FOURIER_HEAT

Calculates the heat-transfer Fourier number, comparing thermal diffusion over time to thermal storage length scale effects.

Excel Usage

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

t (float, required): Time (s)
L (float, required): Characteristic length (m)
rho (float, optional, default: null): Density (kg/m³)
Cp (float, optional, default: null): Heat capacity (J/kg/K)
k (float, optional, default: null): Thermal conductivity (W/m/K)
alpha (float, optional, default: null): Thermal diffusivity (m²/s)

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

Example 1: Heat Fourier number from density, heat capacity, and conductivity

Inputs:

t	L	rho	Cp	k
1.5	2	1000	4000	0.6

Excel formula:

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

Expected output:

5.625e-8

Example 2: Heat Fourier number from thermal diffusivity only

Inputs:

t	L	alpha
1.5	2	1e-7

Excel formula:

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

Expected output:

3.75e-8

Example 3: Different material properties using full property set

Inputs:

t	L	rho	Cp	k
2	1	800	3800	0.5

Excel formula:

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

Expected output:

3.28947e-7

Example 4: Thermal diffusivity path with smaller characteristic length

Inputs:

t	L	alpha
0.5	0.5	2e-7

Excel formula:

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

Expected output:

4e-7

Python Code

Show Code

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.

    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)
        rho (float, optional): Density (kg/m³) Default is None.
        Cp (float, optional): Heat capacity (J/kg/K) Default is None.
        k (float, optional): Thermal conductivity (W/m/K) Default is None.
        alpha (float, optional): Thermal diffusivity (m²/s) Default is None.

    Returns:
        float: Fourier number for heat (float), or error message string.
    """
    try:
        t_val = float(t)
        L_val = float(L)
    except Exception:
        return "Error: t and L must be numeric values."
    # If alpha is provided, use it
    if alpha is not None:
        try:
            alpha_val = float(alpha)
        except Exception:
            return "Error: alpha must be a numeric value."
        try:
            result = fluids_fourier_heat(t_val, L_val, alpha=alpha_val)
        except Exception as e:
            return f"Error: Failed to calculate Fourier number for heat: {str(e)}"
        return result
    # Otherwise, need rho, Cp, k
    if None in (rho, Cp, k):
        return "Error: 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 "Error: rho, Cp, and k must be numeric values."
    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: Failed to calculate Fourier number for heat: {str(e)}"
    return result

Online Calculator

t *

Time (s)

L *

Characteristic length (m)

rho

Density (kg/m³)

Heat capacity (J/kg/K)

Thermal conductivity (W/m/K)

alpha

Thermal diffusivity (m²/s)