Boiling Nucleic

Overview

Nucleate boiling is a two-phase heat-transfer regime in which vapor bubbles form at active surface sites and carry large amounts of latent heat away from a heated wall. In thermal-system design, nucleate boiling correlations are used to estimate heat transfer coefficients and the onset of peak heat flux, both of which strongly influence equipment sizing and safety margins. This category covers practical engineering tools for predicting both boiling performance and critical heat flux (CHF) in pool-boiling and related configurations.

Core Concepts: The functions in this category revolve around two linked quantities: the nucleate boiling heat-transfer coefficient h and the critical heat flux q_{\max} (or q_c). Most correlations use either wall superheat \Delta T_e or imposed heat flux q as the driving variable, combined with reduced pressure, fluid properties, and in some cases surface or geometry terms. A useful conceptual split is h = f(P, P_c, \Delta T_e\;\text{or}\;q, \text{properties, surface terms}), \qquad q_c = g(\rho_l, \rho_g, \sigma, H_{vap}, \text{geometry, pressure}). This separation helps analysts choose whether they are solving a transfer-rate problem (estimating h) or a boiling-limit problem (estimating CHF).

Implementation: These tools are implemented from the ht Python library, specifically the ht.boiling_nucleic module. The ht package is a process and thermal engineering library that collects literature-based correlations with consistent units and API patterns, making it suitable for screening studies, process calculations, and design iteration workflows.

General Nucleate-Boiling Coefficients: The pressure-centered pool-boiling correlations BIER, GORENFLO, MONTINSKY, and HEDH_TABOREK provide fast coefficient estimates when pressure and critical pressure are known, with either \Delta T_e or q as the input driver. GORENFLO is especially useful when fluid-specific reference data (for example via CAS-based lookup) is available, while BIER and MONTINSKY are often used for quick comparative checks. HEDH_TABOREK is a modified corresponding-states style alternative in the same pressure-based family. These models are commonly applied in early evaporator sizing, sensitivity studies, and operating-point comparisons.

Property-Rich and Mechanistic Correlations: ROHSENOW, MCNELLY, and STEPHAN_ABDELSALAM rely more heavily on liquid-vapor thermophysical properties and therefore support more detailed physics-informed estimates. ROHSENOW remains a standard baseline in engineering practice when fluid-surface constants are available; MCNELLY provides an alternative property-group formulation; and STEPHAN_ABDELSALAM offers several variants (general, water, hydrocarbon, cryogenic, refrigerant) for fluid-class-specific behavior. These functions are useful in studies where property fidelity matters, such as refrigerant comparison, cryogenic duty evaluation, and material/surface effects assessments.

Method Selection Utilities: H_NUCLEIC is the high-level dispatcher for computing nucleate boiling coefficients across supported correlations, while H_NUCLEIC_METHODS reports which methods are applicable for a given input set. Together they support robust workflows where available data changes from case to case: engineers can first query feasible methods, then execute a selected correlation (or default selection) without manually checking each equation’s input requirements. This is particularly useful in automated calculators and batch evaluations across many fluids or operating conditions.

Critical Heat Flux (Boiling Limit) Models: CHF-focused functions include ZUBER, SERTH_HEDH, and HEDH_MONTINSKY, plus the selector helpers QMAX_BOILING and QMAX_BOIL_METHODS. ZUBER is the canonical hydrodynamic-form CHF relation for flat-plate-like behavior, SERTH_HEDH adapts CHF prediction to tube-bundle geometry effects, and HEDH_MONTINSKY offers a pressure-based CHF estimate. QMAX_BOILING and QMAX_BOIL_METHODS parallel the coefficient-side dispatch pattern for CHF calculations, helping users move from available inputs to a suitable boiling-limit model quickly. In design terms, these tools support burnout avoidance, heater safety checks, and operating-envelope definition.

BIER

This function estimates nucleate boiling heat transfer coefficient with the Bier correlation using saturation and critical pressure plus either excess wall temperature or heat flux.

In general form, the model scales with reduced pressure and boiling driving force:

h = f\left(P, P_c, \Delta T_e\right) \; \text{or} \; h = f\left(P, P_c, q\right)

It is used for pool-boiling coefficient estimation when limited fluid inputs are available.

Excel Usage

=BIER(P, Pc, Te, q)
  • P (float, required): Saturation pressure of fluid (Pa).
  • Pc (float, required): Critical pressure of fluid (Pa).
  • Te (float, optional, default: null): Excess wall temperature (K).
  • q (float, optional, default: null): Heat flux (W/m^2).

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

Example 1: Water boiling with excess temperature

Inputs:

P Pc Te
101325 22048321 4.3

Excel formula:

=BIER(101325, 22048321, 4.3)

Expected output:

1290.53

Example 2: Water boiling with specified heat flux

Inputs:

P Pc q
101325 22048321 20000

Excel formula:

=BIER(101325, 22048321, 20000)

Expected output:

3166.1

Example 3: Elevated pressure with excess temperature

Inputs:

P Pc Te
300000 22048321 8

Excel formula:

=BIER(300000, 22048321, 8)

Expected output:

8045.32

Example 4: Elevated pressure with heat flux

Inputs:

P Pc q
300000 22048321 35000

Excel formula:

=BIER(300000, 22048321, 35000)

Expected output:

5252.28

Python Code

Show Code 
from ht.boiling_nucleic import Bier as ht_Bier

def Bier(P, Pc, Te=None, q=None):
    """
    Compute nucleate boiling heat transfer coefficient using the Bier 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:
        P (float): Saturation pressure of fluid (Pa).
        Pc (float): Critical pressure of fluid (Pa).
        Te (float, optional): Excess wall temperature (K). Default is None.
        q (float, optional): Heat flux (W/m^2). Default is None.

    Returns:
        float: Heat transfer coefficient (W/m^2/K), or an error message if invalid.
    """
    try:
        return ht_Bier(P=P, Pc=Pc, Te=Te, q=q)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Saturation pressure of fluid (Pa).
Critical pressure of fluid (Pa).
Excess wall temperature (K).
Heat flux (W/m^2).

GORENFLO

This function computes nucleate boiling heat transfer coefficient using the Gorenflo corresponding-states correlation, based on pressure, critical pressure, and either heat flux or excess wall temperature.

A common representation is:

\frac{h}{h_0} = C_w F(p^*)\left(\frac{q}{q_0}\right)^n

The method supports fluid-specific reference data via CAS number or a user-supplied reference coefficient.

