Boiling Plate

Overview

Flow boiling in plate-and-frame exchangers combines convection, phase change, and complex corrugated-channel hydrodynamics in a compact geometry. This category focuses on boiling heat transfer in plate exchangers, where the engineering objective is to predict the two-phase heat-transfer coefficient h for sizing, rating, and operating-point checks. These models matter in refrigeration, heat-pump evaporators, and process cooling because small changes in quality, heat flux, or geometry can shift performance and pressure-drop tradeoffs. Reliable correlation selection helps analysts compare candidate designs before committing to detailed experiments.

Core Concepts: The functions are unified by dimensionless two-phase scaling using Reynolds number (Re), Boiling number (Bo), Prandtl number (Pr), and, in some methods, Martinelli-type parameters (X_{tt}) or geometry factors such as chevron angle and corrugation wavelength. Most boiling correlations are empirical and regime-dependent, so they should be interpreted as calibrated prediction tools within representative operating ranges. A common framing is h_{tp} = f\!\left(\text{mass flux},\ x,\ q,\ \rho,\ \mu,\ k,\ H_{vap},\ \text{geometry}\right), with outputs in W/m^2/K for direct exchanger calculations.

Implementation: These tools are implemented with the Python ht package, primarily in ht.boiling_plate. The ht library provides literature-based heat-transfer and two-phase correlations behind a consistent API, which is useful for spreadsheet integration, quick sensitivity studies, and early-stage thermal design.

For the Han–Lee–Kim formulation, H_BOIL_HAN_LEE_KIM and H_BOIL_HANLEEKIM provide equivalent access to the same underlying correlation structure. These functions model two-phase plate-boiling performance using equivalent-flow scaling with explicit dependence on heat flux and corrugation geometry (including wavelength and chevron angle). They are practical when exchanger geometry is already known and the analyst needs a geometry-aware coefficient estimate across varying quality and load. In workflow terms, the paired names mainly support compatibility across naming conventions while returning the same engineering quantity.

For the Huang–Sheer method, H_BOIL_HUANG_SHEER and H_BOIL_HUANGSHEER estimate boiling coefficients with stronger emphasis on fluid properties, saturation temperature, and applied heat flux. Compared with geometry-intensive alternatives, this pair is often used for rapid comparative calculations when detailed corrugation descriptors are not the primary driver in the model form. Because the correlation includes saturation-temperature effects explicitly, it is typically applied with care when extrapolating to fluids or operating windows far from the source data. As with the Han alias pair, both names map to the same practical modeling intent.

For Lee–Kang–Kim style modeling, H_BOIL_LEE_KANG_KIM and H_BOIL_LEEKANGKIM compute h with piecewise behavior tied to two-phase flow indicators such as Re_g/Re_l, Bo, and X_{tt}. This pair is useful when analysts want a correlation that encodes regime shifts directly, especially in low-to-moderate mass-flux plate-channel boiling where quality effects are important. In addition, H_BOILING_AMALFI and H_BOILING_YAN_LIN provide complementary alternatives: Amalfi offers a broad, modern data-informed prediction route with regime-aware behavior, while Yan–Lin offers a compact equivalent-flow form commonly used for comparative benchmarking. Together, these four functions support correlation cross-checking to bound uncertainty during rating and optimization studies.

Finally, THERMAL_DIFFUSIVITY supplies the material property relation \alpha = k/(\rho C_p), which is frequently used in transient heat-transfer interpretation and in constructing related dimensionless groups. Although it is not itself a boiling correlation, it complements the category by connecting fluid/property data handling to the two-phase heat-transfer calculations above. In practical engineering use, this utility helps keep property calculations explicit and consistent across model variants.

H_BOIL_HAN_LEE_KIM

This function computes the two-phase boiling heat transfer coefficient in a plate heat exchanger using the Han-Lee-Kim correlation. It accounts for fluid properties, heat flux, corrugation geometry, and equivalent two-phase flow effects.

The model can be summarized as a correlation of the form:

h = f\left(Re_{eq}, Bo_{eq}, Pr_l, \frac{\lambda}{D_h}, \beta\right)\frac{k_l}{D_h}

where Re_{eq} and Bo_{eq} are equivalent two-phase Reynolds and boiling numbers, and the output is h in W/m^2/K.

Excel Usage

=H_BOIL_HAN_LEE_KIM(m, x, Dh, rhol, rhog, mul, kl, Hvap, Cpl, q, A_channel_flow, wavelength, chevron_angle)
  • m (float, required): Mass flow rate (kg/s).
  • x (float, required): Quality at the specific point (-).
  • Dh (float, required): Hydraulic diameter of the plate (m).
  • rhol (float, required): Density of the liquid (kg/m^3).
  • rhog (float, required): Density of the gas (kg/m^3).
  • mul (float, required): Viscosity of the liquid (Pa*s).
  • kl (float, required): Thermal conductivity of liquid (W/m/K).
  • Hvap (float, required): Heat of vaporization (J/kg).
  • Cpl (float, required): Heat capacity of liquid (J/kg/K).
  • q (float, required): Heat flux (W/m^2).
  • A_channel_flow (float, required): Channel flow area (m^2).
  • wavelength (float, required): Corrugation wavelength (m).
  • chevron_angle (float, optional, default: 45): Chevron angle of corrugations (degrees).

