RAC_RAYLEIGH_DISK

This function computes the critical Rayleigh number for the onset of natural convection between enclosed parallel disks. It supports insulated and uninsulated top-boundary cases, each with different stability thresholds.

The critical value depends on the disk aspect ratio through spacing and diameter, and is commonly used to determine when convection begins in enclosed disk geometries.

\mathrm{Ra}_c = f\!\left(\frac{D}{H},\text{boundary condition}\right)

Excel Usage

=RAC_RAYLEIGH_DISK(H, D, insulated)

H (float, required): Distance between the two disks (m).
D (float, required): Diameter of the disks (m).
insulated (bool, optional, default: true): Whether the top disk is insulated (-).

Returns (float): Critical Rayleigh number for disks, or error message if invalid.

Example 1: Critical Rayleigh for small uninsulated disks

Inputs:

H	D	insulated
1	0.4	false

Excel formula:

=RAC_RAYLEIGH_DISK(1, 0.4, FALSE)

Expected output:

151200

Example 2: Critical Rayleigh for large uninsulated disks

Inputs:

H	D	insulated
1	4	false

Excel formula:

=RAC_RAYLEIGH_DISK(1, 4, FALSE)

Expected output:

1891.52

Example 3: Critical Rayleigh for insulated disks

Inputs:

H	D	insulated
2	1	true

Excel formula:

=RAC_RAYLEIGH_DISK(2, 1, TRUE)

Expected output:

24347.3

Example 4: Critical Rayleigh at mid aspect ratio

Inputs:

H	D	insulated
0.5	1	true

Excel formula:

=RAC_RAYLEIGH_DISK(0.5, 1, TRUE)

Expected output:

2266.9

Python Code

Show Code

from ht.conv_free_enclosed import Rac_Nusselt_Rayleigh_disk as ht_Rac_Nusselt_Rayleigh_disk

def Rac_Rayleigh_disk(H, D, insulated=True):
    """
    Calculate the critical Rayleigh number for enclosed parallel disks.

    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:
        H (float): Distance between the two disks (m).
        D (float): Diameter of the disks (m).
        insulated (bool, optional): Whether the top disk is insulated (-). Default is True.

    Returns:
        float: Critical Rayleigh number for disks, or error message if invalid.
    """
    try:
        return ht_Rac_Nusselt_Rayleigh_disk(H=H, D=D, insulated=insulated)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

H *

Distance between the two disks (m).

D *

Diameter of the disks (m).

insulated

Whether the top disk is insulated (-).