Excel Usage

=GORENFLO(P, Pc, q, Te, CASRN, h_ref, Ra)
  • P (float, required): Saturation pressure of fluid (Pa).
  • Pc (float, required): Critical pressure of fluid (Pa).
  • q (float, optional, default: null): Heat flux (W/m^2).
  • Te (float, optional, default: null): Excess wall temperature (K).
  • CASRN (str, optional, default: null): CASRN of fluid (-).
  • h_ref (float, optional, default: null): Reference heat transfer coefficient (W/m^2/K).
  • Ra (float, optional, default: 4e-7): Roughness parameter for the Gorenflo method (m).

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

Example 1: Water boiling at 3 bar with heat flux

Inputs:

P Pc q CASRN
300000 22048320 20000 7732-18-5

Excel formula:

=GORENFLO(300000, 22048320, 20000, "7732-18-5")

Expected output:

3043.34

Example 2: Water boiling with excess temperature and reference h0

Inputs:

P Pc Te h_ref
101325 22048320 5 10000

Excel formula:

=GORENFLO(101325, 22048320, 5, 10000)

Expected output:

615.395

Example 3: Custom reference heat transfer coefficient

Inputs:

P Pc q h_ref
200000 22048320 15000 12000

Excel formula:

=GORENFLO(200000, 22048320, 15000, 12000)

Expected output:

3489.92

Example 4: Rougher surface with CASRN

Inputs:

P Pc q CASRN Ra
250000 22048320 18000 7732-18-5 0.000001

Excel formula:

=GORENFLO(250000, 22048320, 18000, "7732-18-5", 0.000001)

Expected output:

3023.12

Python Code

Show Code 
from ht.boiling_nucleic import Gorenflo as ht_Gorenflo

def Gorenflo(P, Pc, q=None, Te=None, CASRN=None, h_ref=None, Ra=4e-07):
    """
    Compute nucleate boiling heat transfer coefficient using the Gorenflo 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:
        P (float): Saturation pressure of fluid (Pa).
        Pc (float): Critical pressure of fluid (Pa).
        q (float, optional): Heat flux (W/m^2). Default is None.
        Te (float, optional): Excess wall temperature (K). Default is None.
        CASRN (str, optional): CASRN of fluid (-). Default is None.
        h_ref (float, optional): Reference heat transfer coefficient (W/m^2/K). Default is None.
        Ra (float, optional): Roughness parameter for the Gorenflo method (m). Default is 4e-07.

    Returns:
        float: Heat transfer coefficient (W/m^2/K), or an error message if invalid.
    """
    try:
        return ht_Gorenflo(P=P, Pc=Pc, q=q, Te=Te, CASRN=CASRN, h0=h_ref, Ra=Ra)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Saturation pressure of fluid (Pa).
Critical pressure of fluid (Pa).
Heat flux (W/m^2).
Excess wall temperature (K).
CASRN of fluid (-).
Reference heat transfer coefficient (W/m^2/K).
Roughness parameter for the Gorenflo method (m).

H_NUCLEIC

This function is a unified nucleate-boiling interface that selects or applies a specific pool-boiling correlation based on provided inputs and optional method choice.

It evaluates a method-specific model of the form:

h = f(\text{thermophysical properties},\; P,\; P_c,\; q\ \text{or}\ \Delta T_e)

The function supports multiple established correlations and exposes key method parameters such as roughness, contact angle, and material properties.

Excel Usage

=H_NUCLEIC(Te, q, Tsat, P, dPsat, Cpl, kl, mul, rhol, sigma, Hvap, rhog, MW, Pc, Csf, n, kw, rhow, Cpw, angle, Rp, Ra, h_ref, CAS, h_nucleic_method)
  • Te (float, optional, default: null): Excess wall temperature (K).
  • q (float, optional, default: null): Heat flux (W/m^2).
  • Tsat (float, optional, default: null): Saturation temperature at operating pressure (K).
  • P (float, optional, default: null): Saturation pressure of fluid (Pa).
  • dPsat (float, optional, default: null): Saturation pressure difference at excess temperature (Pa).
  • Cpl (float, optional, default: null): Heat capacity of liquid (J/kg/K).
  • kl (float, optional, default: null): Thermal conductivity of liquid (W/m/K).
  • mul (float, optional, default: null): Viscosity of liquid (Pa*s).
  • rhol (float, optional, default: null): Density of the liquid (kg/m^3).
  • sigma (float, optional, default: null): Surface tension of liquid (N/m).
  • Hvap (float, optional, default: null): Heat of vaporization of the fluid (J/kg).
  • rhog (float, optional, default: null): Density of the produced gas (kg/m^3).
  • MW (float, optional, default: null): Molecular weight of fluid (g/mol).
  • Pc (float, optional, default: null): Critical pressure of fluid (Pa).
  • Csf (float, optional, default: 0.013): Rohsenow coefficient specific to fluid and metal (-).
  • n (float, optional, default: 1.7): Rohsenow constant (-).
  • 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: 35): Contact angle of bubble with wall (degrees).
  • Rp (float, optional, default: 0.000001): Surface roughness parameter for the Cooper method (m).
  • Ra (float, optional, default: 4e-7): Roughness parameter for the Gorenflo method (m).
  • h_ref (float, optional, default: null): Reference heat transfer coefficient for Gorenflo (W/m^2/K).
  • CAS (str, optional, default: null): CAS number of fluid (-).
  • h_nucleic_method (str, optional, default: null): Correlation method name (-).

