NU_GUPTA

This function computes the supercritical-flow Nusselt number using the Gupta correlation. It combines Reynolds and Prandtl dependence with optional density and viscosity ratio corrections between wall and bulk fluid states.

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

Excel Usage

=NU_GUPTA(Re, Pr, rho_w, rho_b, mu_w, mu_b)

Re (float, required): Reynolds number with wall properties (-).
Pr (float, required): Prandtl number with wall 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).
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 wall fluid properties (-).

Example 1: Gupta 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_GUPTA(100000, 1.2, 330, 290, 0.0008, 0.0009)

Expected output:

186.201

Example 2: Gupta correlation with bulk and wall properties only

Inputs:

Re	Pr
80000	1.1

Excel formula:

=NU_GUPTA(80000, 1.1)

Expected output:

144.414

Example 3: Gupta correlation mid Reynolds number

Inputs:

Re	Pr	rho_w	rho_b	mu_w	mu_b
200000	0.9	360	310	0.0007	0.00085

Excel formula:

=NU_GUPTA(200000, 0.9, 360, 310, 0.0007, 0.00085)

Expected output:

275.904

Example 4: Gupta correlation higher Reynolds number

Inputs:

Re	Pr	rho_w	rho_b	mu_w	mu_b
500000	1.5	380	320	0.0006	0.00075

Excel formula:

=NU_GUPTA(500000, 1.5, 380, 320, 0.0006, 0.00075)

Expected output:

947.852

Python Code

Show Code

from ht.conv_supercritical import Nu_Gupta as ht_Nu_Gupta

def Nu_Gupta(Re, Pr, rho_w=None, rho_b=None, mu_w=None, mu_b=None):
    """
    Calculate Nusselt number for supercritical flow using the Gupta 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 wall properties (-).
        Pr (float): Prandtl number with wall 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.
        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 wall fluid properties (-).
    """
    try:
        return ht_Nu_Gupta(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 wall properties (-).

Pr *

Prandtl number with wall properties (-).

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).