NU_FREE_VPLATE

This function computes the Nusselt number for external free convection from a vertical plate using the ht implementation and optional method selection. It uses Prandtl number, Grashof number, and optional geometry inputs.

Free-convection correlation selection is based on dimensionless groups, primarily the Rayleigh number:

Ra = Gr\,Pr

and returns a dimensionless Nusselt number referenced to plate height.

Excel Usage

=NU_FREE_VPLATE(Pr, Gr, buoyancy, H, W, vplate_method)

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

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

Example 1: Vertical plate default method

Inputs:

Pr	Gr
0.69	2630000000

Excel formula:

=NU_FREE_VPLATE(0.69, 2630000000)

Expected output:

147.162

Example 2: Vertical plate with buoyancy flag

Inputs:

Pr	Gr	buoyancy
0.69	2630000000	false

Excel formula:

=NU_FREE_VPLATE(0.69, 2630000000, FALSE)

Expected output:

147.162

Example 3: Vertical plate with explicit method

Inputs:

Pr	Gr	vplate_method
0.69	2630000000	Churchill

Excel formula:

=NU_FREE_VPLATE(0.69, 2630000000, "Churchill")

Expected output:

147.162

Example 4: Vertical plate with geometry inputs

Inputs:

Pr	Gr	buoyancy	H	W
0.9	2000000	true	1.5	0.4

Excel formula:

=NU_FREE_VPLATE(0.9, 2000000, TRUE, 1.5, 0.4)

Expected output:

19.934

Python Code

Show Code

from ht.conv_free_immersed import Nu_free_vertical_plate as ht_Nu_free_vertical_plate

def Nu_free_vplate(Pr, Gr, buoyancy=None, H=None, W=None, vplate_method=None):
    """
    Calculate the Nusselt number for free convection from a vertical 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, optional): Whether buoyancy assists free convection (dimensionless). Default is None.
        H (float, optional): Plate height (m). Default is None.
        W (float, optional): Plate width (m). Default is None.
        vplate_method (str, optional): Correlation name (string). Default is None.

    Returns:
        float: Nusselt number based on plate height (dimensionless).
    """
    try:
        result = ht_Nu_free_vertical_plate(Pr, Gr, buoyancy=buoyancy, H=H, W=W, Method=vplate_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 height (m).

Plate width (m).

vplate_method

Correlation name (string).