NU_RA_HOLLINGHERWIG

This function evaluates the Holling-Herwig correlation for natural convection between effectively infinite horizontal plates in a Rayleigh-Bénard configuration. It is intended for idealized geometry where one plate dimension is much larger than the other.

The correlation uses \mathrm{Ra} = \mathrm{Pr}\,\mathrm{Gr} in a nonlinear expression that captures turbulent free-convection scaling over high Rayleigh numbers. At low Rayleigh number or when buoyancy does not assist motion, the result falls back to the conduction baseline.

\mathrm{Nu} = 1 \quad \text{for } \mathrm{Ra} < 1708 \text{ or when buoyancy is not assisting convection}

Excel Usage

=NU_RA_HOLLINGHERWIG(Pr, Gr, buoyancy)
  • Pr (float, required): Prandtl number with respect to fluid properties (-).
  • Gr (float, required): Grashof number with respect to fluid properties and plate temperature difference (-).
  • buoyancy (bool, optional, default: true): Whether convection is buoyancy assisted (hot plate) (-).

Returns (float): Nusselt number between plates, or error message if invalid.

Example 1: Holling-Herwig correlation at high Rayleigh

Inputs:

Pr Gr buoyancy
5.54 321000000 true

Excel formula:

=NU_RA_HOLLINGHERWIG(5.54, 321000000, TRUE)

Expected output:

77.5466

Example 2: Holling-Herwig correlation at medium Rayleigh

Inputs:

Pr Gr buoyancy
0.71 10000000 true

Excel formula:

=NU_RA_HOLLINGHERWIG(0.71, 10000000, TRUE)

Expected output:

14.1806

Example 3: Holling-Herwig correlation near onset

Inputs:

Pr Gr buoyancy
1 50000 true

Excel formula:

=NU_RA_HOLLINGHERWIG(1, 50000, TRUE)

Expected output:

3.95402

Example 4: Holling-Herwig correlation with buoyancy opposed

Inputs:

Pr Gr buoyancy
0.9 2000000 false

Excel formula:

=NU_RA_HOLLINGHERWIG(0.9, 2000000, FALSE)

Expected output:

1

Python Code

Show Code 
from ht.conv_free_enclosed import Nu_Nusselt_Rayleigh_Holling_Herwig as ht_Nu_Nusselt_Rayleigh_Holling_Herwig

def Nu_Ra_HollingHerwig(Pr, Gr, buoyancy=True):
    """
    Calculate the Nusselt number between infinite horizontal plates using the Holling-Herwig correlation.

    See: https://ht.readthedocs.io/en/latest/ht.conv_free_enclosed.html

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

    Args:
        Pr (float): Prandtl number with respect to fluid properties (-).
        Gr (float): Grashof number with respect to fluid properties and plate temperature difference (-).
        buoyancy (bool, optional): Whether convection is buoyancy assisted (hot plate) (-). Default is True.

    Returns:
        float: Nusselt number between plates, or error message if invalid.
    """
    try:
        return ht_Nu_Nusselt_Rayleigh_Holling_Herwig(Pr=Pr, Gr=Gr, buoyancy=buoyancy)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Prandtl number with respect to fluid properties (-).
Grashof number with respect to fluid properties and plate temperature difference (-).
Whether convection is buoyancy assisted (hot plate) (-).