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

Example 1: Han Lee Kim correlation example case

Inputs:

m x Dh rhol rhog mul kl Hvap Cpl q A_channel_flow wavelength chevron_angle
0.00003 0.4 0.002 567 18.09 0.000156 0.086 900000 2200 100000 0.0003 0.0037 45

Excel formula:

=H_BOIL_HAN_LEE_KIM(0.00003, 0.4, 0.002, 567, 18.09, 0.000156, 0.086, 900000, 2200, 100000, 0.0003, 0.0037, 45)

Expected output:

675.732

Example 2: Han Lee Kim correlation at low quality

Inputs:

m x Dh rhol rhog mul kl Hvap Cpl q A_channel_flow wavelength
0.00004 0.25 0.0018 600 16 0.00018 0.09 850000 2300 90000 0.00028 0.0034

Excel formula:

=H_BOIL_HAN_LEE_KIM(0.00004, 0.25, 0.0018, 600, 16, 0.00018, 0.09, 850000, 2300, 90000, 0.00028, 0.0034)

Expected output:

733.472

Example 3: Han Lee Kim correlation at higher heat flux

Inputs:

m x Dh rhol rhog mul kl Hvap Cpl q A_channel_flow wavelength chevron_angle
0.00005 0.55 0.0022 520 20 0.00014 0.08 950000 2100 140000 0.00032 0.0042 60

Excel formula:

=H_BOIL_HAN_LEE_KIM(0.00005, 0.55, 0.0022, 520, 20, 0.00014, 0.08, 950000, 2100, 140000, 0.00032, 0.0042, 60)

Expected output:

459.933

Example 4: Han Lee Kim correlation at mid heat flux

Inputs:

m x Dh rhol rhog mul kl Hvap Cpl q A_channel_flow wavelength chevron_angle
0.000025 0.35 0.0019 580 12 0.00017 0.085 870000 2250 95000 0.00029 0.0038 40

Excel formula:

=H_BOIL_HAN_LEE_KIM(0.000025, 0.35, 0.0019, 580, 12, 0.00017, 0.085, 870000, 2250, 95000, 0.00029, 0.0038, 40)

Expected output:

874.439

Python Code

Show Code 
from ht.boiling_plate import h_boiling_Han_Lee_Kim as ht_h_boiling_Han_Lee_Kim

def h_boil_Han_Lee_Kim(m, x, Dh, rhol, rhog, mul, kl, Hvap, Cpl, q, A_channel_flow, wavelength, chevron_angle=45):
    """
    Calculate boiling heat transfer coefficient using Han Lee Kim correlation.

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

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

    Args:
        m (float): Mass flow rate (kg/s).
        x (float): Quality at the specific point (-).
        Dh (float): Hydraulic diameter of the plate (m).
        rhol (float): Density of the liquid (kg/m^3).
        rhog (float): Density of the gas (kg/m^3).
        mul (float): Viscosity of the liquid (Pa*s).
        kl (float): Thermal conductivity of liquid (W/m/K).
        Hvap (float): Heat of vaporization (J/kg).
        Cpl (float): Heat capacity of liquid (J/kg/K).
        q (float): Heat flux (W/m^2).
        A_channel_flow (float): Channel flow area (m^2).
        wavelength (float): Corrugation wavelength (m).
        chevron_angle (float, optional): Chevron angle of corrugations (degrees). Default is 45.

    Returns:
        float: Boiling heat transfer coefficient (W/m^2/K).
    """
    try:
        result = ht_h_boiling_Han_Lee_Kim(m, x, Dh, rhol, rhog, mul, kl, Hvap, Cpl, q, A_channel_flow, wavelength, chevron_angle)
        return result
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Mass flow rate (kg/s).
Quality at the specific point (-).
Hydraulic diameter of the plate (m).
Density of the liquid (kg/m^3).
Density of the gas (kg/m^3).
Viscosity of the liquid (Pa*s).
Thermal conductivity of liquid (W/m/K).
Heat of vaporization (J/kg).
Heat capacity of liquid (J/kg/K).
Heat flux (W/m^2).
Channel flow area (m^2).
Corrugation wavelength (m).
Chevron angle of corrugations (degrees).

H_BOIL_HANLEEKIM

This function computes the two-phase boiling heat transfer coefficient in a plate heat exchanger using the Han-Lee-Kim correlation. It accounts for fluid properties, heat flux, corrugation geometry, and equivalent two-phase flow effects.

The model can be summarized as a correlation of the form:

h = f\left(Re_{eq}, Bo_{eq}, Pr_l, \frac{\lambda}{D_h}, \beta\right)\frac{k_l}{D_h}

where Re_{eq} and Bo_{eq} are equivalent two-phase Reynolds and boiling numbers, and the output is h in W/m^2/K.

Excel Usage

=H_BOIL_HANLEEKIM(m, x, Dh, rhol, rhog, mul, kl, Hvap, Cpl, q, A_channel_flow, wavelength, chevron_angle)
  • m (float, required): Mass flow rate (kg/s).
  • x (float, required): Quality at the specific point (-).
  • Dh (float, required): Hydraulic diameter of the plate (m).
  • rhol (float, required): Density of the liquid (kg/m^3).
  • rhog (float, required): Density of the gas (kg/m^3).
  • mul (float, required): Viscosity of the liquid (Pa*s).
  • kl (float, required): Thermal conductivity of liquid (W/m/K).
  • Hvap (float, required): Heat of vaporization (J/kg).
  • Cpl (float, required): Heat capacity of liquid (J/kg/K).
  • q (float, required): Heat flux (W/m^2).
  • A_channel_flow (float, required): Channel flow area (m^2).
  • wavelength (float, required): Corrugation wavelength (m).
  • chevron_angle (float, optional, default: 45): Chevron angle of corrugations (degrees).

