NU_ZHU

This function estimates supercritical turbulent-convection Nusselt number with the Zhu correlation. It uses Reynolds and Prandtl numbers and optionally includes density and thermal-conductivity ratio corrections between wall and bulk conditions.

Nu = C\,Re^{m}Pr^{n}\,\Phi_{\rho}\,\Phi_{k}

Excel Usage

=NU_ZHU(Re, Pr, rho_w, rho_b, k_w, k_b)

Re (float, required): Reynolds number with bulk fluid properties (-).
Pr (float, required): Prandtl number with bulk properties and averaged heat capacity (-).
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).
k_w (float, optional, default: null): Thermal conductivity at wall temperature (W/m/K).
k_b (float, optional, default: null): Thermal conductivity at bulk temperature (W/m/K).

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

Example 1: Zhu correlation example

Inputs:

Re	Pr	rho_w	rho_b	k_w	k_b
100000	1.2	330	290	0.63	0.69

Excel formula:

=NU_ZHU(100000, 1.2, 330, 290, 0.63, 0.69)

Expected output:

240.146

Example 2: Zhu correlation bulk properties only

Inputs:

Re	Pr
80000	1.1

Excel formula:

=NU_ZHU(80000, 1.1)

Expected output:

186.796

Example 3: Zhu correlation mid Reynolds number

Inputs:

Re	Pr	rho_w	rho_b	k_w	k_b
200000	0.9	360	310	0.7	0.62

Excel formula:

=NU_ZHU(200000, 0.9, 360, 310, 0.7, 0.62)

Expected output:

398.964

Example 4: Zhu correlation higher Reynolds number

Inputs:

Re	Pr	rho_w	rho_b	k_w	k_b
450000	1.4	380	320	0.75	0.66

Excel formula:

=NU_ZHU(450000, 1.4, 380, 320, 0.75, 0.66)

Expected output:

1099.64

Python Code

Show Code

from ht.conv_supercritical import Nu_Zhu as ht_Nu_Zhu

def Nu_Zhu(Re, Pr, rho_w=None, rho_b=None, k_w=None, k_b=None):
    """
    Calculate Nusselt number for supercritical flow using the Zhu 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 (float): Prandtl number with bulk properties and averaged heat capacity (-).
        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.
        k_w (float, optional): Thermal conductivity at wall temperature (W/m/K). Default is None.
        k_b (float, optional): Thermal conductivity at bulk temperature (W/m/K). Default is None.

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

Online Calculator

Re *

Reynolds number with bulk fluid properties (-).

Pr *

Prandtl number with bulk properties and averaged heat capacity (-).

rho_w

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

rho_b

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

k_w

Thermal conductivity at wall temperature (W/m/K).

k_b

Thermal conductivity at bulk temperature (W/m/K).