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

Example 1: Gorenflo selection with CAS

Inputs:

P Pc q CAS
300000 22048320 20000 7732-18-5

Excel formula:

=H_NUCLEIC(300000, 22048320, 20000, "7732-18-5")

Expected output:

3043.34

Example 2: Rohsenow method with excess temperature

Inputs:

rhol rhog mul kl Cpl Hvap sigma Te Csf n h_nucleic_method
957.854 0.595593 0.000279 0.68 4217 2257000 0.0589 4.9 0.011 1.26 Rohsenow

Excel formula:

=H_NUCLEIC(957.854, 0.595593, 0.000279, 0.68, 4217, 2257000, 0.0589, 4.9, 0.011, 1.26, "Rohsenow")

Expected output:

3723.66

Example 3: Cooper method with excess temperature

Inputs:

P Pc MW Te h_nucleic_method
101325 22048321 18.02 4.3 Cooper

Excel formula:

=H_NUCLEIC(101325, 22048321, 18.02, 4.3, "Cooper")

Expected output:

1558.14

Example 4: Stephan-Abdelsalam water method

Inputs:

Te Tsat Cpl kl mul sigma Hvap rhol rhog h_nucleic_method
5 373.15 4180 0.6 0.0003 0.058 2250000 958 0.6 Stephan-Abdelsalam water

Excel formula:

=H_NUCLEIC(5, 373.15, 4180, 0.6, 0.0003, 0.058, 2250000, 958, 0.6, "Stephan-Abdelsalam water")

Expected output:

4865.78

Python Code

Show Code 
from ht.boiling_nucleic import h_nucleic as ht_h_nucleic

def h_nucleic(Te=None, q=None, Tsat=None, P=None, dPsat=None, Cpl=None, kl=None, mul=None, rhol=None, sigma=None, Hvap=None, rhog=None, MW=None, Pc=None, Csf=0.013, n=1.7, kw=401, rhow=8.96, Cpw=384, angle=35, Rp=1e-06, Ra=4e-07, h_ref=None, CAS=None, h_nucleic_method=None):
    """
    Compute nucleate boiling heat transfer coefficient with method selection.

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

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

    Args:
        Te (float, optional): Excess wall temperature (K). Default is None.
        q (float, optional): Heat flux (W/m^2). Default is None.
        Tsat (float, optional): Saturation temperature at operating pressure (K). Default is None.
        P (float, optional): Saturation pressure of fluid (Pa). Default is None.
        dPsat (float, optional): Saturation pressure difference at excess temperature (Pa). Default is None.
        Cpl (float, optional): Heat capacity of liquid (J/kg/K). Default is None.
        kl (float, optional): Thermal conductivity of liquid (W/m/K). Default is None.
        mul (float, optional): Viscosity of liquid (Pa*s). Default is None.
        rhol (float, optional): Density of the liquid (kg/m^3). Default is None.
        sigma (float, optional): Surface tension of liquid (N/m). Default is None.
        Hvap (float, optional): Heat of vaporization of the fluid (J/kg). Default is None.
        rhog (float, optional): Density of the produced gas (kg/m^3). Default is None.
        MW (float, optional): Molecular weight of fluid (g/mol). Default is None.
        Pc (float, optional): Critical pressure of fluid (Pa). Default is None.
        Csf (float, optional): Rohsenow coefficient specific to fluid and metal (-). Default is 0.013.
        n (float, optional): Rohsenow constant (-). Default is 1.7.
        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 35.
        Rp (float, optional): Surface roughness parameter for the Cooper method (m). Default is 1e-06.
        Ra (float, optional): Roughness parameter for the Gorenflo method (m). Default is 4e-07.
        h_ref (float, optional): Reference heat transfer coefficient for Gorenflo (W/m^2/K). Default is None.
        CAS (str, optional): CAS number of fluid (-). Default is None.
        h_nucleic_method (str, optional): Correlation method name (-). Valid options: Gorenflo 1993, Stephan Abdelsalam water, Stephan Abdelsalam cryogenic, Stephan Abdelsalam general, HEDH Taborek, Forster Zuber, Rohsenow, Cooper, Bier, Montinsky, McNelly. Default is None.

    Returns:
        float: Nucleate boiling heat transfer coefficient (W/m^2/K), or an error message if invalid.
    """
    try:
        return ht_h_nucleic(
            Te=Te,
            q=q,
            Tsat=Tsat,
            P=P,
            dPsat=dPsat,
            Cpl=Cpl,
            kl=kl,
            mul=mul,
            rhol=rhol,
            sigma=sigma,
            Hvap=Hvap,
            rhog=rhog,
            MW=MW,
            Pc=Pc,
            Csf=Csf,
            n=n,
            kw=kw,
            rhow=rhow,
            Cpw=Cpw,
            angle=angle,
            Rp=Rp,
            Ra=Ra,
            h0=h_ref,
            CAS=CAS,
            Method=h_nucleic_method,
        )
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Excess wall temperature (K).
Heat flux (W/m^2).
Saturation temperature at operating pressure (K).
Saturation pressure of fluid (Pa).
Saturation pressure difference at excess temperature (Pa).
Heat capacity of liquid (J/kg/K).
Thermal conductivity of liquid (W/m/K).
Viscosity of liquid (Pa*s).
Density of the liquid (kg/m^3).
Surface tension of liquid (N/m).
Heat of vaporization of the fluid (J/kg).
Density of the produced gas (kg/m^3).
Molecular weight of fluid (g/mol).
Critical pressure of fluid (Pa).
Rohsenow coefficient specific to fluid and metal (-).
Rohsenow constant (-).
Thermal conductivity of wall material (W/m/K).
Density of wall material (kg/m^3).
Heat capacity of wall material (J/kg/K).
Contact angle of bubble with wall (degrees).
Surface roughness parameter for the Cooper method (m).
Roughness parameter for the Gorenflo method (m).
Reference heat transfer coefficient for Gorenflo (W/m^2/K).
CAS number of fluid (-).
Correlation method name (-).

H_NUCLEIC_METHODS

This function returns the set of nucleate-boiling correlations that can be evaluated with the supplied inputs.

Conceptually, it performs a method-availability filter:

\mathcal{M}_{\text{available}} = g(\text{provided inputs},\; \text{range checks})

The output is returned as a single-column 2D list for Excel range compatibility.

Excel Usage

=H_NUCLEIC_METHODS(Te, Tsat, P, dPsat, Cpl, kl, mul, rhol, sigma, Hvap, rhog, MW, Pc, CAS, check_ranges)
  • Te (float, optional, default: null): Excess wall temperature (K).
  • Tsat (float, optional, default: null): Saturation temperature at operating pressure (K).
  • P (float, optional, default: null): Saturation pressure of fluid (Pa).
  • dPsat (float, optional, default: null): Saturation pressure difference at excess temperature (Pa).
  • Cpl (float, optional, default: null): Heat capacity of liquid (J/kg/K).
  • kl (float, optional, default: null): Thermal conductivity of liquid (W/m/K).
  • mul (float, optional, default: null): Viscosity of liquid (Pa*s).
  • rhol (float, optional, default: null): Density of the liquid (kg/m^3).
  • sigma (float, optional, default: null): Surface tension of liquid (N/m).
  • Hvap (float, optional, default: null): Heat of vaporization of the fluid (J/kg).
  • rhog (float, optional, default: null): Density of the produced gas (kg/m^3).
  • MW (float, optional, default: null): Molecular weight of fluid (g/mol).
  • Pc (float, optional, default: null): Critical pressure of fluid (Pa).
  • CAS (str, optional, default: null): CAS number of fluid (-).
  • check_ranges (bool, optional, default: false): Whether to filter for methods valid for the inputs (-).