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

Example 1: Han Lee Kim correlation example case

Inputs:

m x Dh rhol rhog mul kl Hvap Cpl q A_channel_flow wavelength chevron_angle
0.00003 0.4 0.002 567 18.09 0.000156 0.086 900000 2200 100000 0.0003 0.0037 45

Excel formula:

=H_BOIL_HANLEEKIM(0.00003, 0.4, 0.002, 567, 18.09, 0.000156, 0.086, 900000, 2200, 100000, 0.0003, 0.0037, 45)

Expected output:

675.732

Example 2: Han Lee Kim correlation at low quality

Inputs:

m x Dh rhol rhog mul kl Hvap Cpl q A_channel_flow wavelength
0.00004 0.25 0.0018 600 16 0.00018 0.09 850000 2300 90000 0.00028 0.0034

Excel formula:

=H_BOIL_HANLEEKIM(0.00004, 0.25, 0.0018, 600, 16, 0.00018, 0.09, 850000, 2300, 90000, 0.00028, 0.0034)

Expected output:

733.472

Example 3: Han Lee Kim correlation at higher heat flux

Inputs:

m x Dh rhol rhog mul kl Hvap Cpl q A_channel_flow wavelength chevron_angle
0.00005 0.55 0.0022 520 20 0.00014 0.08 950000 2100 140000 0.00032 0.0042 60

Excel formula:

=H_BOIL_HANLEEKIM(0.00005, 0.55, 0.0022, 520, 20, 0.00014, 0.08, 950000, 2100, 140000, 0.00032, 0.0042, 60)

Expected output:

459.933

Example 4: Han Lee Kim correlation at mid heat flux

Inputs:

m x Dh rhol rhog mul kl Hvap Cpl q A_channel_flow wavelength chevron_angle
0.000025 0.35 0.0019 580 12 0.00017 0.085 870000 2250 95000 0.00029 0.0038 40

Excel formula:

=H_BOIL_HANLEEKIM(0.000025, 0.35, 0.0019, 580, 12, 0.00017, 0.085, 870000, 2250, 95000, 0.00029, 0.0038, 40)

Expected output:

874.439

Python Code

Show Code 
from ht.boiling_plate import h_boiling_Han_Lee_Kim as ht_h_boiling_Han_Lee_Kim

def h_boil_HanLeeKim(m, x, Dh, rhol, rhog, mul, kl, Hvap, Cpl, q, A_channel_flow, wavelength, chevron_angle=45):
    """
    Calculate boiling heat transfer coefficient using Han Lee Kim correlation.

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

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

    Args:
        m (float): Mass flow rate (kg/s).
        x (float): Quality at the specific point (-).
        Dh (float): Hydraulic diameter of the plate (m).
        rhol (float): Density of the liquid (kg/m^3).
        rhog (float): Density of the gas (kg/m^3).
        mul (float): Viscosity of the liquid (Pa*s).
        kl (float): Thermal conductivity of liquid (W/m/K).
        Hvap (float): Heat of vaporization (J/kg).
        Cpl (float): Heat capacity of liquid (J/kg/K).
        q (float): Heat flux (W/m^2).
        A_channel_flow (float): Channel flow area (m^2).
        wavelength (float): Corrugation wavelength (m).
        chevron_angle (float, optional): Chevron angle of corrugations (degrees). Default is 45.

    Returns:
        float: Boiling heat transfer coefficient (W/m^2/K).
    """
    try:
        result = ht_h_boiling_Han_Lee_Kim(m, x, Dh, rhol, rhog, mul, kl, Hvap, Cpl, q, A_channel_flow, wavelength, chevron_angle)
        return result
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Mass flow rate (kg/s).
Quality at the specific point (-).
Hydraulic diameter of the plate (m).
Density of the liquid (kg/m^3).
Density of the gas (kg/m^3).
Viscosity of the liquid (Pa*s).
Thermal conductivity of liquid (W/m/K).
Heat of vaporization (J/kg).
Heat capacity of liquid (J/kg/K).
Heat flux (W/m^2).
Channel flow area (m^2).
Corrugation wavelength (m).
Chevron angle of corrugations (degrees).

H_BOIL_HUANG_SHEER

This function estimates boiling heat transfer in plate exchangers using the Huang-Sheer correlation. It depends on thermophysical properties, imposed heat flux, and saturation temperature rather than detailed exchanger geometry.

The correlation follows the structure:

h = f\left(k_l, q, T_{sat}, H_{vap}, \alpha_l, Pr_l, \rho_l, \rho_g, \sigma, \theta\right)

where bubble-scale effects are embedded in the model and the function returns h in W/m^2/K.

Excel Usage

=H_BOIL_HUANG_SHEER(rhol, rhog, mul, kl, Hvap, sigma, Cpl, q, Tsat, angle)
  • rhol (float, required): Density of the liquid (kg/m^3).
  • rhog (float, required): Density of the gas (kg/m^3).
  • mul (float, required): Viscosity of the liquid (Pa*s).
  • kl (float, required): Thermal conductivity of liquid (W/m/K).
  • Hvap (float, required): Heat of vaporization (J/kg).
  • sigma (float, required): Surface tension of liquid (N/m).
  • Cpl (float, required): Heat capacity of liquid (J/kg/K).
  • q (float, required): Heat flux (W/m^2).
  • Tsat (float, required): Saturation temperature (K).
  • angle (float, optional, default: 35): Contact angle of bubbles with wall (degrees).

