NU_KRASNOSHCHEKOV

This function estimates the supercritical convection Nusselt number using the Krasnoshchekov correlation. It combines a base turbulent heat-transfer relation with optional corrections for density and heat-capacity ratios and temperature-dependent pseudocritical behavior.

Nu = Nu_0\,\Phi_{\rho}\,\Phi_{Cp}(T_b,T_w,T_{pc})

Excel Usage

=NU_KRASNOSHCHEKOV(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: Krasnoshchekov correlation example

Inputs:

Re Pr
100000 1.2

Excel formula:

=NU_KRASNOSHCHEKOV(100000, 1.2)

Expected output:

234.829

Example 2: Krasnoshchekov correlation with property corrections

Inputs:

Re Pr rho_w rho_b Cp_avg Cp_b T_b T_w T_pc
120000 1.1 350 300 2100 2000 650 700 640

Excel formula:

=NU_KRASNOSHCHEKOV(120000, 1.1, 350, 300, 2100, 2000, 650, 700, 640)

Expected output:

275.091

Example 3: Krasnoshchekov correlation mid Reynolds number

Inputs:

Re Pr rho_w rho_b Cp_avg Cp_b T_b T_w T_pc
220000 0.95 360 310 2300 2100 620 690 640

Excel formula:

=NU_KRASNOSHCHEKOV(220000, 0.95, 360, 310, 2300, 2100, 620, 690, 640)

Expected output:

413.04

Example 4: Krasnoshchekov correlation higher Reynolds number

Inputs:

Re Pr
300000 0.9

Excel formula:

=NU_KRASNOSHCHEKOV(300000, 0.9)

Expected output:

470.84

Python Code

Show Code 
from ht.conv_supercritical import Nu_Krasnoshchekov as ht_Nu_Krasnoshchekov

def Nu_Krasnoshchekov(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 Krasnoshchekov 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_Krasnoshchekov(
            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

Reynolds number with bulk fluid properties (-).
Prandtl number with bulk fluid properties (-).
Density at wall temperature (kg/m^3).
Density at bulk temperature (kg/m^3).
Average heat capacity between wall and bulk temperatures (J/kg/K).
Heat capacity at bulk temperature (J/kg/K).
Bulk temperature (K).
Wall temperature (K).
Pseudocritical temperature at pressure (K).