NU_XU

This function calculates the Nusselt number for supercritical turbulent convection in vertical pipes using the Xu correlation. It applies Reynolds and Prandtl scaling with optional density and viscosity ratio corrections.

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

Excel Usage

=NU_XU(Re, Pr, rho_w, rho_b, mu_w, mu_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).
mu_w (float, optional, default: null): Viscosity at wall temperature (Pa*s).
mu_b (float, optional, default: null): Viscosity at bulk temperature (Pa*s).

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

Example 1: Xu correlation example

Inputs:

Re	Pr	rho_w	rho_b	mu_w	mu_b
100000	1.2	330	290	0.0008	0.0009

Excel formula:

=NU_XU(100000, 1.2, 330, 290, 0.0008, 0.0009)

Expected output:

289.133

Example 2: Xu correlation bulk properties only

Inputs:

Re	Pr
80000	1.1

Excel formula:

=NU_XU(80000, 1.1)

Expected output:

226.556

Example 3: Xu correlation mid Reynolds number

Inputs:

Re	Pr	rho_w	rho_b	mu_w	mu_b
200000	0.9	360	310	0.0007	0.00082

Excel formula:

=NU_XU(200000, 0.9, 360, 310, 0.0007, 0.00082)

Expected output:

380.01

Example 4: Xu correlation higher Reynolds number

Inputs:

Re	Pr	rho_w	rho_b	mu_w	mu_b
450000	1.4	380	320	0.0006	0.00075

Excel formula:

=NU_XU(450000, 1.4, 380, 320, 0.0006, 0.00075)

Expected output:

1054.51

Python Code

Show Code

from ht.conv_supercritical import Nu_Xu as ht_Nu_Xu

def Nu_Xu(Re, Pr, rho_w=None, rho_b=None, mu_w=None, mu_b=None):
    """
    Calculate Nusselt number for supercritical flow using the Xu 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.
        mu_w (float, optional): Viscosity at wall temperature (Pa*s). Default is None.
        mu_b (float, optional): Viscosity at bulk temperature (Pa*s). Default is None.

    Returns:
        float: Nusselt number with bulk fluid properties (-).
    """
    try:
        return ht_Nu_Xu(Re=Re, Pr=Pr, rho_w=rho_w, rho_b=rho_b, mu_w=mu_w, mu_b=mu_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).

mu_w

Viscosity at wall temperature (Pa*s).

mu_b

Viscosity at bulk temperature (Pa*s).