NU_HPLATE_VDI

This function computes natural-convection Nusselt number for an isothermal horizontal plate using the VDI-based ht correlation. It handles both buoyancy-assisted and buoyancy-opposed configurations.

The calculation follows Rayleigh-number scaling with:

Ra = Gr\,Pr

and returns a dimensionless Nusselt number based on plate length.

Excel Usage

=NU_HPLATE_VDI(Pr, Gr, buoyancy)

Pr (float, required): Prandtl number of the fluid (dimensionless).
Gr (float, required): Grashof number for the plate (dimensionless).
buoyancy (bool, optional, default: true): Whether buoyancy assists free convection (dimensionless).

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

Example 1: VDI hot plate example

Inputs:

Pr	Gr	buoyancy
5.54	321000000	true

Excel formula:

=NU_HPLATE_VDI(5.54, 321000000, TRUE)

Expected output:

203.897

Example 2: VDI cold plate example

Inputs:

Pr	Gr	buoyancy
5.54	321000000	false

Excel formula:

=NU_HPLATE_VDI(5.54, 321000000, FALSE)

Expected output:

39.1686

Example 3: VDI mid Grashof

Inputs:

Pr	Gr	buoyancy
0.9	2000000	true

Excel formula:

=NU_HPLATE_VDI(0.9, 2000000, TRUE)

Expected output:

23.9665

Example 4: VDI low Grashof

Inputs:

Pr	Gr	buoyancy
0.7	200000	false

Excel formula:

=NU_HPLATE_VDI(0.7, 200000, FALSE)

Expected output:

5.1868

Python Code

Show Code

from ht.conv_free_immersed import Nu_horizontal_plate_VDI as ht_Nu_horizontal_plate_VDI

def Nu_hplate_VDI(Pr, Gr, buoyancy=True):
    """
    Calculate the Nusselt number for a horizontal plate using VDI.

    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 True.

    Returns:
        float: Nusselt number based on plate length (dimensionless).
    """
    try:
        result = ht_Nu_horizontal_plate_VDI(Pr, Gr, buoyancy=buoyancy)
        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).