Returns (list[list]): Available method names as a single-column list, or an error message if invalid.

Example 1: Water properties with excess temperature

Inputs:

P Pc Te CAS
300000 22048320 4 7732-18-5

Excel formula:

=H_NUCLEIC_METHODS(300000, 22048320, 4, "7732-18-5")

Expected output:

Gorenflo (1993)
HEDH-Taborek
Bier
Montinsky
Example 2: Filtered methods with range checks

Inputs:

P Pc Te CAS check_ranges
300000 22048320 4 7732-18-5 true

Excel formula:

=H_NUCLEIC_METHODS(300000, 22048320, 4, "7732-18-5", TRUE)

Expected output:

Gorenflo (1993)
HEDH-Taborek
Bier
Montinsky
Example 3: Methods from property set

Inputs:

Te Cpl kl mul rhol sigma Hvap rhog
4.9 4217 0.68 0.000279 957.854 0.0589 2257000 0.595593

Excel formula:

=H_NUCLEIC_METHODS(4.9, 4217, 0.68, 0.000279, 957.854, 0.0589, 2257000, 0.595593)

Expected output:

"Rohsenow"

Example 4: Pressure-based methods

Inputs:

P Pc Te
200000 22048320 6

Excel formula:

=H_NUCLEIC_METHODS(200000, 22048320, 6)

Expected output:

HEDH-Taborek
Bier
Montinsky

Python Code

Show Code 
from ht.boiling_nucleic import h_nucleic_methods as ht_h_nucleic_methods

def h_nucleic_methods(Te=None, Tsat=None, P=None, dPsat=None, Cpl=None, kl=None, mul=None, rhol=None, sigma=None, Hvap=None, rhog=None, MW=None, Pc=None, CAS=None, check_ranges=False):
    """
    List available nucleate boiling correlations based on provided inputs.

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

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

    Args:
        Te (float, optional): Excess wall temperature (K). Default is None.
        Tsat (float, optional): Saturation temperature at operating pressure (K). Default is None.
        P (float, optional): Saturation pressure of fluid (Pa). Default is None.
        dPsat (float, optional): Saturation pressure difference at excess temperature (Pa). Default is None.
        Cpl (float, optional): Heat capacity of liquid (J/kg/K). Default is None.
        kl (float, optional): Thermal conductivity of liquid (W/m/K). Default is None.
        mul (float, optional): Viscosity of liquid (Pa*s). Default is None.
        rhol (float, optional): Density of the liquid (kg/m^3). Default is None.
        sigma (float, optional): Surface tension of liquid (N/m). Default is None.
        Hvap (float, optional): Heat of vaporization of the fluid (J/kg). Default is None.
        rhog (float, optional): Density of the produced gas (kg/m^3). Default is None.
        MW (float, optional): Molecular weight of fluid (g/mol). Default is None.
        Pc (float, optional): Critical pressure of fluid (Pa). Default is None.
        CAS (str, optional): CAS number of fluid (-). Default is None.
        check_ranges (bool, optional): Whether to filter for methods valid for the inputs (-). Default is False.

    Returns:
        list[list]: Available method names as a single-column list, or an error message if invalid.
    """
    try:
        methods = ht_h_nucleic_methods(
            Te=Te,
            Tsat=Tsat,
            P=P,
            dPsat=dPsat,
            Cpl=Cpl,
            kl=kl,
            mul=mul,
            rhol=rhol,
            sigma=sigma,
            Hvap=Hvap,
            rhog=rhog,
            MW=MW,
            Pc=Pc,
            CAS=CAS,
            check_ranges=check_ranges,
        )
        return [[method] for method in methods]
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Excess wall temperature (K).
Saturation temperature at operating pressure (K).
Saturation pressure of fluid (Pa).
Saturation pressure difference at excess temperature (Pa).
Heat capacity of liquid (J/kg/K).
Thermal conductivity of liquid (W/m/K).
Viscosity of liquid (Pa*s).
Density of the liquid (kg/m^3).
Surface tension of liquid (N/m).
Heat of vaporization of the fluid (J/kg).
Density of the produced gas (kg/m^3).
Molecular weight of fluid (g/mol).
Critical pressure of fluid (Pa).
CAS number of fluid (-).
Whether to filter for methods valid for the inputs (-).

HEDH_MONTINSKY

This function estimates critical heat flux in nucleate boiling with the HEDH-Montinsky relation from saturation and critical pressures.

The correlation is commonly written as:

q_c = 367P_cP_r^{0.35}(1-P_r)^{0.9}

It provides a pressure-based estimate of peak nucleate-boiling heat flux before transition toward film boiling.

Excel Usage

=HEDH_MONTINSKY(P, Pc)
  • P (float, required): Saturation pressure of fluid (Pa).
  • Pc (float, required): Critical pressure of fluid (Pa).

Returns (float): Critical heat flux (W/m^2), or an error message if invalid.

Example 1: Reference case from handbook

Inputs:

P Pc
310300 2550000

Excel formula:

=HEDH_MONTINSKY(310300, 2550000)

Expected output:

398406

Example 2: Lower saturation pressure

Inputs:

P Pc
150000 2550000

Excel formula:

=HEDH_MONTINSKY(150000, 2550000)

Expected output:

328740

Example 3: Higher saturation pressure

Inputs:

P Pc
800000 2550000

Excel formula:

=HEDH_MONTINSKY(800000, 2550000)

Expected output:

444474

Example 4: Mid range saturation pressure

Inputs:

P Pc
400000 2550000

Excel formula:

=HEDH_MONTINSKY(400000, 2550000)

Expected output:

419707

Python Code

Show Code 
from ht.boiling_nucleic import HEDH_Montinsky as ht_HEDH_Montinsky

def HEDH_Montinsky(P, Pc):
    """
    Compute nucleate boiling critical heat flux using the HEDH-Montinsky 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:
        P (float): Saturation pressure of fluid (Pa).
        Pc (float): Critical pressure of fluid (Pa).

    Returns:
        float: Critical heat flux (W/m^2), or an error message if invalid.
    """
    try:
        return ht_HEDH_Montinsky(P=P, Pc=Pc)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Saturation pressure of fluid (Pa).
Critical pressure of fluid (Pa).

