NU_JACKSON

This function estimates the Nusselt number for turbulent supercritical internal convection via the Jackson correlation. It uses Reynolds and Prandtl numbers, with optional correction factors based on density ratio, heat-capacity ratio, and temperature location relative to the pseudocritical point.

Nu = C\,Re^{m}Pr^{n}\,\Phi_{\rho}\,\Phi_{Cp}(T_b,T_w,T_{pc})

Excel Usage

=NU_JACKSON(Re, Pr, rho_w, rho_b, Cp_avg, Cp_b, T_b, T_w, T_pc)

Re (float, required): Reynolds number with bulk fluid properties (-).
Pr (float, required): Prandtl number with bulk 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).
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).
T_b (float, optional, default: null): Bulk temperature (K).
T_w (float, optional, default: null): Wall temperature (K).
T_pc (float, optional, default: null): Pseudocritical temperature at pressure (K).

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

Example 1: Jackson correlation example

Inputs:

Re	Pr
100000	1.2

Excel formula:

=NU_JACKSON(100000, 1.2)

Expected output:

252.372

Example 2: Jackson correlation with property corrections

Inputs:

Re	Pr	rho_w	rho_b	Cp_avg	Cp_b	T_b	T_w	T_pc
100000	1.2	330	290	2100	2000	650	700	640

Excel formula:

=NU_JACKSON(100000, 1.2, 330, 290, 2100, 2000, 650, 700, 640)

Expected output:

267.743

Example 3: Jackson correlation mid Reynolds number

Inputs:

Re	Pr	rho_w	rho_b	Cp_avg	Cp_b	T_b	T_w	T_pc
200000	0.9	350	300	2300	2100	620	680	640

Excel formula:

=NU_JACKSON(200000, 0.9, 350, 300, 2300, 2100, 620, 680, 640)

Expected output:

419.564

Example 4: Jackson correlation higher Reynolds number

Inputs:

Re	Pr
400000	1.1

Excel formula:

=NU_JACKSON(400000, 1.1)

Expected output:

753.072

Python Code

Show Code

from ht.conv_supercritical import Nu_Jackson as ht_Nu_Jackson

def Nu_Jackson(Re, Pr, rho_w=None, rho_b=None, Cp_avg=None, Cp_b=None, T_b=None, T_w=None, T_pc=None):
    """
    Calculate Nusselt number for supercritical flow using the Jackson 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 (-).
        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.
        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.
        T_b (float, optional): Bulk temperature (K). Default is None.
        T_w (float, optional): Wall temperature (K). Default is None.
        T_pc (float, optional): Pseudocritical temperature at pressure (K). Default is None.

    Returns:
        float: Nusselt number with bulk fluid properties (-).
    """
    try:
        return ht_Nu_Jackson(
            Re=Re,
            Pr=Pr,
            rho_w=rho_w,
            rho_b=rho_b,
            Cp_avg=Cp_avg,
            Cp_b=Cp_b,
            T_b=T_b,
            T_w=T_w,
            T_pc=T_pc,
        )
    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 (-).

rho_w

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

rho_b

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

Cp_avg

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

Cp_b

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

T_b

Bulk temperature (K).

T_w

Wall temperature (K).

T_pc

Pseudocritical temperature at pressure (K).