

• type (string, required): Calculation type. One of "length" (for $Be_L$) or "permeability" (for $Be_p$).
• dP (float, required): Pressure drop in Pascals (Pa).
• L_or_K (float, required): Characteristic length (m) if type is "length", or permeability (m²) if type is "permeability".
• mu (float, required): Dynamic viscosity in Pa·s.
• alpha (float, required): Thermal diffusivity in m²/s.

The function returns a single value (float): the Bejan number for the specified type, or an error message (string) if the input is invalid.

Examples

Example 1: Bejan Number (Length-based)

In Excel:

=BEJAN("length", 10000, 1, 0.001, 0.000001)

Expected output:

Example 2: Bejan Number (Permeability-based)

In Excel:

=BEJAN("permeability", 10000, 1, 0.001, 0.000001)

Expected output:

Example 3: Bejan Number (Length-based, different values)

In Excel:

=BEJAN("length", 500, 0.5, 0.002, 0.00001)

Expected output:

Example 4: Bejan Number (Permeability-based, different values)

In Excel:

=BEJAN("permeability", 2000, 0.05, 0.005, 0.00002)

Expected output:

This means, for example, that for a pressure drop of 10,000 Pa, length or permeability of 1, viscosity of 0.001 Pa·s, and thermal diffusivity of 1e-6 m²/s, the Bejan number is $1 \times 10^{13}$.

Python Code

import micropip
await micropip.install(['fluids'])
from fluids import core as fluids_core
 
def bejan(type, dP, L_or_K, mu, alpha):
    """
    Compute the Bejan number (length-based or permeability-based) using fluids.core library.
 
    Args:
        type: Calculation type. 'length' for Bejan_L, 'permeability' for Bejan_p.
        dP: Pressure drop in Pascals (Pa).
        L_or_K: Characteristic length (m) or permeability (m²).
        mu: Dynamic viscosity in Pa·s.
        alpha: Thermal diffusivity in m²/s.
 
    Returns:
        The Bejan number (float), or an error message (str) if the input is invalid.
 
    This example function is provided as-is without any representation of accuracy.
    """
    try:
        dP = float(dP)
        L_or_K = float(L_or_K)
        mu = float(mu)
        alpha = float(alpha)
    except Exception:
        return "Invalid input: could not convert arguments to float."
    if not isinstance(type, str):
        return "Invalid input: type must be a string."
    t = type.lower()
    try:
        if t == "length":
            return fluids_core.Bejan_L(dP, L_or_K, mu, alpha)
        elif t == "permeability":
            return fluids_core.Bejan_p(dP, L_or_K, mu, alpha)
        else:
            return "Invalid input: type must be 'length' or 'permeability'."
    except Exception as e:
        return f"Error: {str(e)}"
    return "Invalid input: unknown error."

Example Workbook

Link to Workbook