HEDH_TABOREK

This function calculates nucleate boiling heat transfer coefficient with the HEDH-Taborek correlation using saturation and critical pressure with either excess wall temperature or heat flux.

In general form:

h = f\left(P, P_c, \Delta T_e\right) \; \text{or} \; h = f\left(P, P_c, q\right)

It is used as a pressure-based empirical alternative for pool-boiling coefficient prediction.

Excel Usage

=HEDH_TABOREK(P, Pc, Te, q)
  • P (float, required): Saturation pressure of fluid (Pa).
  • Pc (float, required): Critical pressure of fluid (Pa).
  • Te (float, optional, default: null): Excess wall temperature (K).
  • q (float, optional, default: null): Heat flux (W/m^2).

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

Example 1: Reference example with excess temperature

Inputs:

P Pc Te
310300 2550000 16.2

Excel formula:

=HEDH_TABOREK(310300, 2550000, 16.2)

Expected output:

1397.27

Example 2: Reference case with heat flux

Inputs:

P Pc q
310300 2550000 25000

Excel formula:

=HEDH_TABOREK(310300, 2550000, 25000)

Expected output:

1497.9

Example 3: Lower pressure with excess temperature

Inputs:

P Pc Te
150000 2550000 10

Excel formula:

=HEDH_TABOREK(150000, 2550000, 10)

Expected output:

178.873

Example 4: Higher pressure with heat flux

Inputs:

P Pc q
600000 2550000 35000

Excel formula:

=HEDH_TABOREK(600000, 2550000, 35000)

Expected output:

2803.29

Python Code

Show Code 
from ht.boiling_nucleic import HEDH_Taborek as ht_HEDH_Taborek

def HEDH_Taborek(P, Pc, Te=None, q=None):
    """
    Compute nucleate boiling heat transfer coefficient using the HEDH-Taborek 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:
        P (float): Saturation pressure of fluid (Pa).
        Pc (float): Critical pressure of fluid (Pa).
        Te (float, optional): Excess wall temperature (K). Default is None.
        q (float, optional): Heat flux (W/m^2). Default is None.

    Returns:
        float: Heat transfer coefficient (W/m^2/K), or an error message if invalid.
    """
    try:
        return ht_HEDH_Taborek(P=P, Pc=Pc, Te=Te, q=q)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Saturation pressure of fluid (Pa).
Critical pressure of fluid (Pa).
Excess wall temperature (K).
Heat flux (W/m^2).

MCNELLY

This function computes nucleate boiling heat transfer coefficient with the McNelly correlation using fluid properties, pressure, and either excess wall temperature or heat flux.

A representative form is:

h = f\left(\rho_l, \rho_g, k_l, C_{p,l}, H_{vap}, \sigma, P, \Delta T_e\right) \; \text{or} \; h=f(\cdots,q)

It is commonly used for pool-boiling estimation when detailed property inputs are available.

Excel Usage

=MCNELLY(rhol, rhog, kl, Cpl, Hvap, sigma, P, Te, q)
  • rhol (float, required): Density of the liquid (kg/m^3).
  • rhog (float, required): Density of the produced gas (kg/m^3).
  • 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).
  • P (float, required): Saturation pressure of fluid (Pa).
  • Te (float, optional, default: null): Excess wall temperature (K).
  • q (float, optional, default: null): Heat flux (W/m^2).

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

Example 1: Water boiling with excess temperature

Inputs:

Te P Cpl kl sigma Hvap rhol rhog
4.3 101325 4180 0.688 0.0588 2250000 958 0.597

Excel formula:

=MCNELLY(4.3, 101325, 4180, 0.688, 0.0588, 2250000, 958, 0.597)

Expected output:

533.806

Example 2: Water boiling with heat flux

Inputs:

q P Cpl kl sigma Hvap rhol rhog
20000 101325 4180 0.688 0.0588 2250000 958 0.597

Excel formula:

=MCNELLY(20000, 101325, 4180, 0.688, 0.0588, 2250000, 958, 0.597)

Expected output:

2377.42

Example 3: Higher pressure with excess temperature

Inputs:

Te P Cpl kl sigma Hvap rhol rhog
6 200000 3900 0.62 0.05 2100000 1000 1.1

Excel formula:

=MCNELLY(6, 200000, 3900, 0.62, 0.05, 2100000, 1000, 1.1)

Expected output:

1278.46

Example 4: Moderate heat flux with typical properties

Inputs:

q P Cpl kl sigma Hvap rhol rhog
15000 150000 3800 0.6 0.055 2100000 980 0.9

Excel formula:

=MCNELLY(15000, 150000, 3800, 0.6, 0.055, 2100000, 980, 0.9)

Expected output:

1861.15

Python Code

Show Code 
from ht.boiling_nucleic import McNelly as ht_McNelly

def McNelly(rhol, rhog, kl, Cpl, Hvap, sigma, P, Te=None, q=None):
    """
    Compute nucleate boiling heat transfer coefficient using the McNelly 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).
        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).
        P (float): Saturation pressure of fluid (Pa).
        Te (float, optional): Excess wall temperature (K). Default is None.
        q (float, optional): Heat flux (W/m^2). Default is None.

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

Online Calculator

Density of the liquid (kg/m^3).
Density of the produced gas (kg/m^3).
Thermal conductivity of liquid (W/m/K).
Heat capacity of liquid (J/kg/K).
Heat of vaporization of the fluid (J/kg).
Surface tension of liquid (N/m).
Saturation pressure of fluid (Pa).
Excess wall temperature (K).
Heat flux (W/m^2).

MONTINSKY

This function estimates nucleate boiling heat transfer coefficient via the Montinsky correlation as a function of saturation pressure, critical pressure, and either excess wall temperature or heat flux.

In practical use, the model has the form:

h = f\left(P, P_c, \Delta T_e\right) \; \text{or} \; h = f\left(P, P_c, q\right)

It provides a pressure-based empirical boiling coefficient for engineering calculations.

Excel Usage

=MONTINSKY(P, Pc, Te, q)
  • P (float, required): Saturation pressure of fluid (Pa).
  • Pc (float, required): Critical pressure of fluid (Pa).
  • Te (float, optional, default: null): Excess wall temperature (K).
  • q (float, optional, default: null): Heat flux (W/m^2).

