NUSSELT_LAMINAR

This function computes the average laminar film-condensation heat transfer coefficient on a flat plate using classical Nusselt theory. It relates gravity-driven film flow and thermal transport to the wall-to-saturation temperature difference.

The form is:

h = 0.943\left[\frac{g\sin(\theta)\rho_l(\rho_l-\rho_g)k_l^3H_{vap}}{\mu_l(T_{sat}-T_w)L}\right]^{1/4}

The optional inclination angle modifies the gravity component through \sin(\theta). The function returns a scalar coefficient in W/m^2/K.

Excel Usage

=NUSSELT_LAMINAR(Tsat, Tw, rhog, rhol, kl, mul, Hvap, L, angle)
  • Tsat (float, required): Saturation temperature (K).
  • Tw (float, required): Wall temperature (K).
  • rhog (float, required): Gas density (kg/m^3).
  • rhol (float, required): Liquid density (kg/m^3).
  • kl (float, required): Liquid thermal conductivity (W/m/K).
  • mul (float, required): Liquid viscosity (Pa*s).
  • Hvap (float, required): Heat of vaporization (J/kg).
  • L (float, required): Plate length (m).
  • angle (float, optional, default: 90): Plate inclination angle (degrees).

Returns (float): Heat transfer coefficient (W/m^2/K).

Example 1: Example values from reference

Inputs:

Tsat Tw rhog rhol kl mul Hvap L angle
370 350 7 585 0.091 0.0001589 776900 0.1 90

Excel formula:

=NUSSELT_LAMINAR(370, 350, 7, 585, 0.091, 0.0001589, 776900, 0.1, 90)

Expected output:

1482.21

Example 2: Inclined plate at 45 degrees

Inputs:

Tsat Tw rhog rhol kl mul Hvap L angle
360 340 6.5 600 0.095 0.00017 750000 0.15 45

Excel formula:

=NUSSELT_LAMINAR(360, 340, 6.5, 600, 0.095, 0.00017, 750000, 0.15, 45)

Expected output:

1252.37

Example 3: Short plate length

Inputs:

Tsat Tw rhog rhol kl mul Hvap L angle
380 355 8 550 0.085 0.00014 800000 0.05 90

Excel formula:

=NUSSELT_LAMINAR(380, 355, 8, 550, 0.085, 0.00014, 800000, 0.05, 90)

Expected output:

1595.77

Example 4: Small temperature difference

Inputs:

Tsat Tw rhog rhol kl mul Hvap L angle
350 345 5.5 650 0.1 0.0002 700000 0.12 90

Excel formula:

=NUSSELT_LAMINAR(350, 345, 5.5, 650, 0.1, 0.0002, 700000, 0.12, 90)

Expected output:

2086.01

Python Code

Show Code 
from ht.condensation import Nusselt_laminar as ht_Nusselt_laminar

def Nusselt_laminar(Tsat, Tw, rhog, rhol, kl, mul, Hvap, L, angle=90):
    """
    Calculate laminar film condensation heat transfer on a flat plate using Nusselt theory.

    See: https://ht.readthedocs.io/en/latest/ht.condensation.html

    This example function is provided as-is without any representation of accuracy.

    Args:
        Tsat (float): Saturation temperature (K).
        Tw (float): Wall temperature (K).
        rhog (float): Gas density (kg/m^3).
        rhol (float): Liquid density (kg/m^3).
        kl (float): Liquid thermal conductivity (W/m/K).
        mul (float): Liquid viscosity (Pa*s).
        Hvap (float): Heat of vaporization (J/kg).
        L (float): Plate length (m).
        angle (float, optional): Plate inclination angle (degrees). Default is 90.

    Returns:
        float: Heat transfer coefficient (W/m^2/K).
    """
    try:
        result = ht_Nusselt_laminar(Tsat=Tsat, Tw=Tw, rhog=rhog, rhol=rhol, kl=kl, mul=mul, Hvap=Hvap, L=L, angle=angle)
        return result
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Saturation temperature (K).
Wall temperature (K).
Gas density (kg/m^3).
Liquid density (kg/m^3).
Liquid thermal conductivity (W/m/K).
Liquid viscosity (Pa*s).
Heat of vaporization (J/kg).
Plate length (m).
Plate inclination angle (degrees).