FOURIER_HEAT

Overview

The FOURIER_HEAT function calculates the Fourier number for heat transfer, a dimensionless number that characterizes heat conduction relative to thermal energy storage. The Fourier number is used in transient heat conduction analysis and is defined as:

Fo = \frac{k t}{C_p \rho L^2} = \frac{\alpha t}{L^2}

where:

$t$ is time (s)
$L$ is the characteristic length (m)
$\rho$ is density (kg/m³)
$C_p$ is heat capacity (J/kg/K)
$k$ is thermal conductivity (W/m/K)
$\alpha$ is thermal diffusivity (m²/s)

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:


=FOURIER_HEAT(t, L, [rho], [Cp], [k], [alpha])

t (float, required): Time in seconds.
L (float, required): Characteristic length in meters.
rho (float, optional): Density in kg/m³. Required if Cp and k are provided.
Cp (float, optional): Heat capacity in J/kg/K. Required if rho and k are provided.
k (float, optional): Thermal conductivity in W/m/K. Required if rho and Cp are provided.
alpha (float, optional): Thermal diffusivity in m²/s. If provided, rho, Cp, and k are ignored.

The function returns a single value (float): the Fourier number (dimensionless), or an error message (string) if the input is invalid or insufficient.

Examples

Example 1: Using all properties

In Excel:


=FOURIER_HEAT(1.5, 2, 1000, 4000, 0.6)

Expected output:

Result
5.625e-08

Example 2: Using alpha only

In Excel:


=FOURIER_HEAT(1.5, 2, , , , 1E-7)

Expected output:

Result
3.75e-08

Example 3: Different time and length

In Excel:


=FOURIER_HEAT(2, 1, 800, 3800, 0.5)

Expected output:

Result
3.289e-07

Example 4: Alpha with different values

In Excel:


=FOURIER_HEAT(0.5, 0.5, , , , 2E-7)

Expected output:

Result
4e-07

Python Code


import micropip
await micropip.install('fluids')
from fluids.core import Fourier_heat as fluids_fourier_heat
 
def fourier_heat(t, L, rho=None, Cp=None, k=None, alpha=None):
    """
    Calculate the Fourier number for heat transfer.
 
    Args:
        t: Time in seconds.
        L: Characteristic length in meters.
        rho: Density in kg/m³ (optional).
        Cp: Heat capacity in J/kg/K (optional).
        k: Thermal conductivity in W/m/K (optional).
        alpha: Thermal diffusivity in m²/s (optional).
 
    Returns:
        The Fourier number (dimensionless, float), or an error message (str) if input is invalid.
 
    This example function is provided as-is without any representation of accuracy.
    """
    try:
        t_val = float(t)
        L_val = float(L)
    except Exception:
        return "Invalid input: could not convert t or L to float."
    # If alpha is provided, use it
    if alpha is not None:
        try:
            alpha_val = float(alpha)
        except Exception:
            return "Invalid input: could not convert alpha to float."
        try:
            result = fluids_fourier_heat(t_val, L_val, alpha=alpha_val)
        except Exception as e:
            return f"Error: {str(e)}"
        return result
    # Otherwise, need rho, Cp, k
    if None in (rho, Cp, k):
        return "Invalid input: must provide either alpha or all of rho, Cp, and k."
    try:
        rho_val = float(rho)
        Cp_val = float(Cp)
        k_val = float(k)
    except Exception:
        return "Invalid input: could not convert rho, Cp, or k to float."
    try:
        result = fluids_fourier_heat(t_val, L_val, rho=rho_val, Cp=Cp_val, k=k_val)
    except Exception as e:
        return f"Error: {str(e)}"
    return result

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FOURIER_HEAT

Overview

Usage

Examples

Python Code

Live Notebook

Live Demo