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

Example 1: Water boiling with excess temperature

Inputs:

P Pc Te
101325 22048321 4.3

Excel formula:

=MONTINSKY(101325, 22048321, 4.3)

Expected output:

1185.05

Example 2: Water boiling with heat flux

Inputs:

P Pc q
101325 22048321 22000

Excel formula:

=MONTINSKY(101325, 22048321, 22000)

Expected output:

3299.05

Example 3: Higher pressure with excess temperature

Inputs:

P Pc Te
300000 22048321 8

Excel formula:

=MONTINSKY(300000, 22048321, 8)

Expected output:

9895.4

Example 4: Higher pressure with heat flux

Inputs:

P Pc q
300000 22048321 35000

Excel formula:

=MONTINSKY(300000, 22048321, 35000)

Expected output:

5588.75

Python Code

Show Code 
from ht.boiling_nucleic import Montinsky as ht_Montinsky

def Montinsky(P, Pc, Te=None, q=None):
    """
    Compute nucleate boiling heat transfer coefficient using the Montinsky 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:
        P (float): Saturation pressure of fluid (Pa).
        Pc (float): Critical pressure of fluid (Pa).
        Te (float, optional): Excess wall temperature (K). Default is None.
        q (float, optional): Heat flux (W/m^2). Default is None.

    Returns:
        float: Heat transfer coefficient (W/m^2/K), or an error message if invalid.
    """
    try:
        return ht_Montinsky(P=P, Pc=Pc, Te=Te, q=q)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Saturation pressure of fluid (Pa).
Critical pressure of fluid (Pa).
Excess wall temperature (K).
Heat flux (W/m^2).

QMAX_BOIL_METHODS

This function lists which critical-heat-flux correlations are available for nucleate boiling given the current set of inputs.

It applies an availability filter of the form:

\mathcal{M}_{q_{\max}} = g(\rho_l, \rho_g, \sigma, H_{vap}, D, P, P_c, \text{range flags})

The result is returned as a single-column 2D list suitable for Excel dynamic array output.

Excel Usage

=QMAX_BOIL_METHODS(rhol, rhog, sigma, Hvap, D, P, Pc, check_ranges)
  • rhol (float, optional, default: null): Density of the liquid (kg/m^3).
  • rhog (float, optional, default: null): Density of the produced gas (kg/m^3).
  • sigma (float, optional, default: null): Surface tension of liquid (N/m).
  • Hvap (float, optional, default: null): Heat of vaporization of the fluid (J/kg).
  • D (float, optional, default: null): Tube diameter (m).
  • P (float, optional, default: null): Saturation pressure of fluid (Pa).
  • Pc (float, optional, default: null): Critical pressure of fluid (Pa).
  • check_ranges (bool, optional, default: false): Whether to filter for methods valid for the inputs (-).

Returns (list[list]): Available method names as a single-column list, or an error message if invalid.

Example 1: Tube bundle with diameter

Inputs:

D sigma Hvap rhol rhog
0.0127 0.0082 272000 567 18.09

Excel formula:

=QMAX_BOIL_METHODS(0.0127, 0.0082, 272000, 567, 18.09)

Expected output:

Serth-HEDH
Zuber
Example 2: No diameter specified

Inputs:

sigma Hvap rhol rhog
0.0082 272000 567 18.09

Excel formula:

=QMAX_BOIL_METHODS(0.0082, 272000, 567, 18.09)

Expected output:

"Zuber"

Example 3: Pressure inputs available

Inputs:

P Pc
310300 2550000

Excel formula:

=QMAX_BOIL_METHODS(310300, 2550000)

Expected output:

"HEDH-Montinsky"

Example 4: Filter methods with range checks

Inputs:

D sigma Hvap rhol rhog check_ranges
0.015 0.01 280000 700 12 true

Excel formula:

=QMAX_BOIL_METHODS(0.015, 0.01, 280000, 700, 12, TRUE)

Expected output:

Serth-HEDH
Zuber

Python Code

Show Code 
from ht.boiling_nucleic import qmax_boiling_methods as ht_qmax_boiling_methods

def qmax_boil_methods(rhol=None, rhog=None, sigma=None, Hvap=None, D=None, P=None, Pc=None, check_ranges=False):
    """
    List available nucleate boiling critical heat flux correlations.

    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, optional): Density of the liquid (kg/m^3). Default is None.
        rhog (float, optional): Density of the produced gas (kg/m^3). Default is None.
        sigma (float, optional): Surface tension of liquid (N/m). Default is None.
        Hvap (float, optional): Heat of vaporization of the fluid (J/kg). Default is None.
        D (float, optional): Tube diameter (m). Default is None.
        P (float, optional): Saturation pressure of fluid (Pa). Default is None.
        Pc (float, optional): Critical pressure of fluid (Pa). Default is None.
        check_ranges (bool, optional): Whether to filter for methods valid for the inputs (-). Default is False.

    Returns:
        list[list]: Available method names as a single-column list, or an error message if invalid.
    """
    try:
        methods = ht_qmax_boiling_methods(
            rhol=rhol,
            rhog=rhog,
            sigma=sigma,
            Hvap=Hvap,
            D=D,
            P=P,
            Pc=Pc,
            check_ranges=check_ranges,
        )
        return [[method] for method in methods]
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Density of the liquid (kg/m^3).
Density of the produced gas (kg/m^3).
Surface tension of liquid (N/m).
Heat of vaporization of the fluid (J/kg).
Tube diameter (m).
Saturation pressure of fluid (Pa).
Critical pressure of fluid (Pa).
Whether to filter for methods valid for the inputs (-).

QMAX_BOILING

This function computes critical heat flux for nucleate boiling by selecting among supported correlations based on the provided geometry and fluid data.

The returned value corresponds to:

q_{\max} = f(\rho_l, \rho_g, \sigma, H_{vap}, D, P, P_c, \text{Method})

It supports method override and defaults to preferred correlations when enough inputs are present.

Excel Usage

=QMAX_BOILING(rhol, rhog, sigma, Hvap, D, P, Pc, qmax_boiling_method)
  • rhol (float, optional, default: null): Density of the liquid (kg/m^3).
  • rhog (float, optional, default: null): Density of the produced gas (kg/m^3).
  • sigma (float, optional, default: null): Surface tension of liquid (N/m).
  • Hvap (float, optional, default: null): Heat of vaporization of the fluid (J/kg).
  • D (float, optional, default: null): Tube diameter (m).
  • P (float, optional, default: null): Saturation pressure of fluid (Pa).
  • Pc (float, optional, default: null): Critical pressure of fluid (Pa).
  • qmax_boiling_method (str, optional, default: null): Correlation method name (-).

