NU_VCYL_HANESIAN

This function computes natural-convection Nusselt number for a vertical isothermal cylinder using the Hanesian-Kalish-Morgan correlation from ht. It takes Prandtl and Grashof numbers and evaluates the laminar-range relation.

The expression is represented through Rayleigh-number scaling:

Nu = C\,Ra^n,\qquad Ra = Gr\,Pr

and returns a dimensionless Nusselt number based on cylinder height.

Excel Usage

=NU_VCYL_HANESIAN(Pr, Gr)

Pr (float, required): Prandtl number of the fluid (dimensionless).
Gr (float, required): Grashof number based on cylinder height (dimensionless).

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

Example 1: Hanesian Kalish Morgan example

Inputs:

Pr	Gr
0.7	10000000

Excel formula:

=NU_VCYL_HANESIAN(0.7, 10000000)

Expected output:

18.0142

Example 2: Hanesian Kalish Morgan low Grashof

Inputs:

Pr	Gr
0.9	1000000

Excel formula:

=NU_VCYL_HANESIAN(0.9, 1000000)

Expected output:

11.2387

Example 3: Hanesian Kalish Morgan mid Grashof

Inputs:

Pr	Gr
1.2	5000000

Excel formula:

=NU_VCYL_HANESIAN(1.2, 5000000)

Expected output:

17.3867

Example 4: Hanesian Kalish Morgan high Grashof

Inputs:

Pr	Gr
0.8	50000000

Excel formula:

=NU_VCYL_HANESIAN(0.8, 50000000)

Expected output:

26.8977

Python Code

Show Code

from ht.conv_free_immersed import Nu_vertical_cylinder_Hanesian_Kalish_Morgan as ht_Nu_vertical_cylinder_Hanesian_Kalish_Morgan

def Nu_vcyl_Hanesian(Pr, Gr):
    """
    Calculate the Nusselt number for a vertical cylinder using Hanesian-Kalish-Morgan.

    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 based on cylinder height (dimensionless).

    Returns:
        float: Nusselt number based on cylinder height (dimensionless).
    """
    try:
        result = ht_Nu_vertical_cylinder_Hanesian_Kalish_Morgan(Pr, Gr)
        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 based on cylinder height (dimensionless).