NU_ORNATSKY

This function computes the Nusselt number for supercritical turbulent flow with the Ornatsky correlation. It uses Reynolds number, both bulk and wall Prandtl numbers, and optionally applies a density-ratio correction.

Nu = C\,Re^{m}\,(\min(Pr_b,Pr_w))^{n}\,\Phi_{\rho}

Excel Usage

=NU_ORNATSKY(Re, Pr_b, Pr_w, rho_w, rho_b)

Re (float, required): Reynolds number with bulk fluid properties (-).
Pr_b (float, required): Prandtl number with bulk fluid properties (-).
Pr_w (float, required): Prandtl number with wall fluid properties (-).
rho_w (float, optional, default: null): Density at wall temperature (kg/m^3).
rho_b (float, optional, default: null): Density at bulk temperature (kg/m^3).

Returns (float): Nusselt number with bulk fluid properties (-).

Example 1: Ornatsky correlation example

Inputs:

Re	Pr_b	Pr_w	rho_w	rho_b
100000	1.2	1.5	330	290

Excel formula:

=NU_ORNATSKY(100000, 1.2, 1.5, 330, 290)

Expected output:

276.635

Example 2: Ornatsky correlation bulk properties only

Inputs:

Re	Pr_b	Pr_w
80000	1	1.1

Excel formula:

=NU_ORNATSKY(80000, 1, 1.1)

Expected output:

192.398

Example 3: Ornatsky correlation mid Reynolds number

Inputs:

Re	Pr_b	Pr_w	rho_w	rho_b
200000	0.9	1.3	360	310

Excel formula:

=NU_ORNATSKY(200000, 0.9, 1.3, 360, 310)

Expected output:

384.971

Example 4: Ornatsky correlation higher Reynolds number

Inputs:

Re	Pr_b	Pr_w	rho_w	rho_b
450000	1.4	1.8	380	320

Excel formula:

=NU_ORNATSKY(450000, 1.4, 1.8, 380, 320)

Expected output:

1055.82

Python Code

Show Code

from ht.conv_supercritical import Nu_Ornatsky as ht_Nu_Ornatsky

def Nu_Ornatsky(Re, Pr_b, Pr_w, rho_w=None, rho_b=None):
    """
    Calculate Nusselt number for supercritical flow using the Ornatsky correlation.

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

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

    Args:
        Re (float): Reynolds number with bulk fluid properties (-).
        Pr_b (float): Prandtl number with bulk fluid properties (-).
        Pr_w (float): Prandtl number with wall fluid properties (-).
        rho_w (float, optional): Density at wall temperature (kg/m^3). Default is None.
        rho_b (float, optional): Density at bulk temperature (kg/m^3). Default is None.

    Returns:
        float: Nusselt number with bulk fluid properties (-).
    """
    try:
        return ht_Nu_Ornatsky(Re=Re, Pr_b=Pr_b, Pr_w=Pr_w, rho_w=rho_w, rho_b=rho_b)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Re *

Reynolds number with bulk fluid properties (-).

Pr_b *

Prandtl number with bulk fluid properties (-).

Pr_w *

Prandtl number with wall fluid properties (-).

rho_w

Density at wall temperature (kg/m^3).

rho_b

Density at bulk temperature (kg/m^3).