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

Example 1: Huang Sheer correlation example case

Inputs:

rhol rhog mul kl Hvap sigma Cpl q Tsat
567 18.09 0.000156 0.086 900000 0.02 2200 10000 279.15

Excel formula:

=H_BOIL_HUANG_SHEER(567, 18.09, 0.000156, 0.086, 900000, 0.02, 2200, 10000, 279.15)

Expected output:

4401.06

Example 2: Huang Sheer correlation at lower heat flux

Inputs:

rhol rhog mul kl Hvap sigma Cpl q Tsat angle
600 15 0.0002 0.09 850000 0.018 2300 8000 285 30

Excel formula:

=H_BOIL_HUANG_SHEER(600, 15, 0.0002, 0.09, 850000, 0.018, 2300, 8000, 285, 30)

Expected output:

4140.01

Example 3: Huang Sheer correlation at higher heat flux

Inputs:

rhol rhog mul kl Hvap sigma Cpl q Tsat angle
520 20 0.00014 0.08 950000 0.021 2100 15000 275 40

Excel formula:

=H_BOIL_HUANG_SHEER(520, 20, 0.00014, 0.08, 950000, 0.021, 2100, 15000, 275, 40)

Expected output:

5334.58

Example 4: Huang Sheer correlation at mid heat flux

Inputs:

rhol rhog mul kl Hvap sigma Cpl q Tsat angle
580 12 0.00017 0.085 870000 0.019 2250 12000 282 35

Excel formula:

=H_BOIL_HUANG_SHEER(580, 12, 0.00017, 0.085, 870000, 0.019, 2250, 12000, 282, 35)

Expected output:

5102.77

Python Code

Show Code 
from ht.boiling_plate import h_boiling_Huang_Sheer as ht_h_boiling_Huang_Sheer

def h_boil_Huang_Sheer(rhol, rhog, mul, kl, Hvap, sigma, Cpl, q, Tsat, angle=35):
    """
    Calculate boiling heat transfer coefficient using Huang Sheer correlation.

    See: https://ht.readthedocs.io/en/latest/ht.boiling_plate.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 gas (kg/m^3).
        mul (float): Viscosity of the liquid (Pa*s).
        kl (float): Thermal conductivity of liquid (W/m/K).
        Hvap (float): Heat of vaporization (J/kg).
        sigma (float): Surface tension of liquid (N/m).
        Cpl (float): Heat capacity of liquid (J/kg/K).
        q (float): Heat flux (W/m^2).
        Tsat (float): Saturation temperature (K).
        angle (float, optional): Contact angle of bubbles with wall (degrees). Default is 35.

    Returns:
        float: Boiling heat transfer coefficient (W/m^2/K).
    """
    try:
        result = ht_h_boiling_Huang_Sheer(rhol, rhog, mul, kl, Hvap, sigma, Cpl, q, Tsat, angle)
        return result
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Density of the liquid (kg/m^3).
Density of the gas (kg/m^3).
Viscosity of the liquid (Pa*s).
Thermal conductivity of liquid (W/m/K).
Heat of vaporization (J/kg).
Surface tension of liquid (N/m).
Heat capacity of liquid (J/kg/K).
Heat flux (W/m^2).
Saturation temperature (K).
Contact angle of bubbles with wall (degrees).

H_BOIL_HUANGSHEER

This function estimates boiling heat transfer in plate exchangers using the Huang-Sheer correlation. It depends on thermophysical properties, imposed heat flux, and saturation temperature rather than detailed exchanger geometry.

The correlation follows the structure:

h = f\left(k_l, q, T_{sat}, H_{vap}, \alpha_l, Pr_l, \rho_l, \rho_g, \sigma, \theta\right)

where bubble-scale effects are embedded in the model and the function returns h in W/m^2/K.

Excel Usage

=H_BOIL_HUANGSHEER(rhol, rhog, mul, kl, Hvap, sigma, Cpl, q, Tsat, angle)
  • rhol (float, required): Density of the liquid (kg/m^3).
  • rhog (float, required): Density of the gas (kg/m^3).
  • mul (float, required): Viscosity of the liquid (Pa*s).
  • kl (float, required): Thermal conductivity of liquid (W/m/K).
  • Hvap (float, required): Heat of vaporization (J/kg).
  • sigma (float, required): Surface tension of liquid (N/m).
  • Cpl (float, required): Heat capacity of liquid (J/kg/K).
  • q (float, required): Heat flux (W/m^2).
  • Tsat (float, required): Saturation temperature (K).
  • angle (float, optional, default: 35): Contact angle of bubbles with wall (degrees).

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

Example 1: Huang Sheer correlation example case

Inputs:

rhol rhog mul kl Hvap sigma Cpl q Tsat
567 18.09 0.000156 0.086 900000 0.02 2200 10000 279.15

Excel formula:

=H_BOIL_HUANGSHEER(567, 18.09, 0.000156, 0.086, 900000, 0.02, 2200, 10000, 279.15)

Expected output:

4401.06

Example 2: Huang Sheer correlation at lower heat flux

Inputs:

rhol rhog mul kl Hvap sigma Cpl q Tsat angle
600 15 0.0002 0.09 850000 0.018 2300 8000 285 30

Excel formula:

=H_BOIL_HUANGSHEER(600, 15, 0.0002, 0.09, 850000, 0.018, 2300, 8000, 285, 30)

Expected output:

4140.01

Example 3: Huang Sheer correlation at higher heat flux

Inputs:

rhol rhog mul kl Hvap sigma Cpl q Tsat angle
520 20 0.00014 0.08 950000 0.021 2100 15000 275 40

