STEPHAN_ABDELSALAM

This function computes nucleate boiling heat transfer coefficient using the Stephan-Abdelsalam framework, including general, water, hydrocarbon, cryogenic, and refrigerant variants.

The method can be expressed as a dimensionless correlation structure:

h = f(X_1, X_2, \dots, X_8)\,\frac{k_l}{d_B}

It supports either excess wall temperature or heat flux inputs and optional wall-material properties for cryogenic cases.

Excel Usage

=STEPHAN_ABDELSALAM(rhol, rhog, mul, kl, Cpl, Hvap, sigma, Tsat, Te, q, kw, rhow, Cpw, angle, correlation)

• rhol (float, required): Density of the liquid (kg/m^3).
• rhog (float, required): Density of the produced gas (kg/m^3).
• mul (float, required): Viscosity of liquid (Pa*s).
• kl (float, required): Thermal conductivity of liquid (W/m/K).
• Cpl (float, required): Heat capacity of liquid (J/kg/K).
• Hvap (float, required): Heat of vaporization of the fluid (J/kg).
• sigma (float, required): Surface tension of liquid (N/m).
• Tsat (float, required): Saturation temperature at operating pressure (K).
• Te (float, optional, default: null): Excess wall temperature (K).
• q (float, optional, default: null): Heat flux (W/m^2).
• kw (float, optional, default: 401): Thermal conductivity of wall material (W/m/K).
• rhow (float, optional, default: 8.96): Density of wall material (kg/m^3).
• Cpw (float, optional, default: 384): Heat capacity of wall material (J/kg/K).
• angle (float, optional, default: null): Contact angle of bubble with wall (degrees).
• correlation (str, optional, default: “general”): Stephan-Abdelsalam correlation selection (-).

Returns (float): Heat transfer coefficient (W/m^2/K), or an error message if invalid.

Example 1: Reference example with specified contact angle

Inputs:

Te	Tsat	Cpl	kl	mul	sigma	Hvap	rhol	rhog	angle
16.2	437.5	2730	0.086	0.000156	0.0082	272000	567	18.09	35

Excel formula:

=STEPHAN_ABDELSALAM(16.2, 437.5, 2730, 0.086, 0.000156, 0.0082, 272000, 567, 18.09, 35)

Expected output:

26722.4

Example 2: General correlation with heat flux

Inputs:

q	Tsat	Cpl	kl	mul	sigma	Hvap	rhol	rhog
25000	373.15	4180	0.6	0.0003	0.058	2250000	958	0.6

Excel formula:

=STEPHAN_ABDELSALAM(25000, 373.15, 4180, 0.6, 0.0003, 0.058, 2250000, 958, 0.6)

Expected output:

3218.34

Example 3: Water correlation with excess temperature

Inputs:

Te	Tsat	Cpl	kl	mul	sigma	Hvap	rhol	rhog	correlation
5	373.15	4180	0.6	0.0003	0.058	2250000	958	0.6	water

Excel formula:

=STEPHAN_ABDELSALAM(5, 373.15, 4180, 0.6, 0.0003, 0.058, 2250000, 958, 0.6, "water")

Expected output:

4865.78

Example 4: Refrigerant correlation with heat flux

Inputs:

q	Tsat	Cpl	kl	mul	sigma	Hvap	rhol	rhog	correlation
18000	300	1400	0.08	0.0002	0.01	200000	1200	40	refrigerant

Excel formula:

=STEPHAN_ABDELSALAM(18000, 300, 1400, 0.08, 0.0002, 0.01, 200000, 1200, 40, "refrigerant")

Expected output:

3989.06

Python Code

Show Code

from ht.boiling_nucleic import Stephan_Abdelsalam as ht_Stephan_Abdelsalam

def Stephan_Abdelsalam(rhol, rhog, mul, kl, Cpl, Hvap, sigma, Tsat, Te=None, q=None, kw=401, rhow=8.96, Cpw=384, angle=None, correlation='general'):
    """
    Compute nucleate boiling heat transfer coefficient using the Stephan-Abdelsalam correlation.

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

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

    Args:
        rhol (float): Density of the liquid (kg/m^3).
        rhog (float): Density of the produced gas (kg/m^3).
        mul (float): Viscosity of liquid (Pa*s).
        kl (float): Thermal conductivity of liquid (W/m/K).
        Cpl (float): Heat capacity of liquid (J/kg/K).
        Hvap (float): Heat of vaporization of the fluid (J/kg).
        sigma (float): Surface tension of liquid (N/m).
        Tsat (float): Saturation temperature at operating pressure (K).
        Te (float, optional): Excess wall temperature (K). Default is None.
        q (float, optional): Heat flux (W/m^2). Default is None.
        kw (float, optional): Thermal conductivity of wall material (W/m/K). Default is 401.
        rhow (float, optional): Density of wall material (kg/m^3). Default is 8.96.
        Cpw (float, optional): Heat capacity of wall material (J/kg/K). Default is 384.
        angle (float, optional): Contact angle of bubble with wall (degrees). Default is None.
        correlation (str, optional): Stephan-Abdelsalam correlation selection (-). Valid options: General, Water, Hydrocarbon, Cryogenic, Refrigerant. Default is 'general'.

    Returns:
        float: Heat transfer coefficient (W/m^2/K), or an error message if invalid.
    """
    try:
        return ht_Stephan_Abdelsalam(
            rhol=rhol,
            rhog=rhog,
            mul=mul,
            kl=kl,
            Cpl=Cpl,
            Hvap=Hvap,
            sigma=sigma,
            Tsat=Tsat,
            Te=Te,
            q=q,
            kw=kw,
            rhow=rhow,
            Cpw=Cpw,
            angle=angle,
            correlation=correlation,
        )
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

rhol *

Density of the liquid (kg/m^3).

rhog *

Density of the produced gas (kg/m^3).

mul *

Viscosity of liquid (Pa*s).

kl *

Thermal conductivity of liquid (W/m/K).

Cpl *

Heat capacity of liquid (J/kg/K).

Hvap *

Heat of vaporization of the fluid (J/kg).

sigma *

Surface tension of liquid (N/m).

Tsat *

Saturation temperature at operating pressure (K).

Te

Excess wall temperature (K).

q

Heat flux (W/m^2).

kw

Thermal conductivity of wall material (W/m/K).

rhow

Density of wall material (kg/m^3).

Cpw

Heat capacity of wall material (J/kg/K).

angle

Contact angle of bubble with wall (degrees).

correlation Optional General Water Hydrocarbon Cryogenic Refrigerant

Stephan-Abdelsalam correlation selection (-).