Returns (float): Critical heat flux (W/m^2), or an error message if invalid.

Example 1: Serth-HEDH with tube diameter

Inputs:

D sigma Hvap rhol rhog
0.0127 0.0082 272000 567 18.09

Excel formula:

=QMAX_BOILING(0.0127, 0.0082, 272000, 567, 18.09)

Expected output:

351867

Example 2: Zuber method without diameter

Inputs:

sigma Hvap rhol rhog qmax_boiling_method
0.0082 272000 567 18.09 Zuber

Excel formula:

=QMAX_BOILING(0.0082, 272000, 567, 18.09, "Zuber")

Expected output:

536747

Example 3: HEDH-Montinsky method with pressures

Inputs:

P Pc qmax_boiling_method
310300 2550000 HEDH-Montinsky

Excel formula:

=QMAX_BOILING(310300, 2550000, "HEDH-Montinsky")

Expected output:

398406

Example 4: Zuber method with diameter

Inputs:

D sigma Hvap rhol rhog qmax_boiling_method
0.015 0.01 280000 700 12 Zuber

Excel formula:

=QMAX_BOILING(0.015, 0.01, 280000, 700, 12, "Zuber")

Expected output:

500378

Python Code

Show Code 
from ht.boiling_nucleic import qmax_boiling as ht_qmax_boiling

def qmax_boiling(rhol=None, rhog=None, sigma=None, Hvap=None, D=None, P=None, Pc=None, qmax_boiling_method=None):
    """
    Compute nucleate boiling critical heat flux with method selection.

    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, optional): Density of the liquid (kg/m^3). Default is None.
        rhog (float, optional): Density of the produced gas (kg/m^3). Default is None.
        sigma (float, optional): Surface tension of liquid (N/m). Default is None.
        Hvap (float, optional): Heat of vaporization of the fluid (J/kg). Default is None.
        D (float, optional): Tube diameter (m). Default is None.
        P (float, optional): Saturation pressure of fluid (Pa). Default is None.
        Pc (float, optional): Critical pressure of fluid (Pa). Default is None.
        qmax_boiling_method (str, optional): Correlation method name (-). Valid options: Serth HEDH, Zuber, HEDH Montinsky. Default is None.

    Returns:
        float: Critical heat flux (W/m^2), or an error message if invalid.
    """
    try:
        return ht_qmax_boiling(
            rhol=rhol,
            rhog=rhog,
            sigma=sigma,
            Hvap=Hvap,
            D=D,
            P=P,
            Pc=Pc,
            Method=qmax_boiling_method,
        )
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Density of the liquid (kg/m^3).
Density of the produced gas (kg/m^3).
Surface tension of liquid (N/m).
Heat of vaporization of the fluid (J/kg).
Tube diameter (m).
Saturation pressure of fluid (Pa).
Critical pressure of fluid (Pa).
Correlation method name (-).

ROHSENOW

This function calculates nucleate boiling heat transfer coefficient with the Rohsenow correlation from fluid properties and either excess wall temperature or heat flux.

The classic Rohsenow form relates boiling transfer to property groups and wall superheat:

h = f\left(\rho_l,\rho_g,\mu_l,k_l,C_{p,l},H_{vap},\sigma,C_{sf},n,\Delta T_e\right)

It is a foundational pool-boiling model widely used for engineering calculations.

Excel Usage

=ROHSENOW(rhol, rhog, mul, kl, Cpl, Hvap, sigma, Te, q, Csf, n)
  • 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).
  • Te (float, optional, default: null): Excess wall temperature (K).
  • q (float, optional, default: null): Heat flux (W/m^2).
  • Csf (float, optional, default: 0.013): Rohsenow coefficient specific to fluid and metal (-).
  • n (float, optional, default: 1.7): Rohsenow constant (-).

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

Example 1: Water boiling with excess temperature

Inputs:

rhol rhog mul kl Cpl Hvap sigma Te Csf n
957.854 0.595593 0.000279 0.68 4217 2257000 0.0589 4.9 0.011 1.26

Excel formula:

=ROHSENOW(957.854, 0.595593, 0.000279, 0.68, 4217, 2257000, 0.0589, 4.9, 0.011, 1.26)

Expected output:

3723.66

Example 2: Water boiling with heat flux

Inputs:

rhol rhog mul kl Cpl Hvap sigma q Csf n
957.854 0.595593 0.000279 0.68 4217 2257000 0.0589 25000 0.011 1.26

Excel formula:

=ROHSENOW(957.854, 0.595593, 0.000279, 0.68, 4217, 2257000, 0.0589, 25000, 0.011, 1.26)

Expected output:

4593.59

Example 3: Higher viscosity and excess temperature

Inputs:

rhol rhog mul kl Cpl Hvap sigma Te Csf n
950 0.8 0.0005 0.62 3900 2100000 0.055 7 0.013 1.7

Excel formula:

=ROHSENOW(950, 0.8, 0.0005, 0.62, 3900, 2100000, 0.055, 7, 0.013, 1.7)

Expected output:

178.801

Example 4: Moderate heat flux with typical properties

Inputs:

rhol rhog mul kl Cpl Hvap sigma q
980 1.1 0.00035 0.6 3800 2100000 0.05 18000

Excel formula:

=ROHSENOW(980, 1.1, 0.00035, 0.6, 3800, 2100000, 0.05, 18000)

Expected output:

1693.39

Python Code

Show Code 
from ht.boiling_nucleic import Rohsenow as ht_Rohsenow

def Rohsenow(rhol, rhog, mul, kl, Cpl, Hvap, sigma, Te=None, q=None, Csf=0.013, n=1.7):
    """
    Compute nucleate boiling heat transfer coefficient using the Rohsenow 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).
        Te (float, optional): Excess wall temperature (K). Default is None.
        q (float, optional): Heat flux (W/m^2). Default is None.
        Csf (float, optional): Rohsenow coefficient specific to fluid and metal (-). Default is 0.013.
        n (float, optional): Rohsenow constant (-). Default is 1.7.

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

Online Calculator

Density of the liquid (kg/m^3).
Density of the produced gas (kg/m^3).
Viscosity of liquid (Pa*s).
Thermal conductivity of liquid (W/m/K).
Heat capacity of liquid (J/kg/K).
Heat of vaporization of the fluid (J/kg).
Surface tension of liquid (N/m).
Excess wall temperature (K).
Heat flux (W/m^2).
Rohsenow coefficient specific to fluid and metal (-).
Rohsenow constant (-).

