NU_VERT_THESS

This function computes the natural-convection Nusselt number between vertical plates using the Thess correlation. It supports both a general Rayleigh-based form and a geometry-adjusted form when plate height and length are provided.

Using \mathrm{Ra} = \mathrm{Pr}\,\mathrm{Gr}, the correlation applies a regime-dependent scaling and optionally adjusts by aspect ratio H/L. This allows a simple estimate when geometry is unknown and a more specific estimate when dimensions are available.

\mathrm{Nu} = 0.42\,\mathrm{Pr}^{0.012}\,\mathrm{Ra}^{0.25}\left(\frac{H}{L}\right)^{-0.25}

Excel Usage

=NU_VERT_THESS(Pr, Gr, H, L)

Pr (float, required): Prandtl number with respect to fluid properties (-).
Gr (float, required): Grashof number with respect to fluid properties and plate temperature difference (-).
H (float, optional, default: null): Height of vertical plate (m).
L (float, optional, default: null): Length of vertical plate (m).

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

Example 1: Thess correlation without geometry

Inputs:

Pr	Gr
0.7	3210000

Excel formula:

=NU_VERT_THESS(0.7, 3210000)

Expected output:

6.11259

Example 2: Thess correlation with plate geometry

Inputs:

Pr	Gr	L	H
0.7	3210000	10	1

Excel formula:

=NU_VERT_THESS(0.7, 3210000, 10, 1)

Expected output:

28.7933

Example 3: Thess correlation with small aspect ratio

Inputs:

Pr	Gr	L	H
1.2	500000	2	0.5

Excel formula:

=NU_VERT_THESS(1.2, 500000, 2, 0.5)

Expected output:

16.5673

Example 4: Thess correlation at higher Rayleigh

Inputs:

Pr	Gr
0.9	100000000

Excel formula:

=NU_VERT_THESS(0.9, 100000000)

Expected output:

20.6584

Python Code

Show Code

from ht.conv_free_enclosed import Nu_Nusselt_vertical_Thess as ht_Nu_Nusselt_vertical_Thess

def Nu_Vert_Thess(Pr, Gr, H=None, L=None):
    """
    Calculate the Nusselt number between vertical plates using the Thess 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 (-).
        H (float, optional): Height of vertical plate (m). Default is None.
        L (float, optional): Length of vertical plate (m). Default is None.

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

Online Calculator

Pr *

Prandtl number with respect to fluid properties (-).

Gr *

Grashof number with respect to fluid properties and plate temperature difference (-).

Height of vertical plate (m).

Length of vertical plate (m).