Excel formula:

=H_BOIL_HUANGSHEER(520, 20, 0.00014, 0.08, 950000, 0.021, 2100, 15000, 275, 40)

Expected output:

5334.58

Example 4: Huang Sheer correlation at mid heat flux

Inputs:

rhol rhog mul kl Hvap sigma Cpl q Tsat angle
580 12 0.00017 0.085 870000 0.019 2250 12000 282 35

Excel formula:

=H_BOIL_HUANGSHEER(580, 12, 0.00017, 0.085, 870000, 0.019, 2250, 12000, 282, 35)

Expected output:

5102.77

Python Code

Show Code 
from ht.boiling_plate import h_boiling_Huang_Sheer as ht_h_boiling_Huang_Sheer

def h_boil_HuangSheer(rhol, rhog, mul, kl, Hvap, sigma, Cpl, q, Tsat, angle=35):
    """
    Calculate boiling heat transfer coefficient using Huang Sheer correlation.

    See: https://ht.readthedocs.io/en/latest/ht.boiling_plate.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 gas (kg/m^3).
        mul (float): Viscosity of the liquid (Pa*s).
        kl (float): Thermal conductivity of liquid (W/m/K).
        Hvap (float): Heat of vaporization (J/kg).
        sigma (float): Surface tension of liquid (N/m).
        Cpl (float): Heat capacity of liquid (J/kg/K).
        q (float): Heat flux (W/m^2).
        Tsat (float): Saturation temperature (K).
        angle (float, optional): Contact angle of bubbles with wall (degrees). Default is 35.

    Returns:
        float: Boiling heat transfer coefficient (W/m^2/K).
    """
    try:
        result = ht_h_boiling_Huang_Sheer(rhol, rhog, mul, kl, Hvap, sigma, Cpl, q, Tsat, angle)
        return result
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Density of the liquid (kg/m^3).
Density of the gas (kg/m^3).
Viscosity of the liquid (Pa*s).
Thermal conductivity of liquid (W/m/K).
Heat of vaporization (J/kg).
Surface tension of liquid (N/m).
Heat capacity of liquid (J/kg/K).
Heat flux (W/m^2).
Saturation temperature (K).
Contact angle of bubbles with wall (degrees).

H_BOIL_LEE_KANG_KIM

This function calculates the boiling heat transfer coefficient for corrugated plate channels using the Lee-Kang-Kim correlation. It uses quality, equivalent diameter, liquid/gas properties, mass flow, and heat flux to evaluate two-phase boiling intensity.

The model uses piecewise expressions based on flow-regime indicators and can be represented as:

h = f\left(\frac{Re_g}{Re_l}, Bo, X_{tt}\right)\frac{k_l}{D_{eq}}

where X_{tt} is the Martinelli-type parameter and the result is returned in W/m^2/K.

Excel Usage

=H_BOIL_LEE_KANG_KIM(m, x, D_eq, rhol, rhog, mul, mug, kl, Hvap, q, A_channel_flow)
  • m (float, required): Mass flow rate (kg/s).
  • x (float, required): Quality at the specific point (-).
  • D_eq (float, required): Equivalent diameter of the channels (m).
  • rhol (float, required): Density of the liquid (kg/m^3).
  • rhog (float, required): Density of the gas (kg/m^3).
  • mul (float, required): Viscosity of the liquid (Pa*s).
  • mug (float, required): Viscosity of the gas (Pa*s).
  • kl (float, required): Thermal conductivity of liquid (W/m/K).
  • Hvap (float, required): Heat of vaporization (J/kg).
  • q (float, required): Heat flux (W/m^2).
  • A_channel_flow (float, required): Channel flow area (m^2).

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

Example 1: Lee Kang Kim correlation example case

Inputs:

m x D_eq rhol rhog mul mug kl Hvap q A_channel_flow
0.00003 0.4 0.002 567 18.09 0.000156 0.000009 0.086 900000 100000 0.0003

Excel formula:

=H_BOIL_LEE_KANG_KIM(0.00003, 0.4, 0.002, 567, 18.09, 0.000156, 0.000009, 0.086, 900000, 100000, 0.0003)

Expected output:

1229.63

Example 2: Lee Kang Kim correlation at low quality

Inputs:

m x D_eq rhol rhog mul mug kl Hvap q A_channel_flow
0.00004 0.2 0.0018 600 16 0.00018 0.00001 0.09 850000 90000 0.00028

Excel formula:

=H_BOIL_LEE_KANG_KIM(0.00004, 0.2, 0.0018, 600, 16, 0.00018, 0.00001, 0.09, 850000, 90000, 0.00028)

Expected output:

4321.25

Example 3: Lee Kang Kim correlation at higher heat flux

Inputs:

m x D_eq rhol rhog mul mug kl Hvap q A_channel_flow
0.00005 0.55 0.0022 520 20 0.00014 0.000008 0.08 950000 140000 0.00032

Excel formula:

=H_BOIL_LEE_KANG_KIM(0.00005, 0.55, 0.0022, 520, 20, 0.00014, 0.000008, 0.08, 950000, 140000, 0.00032)

Expected output:

572.31

Example 4: Lee Kang Kim correlation at mid heat flux

Inputs:

m x D_eq rhol rhog mul mug kl Hvap q A_channel_flow
0.000025 0.35 0.0019 580 12 0.00017 0.000009 0.085 870000 95000 0.00029

Excel formula:

=H_BOIL_LEE_KANG_KIM(0.000025, 0.35, 0.0019, 580, 12, 0.00017, 0.000009, 0.085, 870000, 95000, 0.00029)

Expected output:

1311.66

Python Code

Show Code 
from ht.boiling_plate import h_boiling_Lee_Kang_Kim as ht_h_boiling_Lee_Kang_Kim

def h_boil_Lee_Kang_Kim(m, x, D_eq, rhol, rhog, mul, mug, kl, Hvap, q, A_channel_flow):
    """
    Calculate boiling heat transfer coefficient using Lee Kang Kim correlation.