SERTH_HEDH

This function estimates critical heat flux for nucleate boiling in tube bundles using the Serth-HEDH correlation.

The model follows:

q_c = KH_{vap}\rho_g^{0.5}\left[\sigma g(\rho_l-\rho_g)\right]^{0.25}

The coefficient K depends on a reduced geometry term involving tube diameter and property ratios.

Excel Usage

=SERTH_HEDH(D, sigma, Hvap, rhol, rhog)
  • D (float, required): Tube diameter (m).
  • sigma (float, required): Surface tension of liquid (N/m).
  • Hvap (float, required): Heat of vaporization of the fluid (J/kg).
  • rhol (float, required): Density of the liquid (kg/m^3).
  • rhog (float, required): Density of the produced gas (kg/m^3).

Returns (float): Critical heat flux (W/m^2), or an error message if invalid.

Example 1: Reference tube bundle example

Inputs:

D sigma Hvap rhol rhog
0.0127 0.0082 272000 567 18.09

Excel formula:

=SERTH_HEDH(0.0127, 0.0082, 272000, 567, 18.09)

Expected output:

351867

Example 2: Larger tube diameter

Inputs:

D sigma Hvap rhol rhog
0.02 0.01 300000 800 12

Excel formula:

=SERTH_HEDH(0.02, 0.01, 300000, 800, 12)

Expected output:

363585

Example 3: Smaller tube diameter

Inputs:

D sigma Hvap rhol rhog
0.01 0.007 250000 600 15

Excel formula:

=SERTH_HEDH(0.01, 0.007, 250000, 600, 15)

Expected output:

287615

Example 4: Higher surface tension case

Inputs:

D sigma Hvap rhol rhog
0.015 0.012 280000 700 10

Excel formula:

=SERTH_HEDH(0.015, 0.012, 280000, 700, 10)

Expected output:

313637

Python Code

Show Code 
from ht.boiling_nucleic import Serth_HEDH as ht_Serth_HEDH

def Serth_HEDH(D, sigma, Hvap, rhol, rhog):
    """
    Compute nucleate boiling critical heat flux for tube bundles using the Serth-HEDH 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:
        D (float): Tube diameter (m).
        sigma (float): Surface tension of liquid (N/m).
        Hvap (float): Heat of vaporization of the fluid (J/kg).
        rhol (float): Density of the liquid (kg/m^3).
        rhog (float): Density of the produced gas (kg/m^3).

    Returns:
        float: Critical heat flux (W/m^2), or an error message if invalid.
    """
    try:
        return ht_Serth_HEDH(D=D, sigma=sigma, Hvap=Hvap, rhol=rhol, rhog=rhog)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Tube diameter (m).
Surface tension of liquid (N/m).
Heat of vaporization of the fluid (J/kg).
Density of the liquid (kg/m^3).
Density of the produced gas (kg/m^3).

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

Density of the liquid (kg/m^3).
Density of the produced gas (kg/m^3).
Viscosity of liquid (Pa*s).
Thermal conductivity of liquid (W/m/K).
Heat capacity of liquid (J/kg/K).
Heat of vaporization of the fluid (J/kg).
Surface tension of liquid (N/m).
Saturation temperature at operating pressure (K).
Excess wall temperature (K).
Heat flux (W/m^2).
Thermal conductivity of wall material (W/m/K).
Density of wall material (kg/m^3).
Heat capacity of wall material (J/kg/K).
Contact angle of bubble with wall (degrees).
Stephan-Abdelsalam correlation selection (-).

ZUBER

This function calculates nucleate boiling critical heat flux using the Zuber correlation for flat plates and related geometries.

The relation is:

q_c = KH_{vap}\rho_g^{0.5}\left[\sigma g(\rho_l-\rho_g)\right]^{0.25}

The constant K is configurable to match different literature conventions.

Excel Usage

=ZUBER(sigma, Hvap, rhol, rhog, K)
  • sigma (float, required): Surface tension of liquid (N/m).
  • Hvap (float, required): Heat of vaporization of the fluid (J/kg).
  • rhol (float, required): Density of the liquid (kg/m^3).
  • rhog (float, required): Density of the produced gas (kg/m^3).
  • K (float, optional, default: 0.18): Correlation constant (-).

Returns (float): Critical heat flux (W/m^2), or an error message if invalid.

Example 1: Zuber correlation with K 0.149

Inputs:

sigma Hvap rhol rhog K
0.0082 272000 567 18.09 0.149

Excel formula:

=ZUBER(0.0082, 272000, 567, 18.09, 0.149)

Expected output:

444307

Example 2: Zuber correlation with K 0.18

Inputs:

sigma Hvap rhol rhog K
0.0082 272000 567 18.09 0.18

Excel formula:

=ZUBER(0.0082, 272000, 567, 18.09, 0.18)

Expected output:

536747

Example 3: Lower surface tension case

Inputs:

sigma Hvap rhol rhog
0.006 220000 700 12

Excel formula:

=ZUBER(0.006, 220000, 700, 12)

Expected output:

346020

Example 4: Higher surface tension case

Inputs:

sigma Hvap rhol rhog K
0.012 300000 900 8 0.18

Excel formula:

=ZUBER(0.012, 300000, 900, 8, 0.18)

Expected output:

488884

Python Code

Show Code 
from ht.boiling_nucleic import Zuber as ht_Zuber

def Zuber(sigma, Hvap, rhol, rhog, K=0.18):
    """
    Compute nucleate boiling critical heat flux using the Zuber 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:
        sigma (float): Surface tension of liquid (N/m).
        Hvap (float): Heat of vaporization of the fluid (J/kg).
        rhol (float): Density of the liquid (kg/m^3).
        rhog (float): Density of the produced gas (kg/m^3).
        K (float, optional): Correlation constant (-). Default is 0.18.

    Returns:
        float: Critical heat flux (W/m^2), or an error message if invalid.
    """
    try:
        return ht_Zuber(sigma=sigma, Hvap=Hvap, rhol=rhol, rhog=rhog, K=K)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Surface tension of liquid (N/m).
Heat of vaporization of the fluid (J/kg).
Density of the liquid (kg/m^3).
Density of the produced gas (kg/m^3).
Correlation constant (-).