RAC_RAYLEIGH

This function estimates the critical Rayleigh number for the onset of natural convection between enclosed parallel horizontal plates. It distinguishes insulated and uninsulated top-boundary conditions, which shift the instability threshold.

The result is a geometry-dependent stability limit based on plate spacing and in-plane dimensions. This value is typically used as an input to enclosed-convection Nusselt correlations.

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

Excel Usage

=RAC_RAYLEIGH(H, L, W, insulated)
  • H (float, required): Distance between the two plates (m).
  • L (float, required): Length of the plates (m).
  • W (float, required): Width of the plates (m).
  • insulated (bool, optional, default: true): Whether the top plate is insulated (-).

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

Example 1: Critical Rayleigh for uninsulated top plate

Inputs:

H L W insulated
1 0.5 2 false

Excel formula:

=RAC_RAYLEIGH(1, 0.5, 2, FALSE)

Expected output:

2530.5

Example 2: Critical Rayleigh for insulated top plate

Inputs:

H L W insulated
1 0.5 2 true

Excel formula:

=RAC_RAYLEIGH(1, 0.5, 2, TRUE)

Expected output:

2071.01

Example 3: Critical Rayleigh for square plates

Inputs:

H L W insulated
1 1 1 false

Excel formula:

=RAC_RAYLEIGH(1, 1, 1, FALSE)

Expected output:

6974

Example 4: Critical Rayleigh for thin gap

Inputs:

H L W insulated
0.2 1 2 true

Excel formula:

=RAC_RAYLEIGH(0.2, 1, 2, TRUE)

Expected output:

16998.4

Python Code

Show Code 
from ht.conv_free_enclosed import Rac_Nusselt_Rayleigh as ht_Rac_Nusselt_Rayleigh

def Rac_Rayleigh(H, L, W, insulated=True):
    """
    Calculate the critical Rayleigh number for enclosed parallel plates.

    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 plates (m).
        L (float): Length of the plates (m).
        W (float): Width of the plates (m).
        insulated (bool, optional): Whether the top plate is insulated (-). Default is True.

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

Online Calculator

Distance between the two plates (m).
Length of the plates (m).
Width of the plates (m).
Whether the top plate is insulated (-).