NU_KRASN_PROTO

This function computes the Nusselt number using the Krasnoshchekov-Protopopov supercritical correlation. It applies Reynolds and Prandtl scaling with optional correction multipliers from heat-capacity, thermal-conductivity, and viscosity ratios between wall and bulk states.

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

Excel Usage

=NU_KRASN_PROTO(Re, Pr, Cp_avg, Cp_b, k_w, k_b, mu_w, mu_b)

Re (float, required): Reynolds number with bulk fluid properties (-).
Pr (float, required): Prandtl number with bulk fluid properties (-).
Cp_avg (float, optional, default: null): Average heat capacity between wall and bulk temperatures (J/kg/K).
Cp_b (float, optional, default: null): Heat capacity at bulk temperature (J/kg/K).
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).
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: Krasnoshchekov-Protopopov example

Inputs:

Re	Pr	Cp_avg	Cp_b	k_w	k_b	mu_w	mu_b
100000	1.2	330	290	0.62	0.52	0.0008	0.0009

Excel formula:

=NU_KRASN_PROTO(100000, 1.2, 330, 290, 0.62, 0.52, 0.0008, 0.0009)

Expected output:

228.853

Example 2: Krasnoshchekov-Protopopov bulk properties only

Inputs:

Re	Pr
80000	1.1

Excel formula:

=NU_KRASN_PROTO(80000, 1.1)

Expected output:

186.725

Example 3: Krasnoshchekov-Protopopov mid Reynolds number

Inputs:

Re	Pr	Cp_avg	Cp_b	k_w	k_b	mu_w	mu_b
200000	0.95	2200	2050	0.68	0.58	0.0007	0.00082

Excel formula:

=NU_KRASN_PROTO(200000, 0.95, 2200, 2050, 0.68, 0.58, 0.0007, 0.00082)

Expected output:

336.777

Example 4: Krasnoshchekov-Protopopov higher Reynolds number

Inputs:

Re	Pr	Cp_avg	Cp_b	k_w	k_b	mu_w	mu_b
500000	1.4	2500	2200	0.75	0.65	0.0006	0.00075

Excel formula:

=NU_KRASN_PROTO(500000, 1.4, 2500, 2200, 0.75, 0.65, 0.0006, 0.00075)

Expected output:

931.323

Python Code

Show Code

from ht.conv_supercritical import Nu_Krasnoshchekov_Protopopov as ht_Nu_Krasnoshchekov_Protopopov

def Nu_Krasn_Proto(Re, Pr, Cp_avg=None, Cp_b=None, k_w=None, k_b=None, mu_w=None, mu_b=None):
    """
    Calculate Nusselt number for supercritical flow using the Krasnoshchekov-Protopopov 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 fluid properties (-).
        Cp_avg (float, optional): Average heat capacity between wall and bulk temperatures (J/kg/K). Default is None.
        Cp_b (float, optional): Heat capacity at bulk temperature (J/kg/K). 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.
        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_Krasnoshchekov_Protopopov(
            Re=Re,
            Pr=Pr,
            Cp_avg=Cp_avg,
            Cp_b=Cp_b,
            k_w=k_w,
            k_b=k_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 fluid properties (-).

Cp_avg

Average heat capacity between wall and bulk temperatures (J/kg/K).

Cp_b

Heat capacity at bulk temperature (J/kg/K).

k_w

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

k_b

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

mu_w

Viscosity at wall temperature (Pa*s).

mu_b

Viscosity at bulk temperature (Pa*s).