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

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

    Args:
        m (float): Mass flow rate (kg/s).
        x (float): Quality at the specific point (-).
        D_eq (float): Equivalent diameter of the channels (m).
        rhol (float): Density of the liquid (kg/m^3).
        rhog (float): Density of the gas (kg/m^3).
        mul (float): Viscosity of the liquid (Pa*s).
        mug (float): Viscosity of the gas (Pa*s).
        kl (float): Thermal conductivity of liquid (W/m/K).
        Hvap (float): Heat of vaporization (J/kg).
        q (float): Heat flux (W/m^2).
        A_channel_flow (float): Channel flow area (m^2).

    Returns:
        float: Boiling heat transfer coefficient (W/m^2/K).
    """
    try:
        result = ht_h_boiling_Lee_Kang_Kim(m, x, D_eq, rhol, rhog, mul, mug, kl, Hvap, q, A_channel_flow)
        return result
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Mass flow rate (kg/s).
Quality at the specific point (-).
Equivalent diameter of the channels (m).
Density of the liquid (kg/m^3).
Density of the gas (kg/m^3).
Viscosity of the liquid (Pa*s).
Viscosity of the gas (Pa*s).
Thermal conductivity of liquid (W/m/K).
Heat of vaporization (J/kg).
Heat flux (W/m^2).
Channel flow area (m^2).

H_BOIL_LEEKANGKIM

This function calculates the boiling heat transfer coefficient for corrugated plate channels using the Lee-Kang-Kim correlation. It uses quality, equivalent diameter, liquid/gas properties, mass flow, and heat flux to evaluate two-phase boiling intensity.

The model uses piecewise expressions based on flow-regime indicators and can be represented as:

h = f\left(\frac{Re_g}{Re_l}, Bo, X_{tt}\right)\frac{k_l}{D_{eq}}

where X_{tt} is the Martinelli-type parameter and the result is returned in W/m^2/K.

Excel Usage

=H_BOIL_LEEKANGKIM(m, x, D_eq, rhol, rhog, mul, mug, kl, Hvap, q, A_channel_flow)
  • m (float, required): Mass flow rate (kg/s).
  • x (float, required): Quality at the specific point (-).
  • D_eq (float, required): Equivalent diameter of the channels (m).
  • rhol (float, required): Density of the liquid (kg/m^3).
  • rhog (float, required): Density of the gas (kg/m^3).
  • mul (float, required): Viscosity of the liquid (Pa*s).
  • mug (float, required): Viscosity of the gas (Pa*s).
  • kl (float, required): Thermal conductivity of liquid (W/m/K).
  • Hvap (float, required): Heat of vaporization (J/kg).
  • q (float, required): Heat flux (W/m^2).
  • A_channel_flow (float, required): Channel flow area (m^2).

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

Example 1: Lee Kang Kim correlation example case

Inputs:

m x D_eq rhol rhog mul mug kl Hvap q A_channel_flow
0.00003 0.4 0.002 567 18.09 0.000156 0.000009 0.086 900000 100000 0.0003

Excel formula:

=H_BOIL_LEEKANGKIM(0.00003, 0.4, 0.002, 567, 18.09, 0.000156, 0.000009, 0.086, 900000, 100000, 0.0003)

Expected output:

1229.63

Example 2: Lee Kang Kim correlation at low quality

Inputs:

m x D_eq rhol rhog mul mug kl Hvap q A_channel_flow
0.00004 0.2 0.0018 600 16 0.00018 0.00001 0.09 850000 90000 0.00028

Excel formula:

=H_BOIL_LEEKANGKIM(0.00004, 0.2, 0.0018, 600, 16, 0.00018, 0.00001, 0.09, 850000, 90000, 0.00028)

Expected output:

4321.25

Example 3: Lee Kang Kim correlation at higher heat flux

Inputs:

m x D_eq rhol rhog mul mug kl Hvap q A_channel_flow
0.00005 0.55 0.0022 520 20 0.00014 0.000008 0.08 950000 140000 0.00032

Excel formula:

=H_BOIL_LEEKANGKIM(0.00005, 0.55, 0.0022, 520, 20, 0.00014, 0.000008, 0.08, 950000, 140000, 0.00032)

Expected output:

572.31

Example 4: Lee Kang Kim correlation at mid heat flux

Inputs:

m x D_eq rhol rhog mul mug kl Hvap q A_channel_flow
0.000025 0.35 0.0019 580 12 0.00017 0.000009 0.085 870000 95000 0.00029

Excel formula:

=H_BOIL_LEEKANGKIM(0.000025, 0.35, 0.0019, 580, 12, 0.00017, 0.000009, 0.085, 870000, 95000, 0.00029)

Expected output:

1311.66

Python Code

Show Code 
from ht.boiling_plate import h_boiling_Lee_Kang_Kim as ht_h_boiling_Lee_Kang_Kim

def h_boil_LeeKangKim(m, x, D_eq, rhol, rhog, mul, mug, kl, Hvap, q, A_channel_flow):
    """
    Calculate boiling heat transfer coefficient using Lee Kang Kim correlation.

