NU_FREE_HPLATE

This function computes the Nusselt number for external free convection from a horizontal plate using selectable correlations available in ht.conv_free_immersed. Inputs are the Prandtl and Grashof numbers, buoyancy direction, and optional geometry information.

The selected model evaluates natural-convection heat transfer using a dimensionless form based on Rayleigh number:

Ra = Gr\,Pr

and returns a dimensionless Nusselt number for the plate characteristic length.

Excel Usage

=NU_FREE_HPLATE(Pr, Gr, buoyancy, L, W, hplate_method)

Pr (float, required): Prandtl number of the fluid (dimensionless).
Gr (float, required): Grashof number for the plate (dimensionless).
buoyancy (bool, required): Whether buoyancy assists free convection (dimensionless).
L (float, optional, default: null): Plate length (m).
W (float, optional, default: null): Plate width (m).
hplate_method (str, optional, default: null): Correlation name (string).

Returns (float): Nusselt number based on plate length (dimensionless).

Example 1: Horizontal plate with default VDI

Inputs:

Pr	Gr	buoyancy
5.54	321000000	true

Excel formula:

=NU_FREE_HPLATE(5.54, 321000000, TRUE)

Expected output:

203.897

Example 2: Horizontal plate using McAdams

Inputs:

Pr	Gr	buoyancy	hplate_method
5.54	321000000	true	McAdams

Excel formula:

=NU_FREE_HPLATE(5.54, 321000000, TRUE, "McAdams")

Expected output:

181.731

Example 3: Horizontal plate Rohsenow cold plate

Inputs:

Pr	Gr	buoyancy	hplate_method
5.54	321000000	false	Rohsenow

Excel formula:

=NU_FREE_HPLATE(5.54, 321000000, FALSE, "Rohsenow")

Expected output:

35.958

Example 4: Horizontal plate with geometry inputs

Inputs:

Pr	Gr	buoyancy	L	W
0.7	2000000	true	1.2	0.6

Excel formula:

=NU_FREE_HPLATE(0.7, 2000000, TRUE, 1.2, 0.6)

Expected output:

22.7506

Python Code

Show Code

from ht.conv_free_immersed import Nu_free_horizontal_plate as ht_Nu_free_horizontal_plate

def Nu_free_hplate(Pr, Gr, buoyancy, L=None, W=None, hplate_method=None):
    """
    Calculate the Nusselt number for free convection from a horizontal plate.

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

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

    Args:
        Pr (float): Prandtl number of the fluid (dimensionless).
        Gr (float): Grashof number for the plate (dimensionless).
        buoyancy (bool): Whether buoyancy assists free convection (dimensionless).
        L (float, optional): Plate length (m). Default is None.
        W (float, optional): Plate width (m). Default is None.
        hplate_method (str, optional): Correlation name (string). Valid options: VDI, McAdams, Rohsenow. Default is None.

    Returns:
        float: Nusselt number based on plate length (dimensionless).
    """
    try:
        result = ht_Nu_free_horizontal_plate(Pr, Gr, buoyancy, L=L, W=W, Method=hplate_method)
        if result is None:
            return "Error: Result is None"
        return float(result)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Pr *

Prandtl number of the fluid (dimensionless).

Gr *

Grashof number for the plate (dimensionless).

buoyancy *

Whether buoyancy assists free convection (dimensionless).

Plate length (m).

Plate width (m).

hplate_method

Correlation name (string).