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

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

    Args:
        m (float): Mass flow rate (kg/s).
        x (float): Quality at the specific point (-).
        D_eq (float): Equivalent diameter of the channels (m).
        rhol (float): Density of the liquid (kg/m^3).
        rhog (float): Density of the gas (kg/m^3).
        mul (float): Viscosity of the liquid (Pa*s).
        mug (float): Viscosity of the gas (Pa*s).
        kl (float): Thermal conductivity of liquid (W/m/K).
        Hvap (float): Heat of vaporization (J/kg).
        q (float): Heat flux (W/m^2).
        A_channel_flow (float): Channel flow area (m^2).

    Returns:
        float: Boiling heat transfer coefficient (W/m^2/K).
    """
    try:
        result = ht_h_boiling_Lee_Kang_Kim(m, x, D_eq, rhol, rhog, mul, mug, kl, Hvap, q, A_channel_flow)
        return result
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Mass flow rate (kg/s).
Quality at the specific point (-).
Equivalent diameter of the channels (m).
Density of the liquid (kg/m^3).
Density of the gas (kg/m^3).
Viscosity of the liquid (Pa*s).
Viscosity of the gas (Pa*s).
Thermal conductivity of liquid (W/m/K).
Heat of vaporization (J/kg).
Heat flux (W/m^2).
Channel flow area (m^2).

H_BOILING_AMALFI

This function estimates the two-phase boiling heat transfer coefficient for flow in plate heat exchangers using the Amalfi correlation. It combines fluid properties, channel geometry, flow quality, and heat flux to predict convective boiling performance across different operating regimes.

The predicted coefficient is represented as:

h = f\left(m, x, D_h, \rho_l, \rho_g, \mu_l, \mu_g, k_l, H_{vap}, \sigma, q, A_{channel}, \beta\right)

where the implemented model uses regime-dependent relationships from the published correlation and returns h in W/m^2/K.

Excel Usage

=H_BOILING_AMALFI(m, x, Dh, rhol, rhog, mul, mug, kl, Hvap, sigma, q, A_channel_flow, chevron_angle)
  • m (float, required): Mass flow rate (kg/s).
  • x (float, required): Quality at the specific point (-).
  • Dh (float, required): Hydraulic diameter of the plate (m).
  • rhol (float, required): Density of the liquid (kg/m^3).
  • rhog (float, required): Density of the gas (kg/m^3).
  • mul (float, required): Viscosity of the liquid (Pa*s).
  • mug (float, required): Viscosity of the gas (Pa*s).
  • kl (float, required): Thermal conductivity of liquid (W/m/K).
  • Hvap (float, required): Heat of vaporization (J/kg).
  • sigma (float, required): Surface tension of liquid (N/m).
  • q (float, required): Heat flux (W/m^2).
  • A_channel_flow (float, required): Channel flow area (m^2).
  • chevron_angle (float, optional, default: 45): Chevron angle of corrugations (degrees).

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

Example 1: Amalfi correlation example case

Inputs:

m x Dh rhol rhog mul mug kl Hvap sigma q A_channel_flow
0.00003 0.4 0.00172 567 18.09 0.000156 0.00000711 0.086 900000 0.02 100000 0.0003

Excel formula:

=H_BOILING_AMALFI(0.00003, 0.4, 0.00172, 567, 18.09, 0.000156, 0.00000711, 0.086, 900000, 0.02, 100000, 0.0003)

Expected output:

776.078

Example 2: Amalfi correlation at low quality

Inputs:

m x Dh rhol rhog mul mug kl Hvap sigma q A_channel_flow chevron_angle
0.00004 0.2 0.0015 600 15 0.0002 0.00001 0.09 800000 0.018 80000 0.00025 35

Excel formula:

=H_BOILING_AMALFI(0.00004, 0.2, 0.0015, 600, 15, 0.0002, 0.00001, 0.09, 800000, 0.018, 80000, 0.00025, 35)

Expected output:

641.155

Example 3: Amalfi correlation at higher heat flux

Inputs:

m x Dh rhol rhog mul mug kl Hvap sigma q A_channel_flow chevron_angle
0.00005 0.5 0.0018 520 20 0.00014 0.000008 0.08 950000 0.021 150000 0.00032 60

Excel formula:

=H_BOILING_AMALFI(0.00005, 0.5, 0.0018, 520, 20, 0.00014, 0.000008, 0.08, 950000, 0.021, 150000, 0.00032, 60)

Expected output:

1313.77

Example 4: Amalfi correlation at mid heat flux

Inputs:

m x Dh rhol rhog mul mug kl Hvap sigma q A_channel_flow chevron_angle
0.000025 0.35 0.0016 580 12 0.00017 0.000009 0.085 870000 0.019 90000 0.00028 45

Excel formula:

=H_BOILING_AMALFI(0.000025, 0.35, 0.0016, 580, 12, 0.00017, 0.000009, 0.085, 870000, 0.019, 90000, 0.00028, 45)

Expected output:

763.275

Python Code

Show Code 
from ht.boiling_plate import h_boiling_Amalfi as ht_h_boiling_Amalfi

def h_boiling_Amalfi(m, x, Dh, rhol, rhog, mul, mug, kl, Hvap, sigma, q, A_channel_flow, chevron_angle=45):
    """
    Calculate boiling heat transfer coefficient using Amalfi correlation.

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

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

    Args:
        m (float): Mass flow rate (kg/s).
        x (float): Quality at the specific point (-).
        Dh (float): Hydraulic diameter of the plate (m).
        rhol (float): Density of the liquid (kg/m^3).
        rhog (float): Density of the gas (kg/m^3).
        mul (float): Viscosity of the liquid (Pa*s).
        mug (float): Viscosity of the gas (Pa*s).
        kl (float): Thermal conductivity of liquid (W/m/K).
        Hvap (float): Heat of vaporization (J/kg).
        sigma (float): Surface tension of liquid (N/m).
        q (float): Heat flux (W/m^2).
        A_channel_flow (float): Channel flow area (m^2).
        chevron_angle (float, optional): Chevron angle of corrugations (degrees). Default is 45.

    Returns:
        float: Boiling heat transfer coefficient (W/m^2/K).
    """
    try:
        result = ht_h_boiling_Amalfi(m, x, Dh, rhol, rhog, mul, mug, kl, Hvap, sigma, q, A_channel_flow, chevron_angle)
        return result
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Mass flow rate (kg/s).
Quality at the specific point (-).
Hydraulic diameter of the plate (m).
Density of the liquid (kg/m^3).
Density of the gas (kg/m^3).
Viscosity of the liquid (Pa*s).
Viscosity of the gas (Pa*s).
Thermal conductivity of liquid (W/m/K).
Heat of vaporization (J/kg).
Surface tension of liquid (N/m).
Heat flux (W/m^2).
Channel flow area (m^2).
Chevron angle of corrugations (degrees).

H_BOILING_YAN_LIN

This function predicts the boiling heat transfer coefficient in plate heat exchangers with the Yan-Lin correlation. It combines equivalent two-phase flow scaling, boiling number effects, and fluid thermophysical properties.

The implemented relationship is of the form:

h = f\left(Re_{eq}, Bo_{eq}, Re, Pr_l\right)\frac{k_l}{D_h}

where the required flow and property inputs are used to compute h in W/m^2/K.

Excel Usage

=H_BOILING_YAN_LIN(m, x, Dh, rhol, rhog, mul, kl, Hvap, Cpl, q, A_channel_flow)
  • m (float, required): Mass flow rate (kg/s).
  • x (float, required): Quality at the specific point (-).
  • Dh (float, required): Hydraulic diameter of the plate (m).
  • rhol (float, required): Density of the liquid (kg/m^3).
  • rhog (float, required): Density of the gas (kg/m^3).
  • mul (float, required): Viscosity of the liquid (Pa*s).
  • kl (float, required): Thermal conductivity of liquid (W/m/K).
  • Hvap (float, required): Heat of vaporization (J/kg).
  • Cpl (float, required): Heat capacity of liquid (J/kg/K).
  • q (float, required): Heat flux (W/m^2).
  • A_channel_flow (float, required): Channel flow area (m^2).

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

Example 1: Yan Lin correlation example case

Inputs:

m x Dh rhol rhog mul kl Hvap Cpl q A_channel_flow
0.00003 0.4 0.002 567 18.09 0.000156 0.086 900000 2200 100000 0.0003

Excel formula:

=H_BOILING_YAN_LIN(0.00003, 0.4, 0.002, 567, 18.09, 0.000156, 0.086, 900000, 2200, 100000, 0.0003)

Expected output:

318.723

Example 2: Yan Lin correlation at low quality

Inputs:

m x Dh rhol rhog mul kl Hvap Cpl q A_channel_flow
0.00004 0.25 0.0018 600 16 0.00018 0.09 850000 2300 90000 0.00028

Excel formula:

=H_BOILING_YAN_LIN(0.00004, 0.25, 0.0018, 600, 16, 0.00018, 0.09, 850000, 2300, 90000, 0.00028)

Expected output:

311.639

Example 3: Yan Lin correlation at higher heat flux

Inputs:

m x Dh rhol rhog mul kl Hvap Cpl q A_channel_flow
0.00005 0.55 0.0022 520 20 0.00014 0.08 950000 2100 140000 0.00032

Excel formula:

=H_BOILING_YAN_LIN(0.00005, 0.55, 0.0022, 520, 20, 0.00014, 0.08, 950000, 2100, 140000, 0.00032)

Expected output:

380.111

Example 4: Yan Lin correlation at mid heat flux

Inputs:

m x Dh rhol rhog mul kl Hvap Cpl q A_channel_flow
0.000025 0.35 0.0019 580 12 0.00017 0.085 870000 2250 95000 0.00029

Excel formula:

=H_BOILING_YAN_LIN(0.000025, 0.35, 0.0019, 580, 12, 0.00017, 0.085, 870000, 2250, 95000, 0.00029)

Expected output:

329.678

Python Code

Show Code 
from ht.boiling_plate import h_boiling_Yan_Lin as ht_h_boiling_Yan_Lin

def h_boiling_Yan_Lin(m, x, Dh, rhol, rhog, mul, kl, Hvap, Cpl, q, A_channel_flow):
    """
    Calculate boiling heat transfer coefficient using Yan Lin correlation.

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

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

    Args:
        m (float): Mass flow rate (kg/s).
        x (float): Quality at the specific point (-).
        Dh (float): Hydraulic diameter of the plate (m).
        rhol (float): Density of the liquid (kg/m^3).
        rhog (float): Density of the gas (kg/m^3).
        mul (float): Viscosity of the liquid (Pa*s).
        kl (float): Thermal conductivity of liquid (W/m/K).
        Hvap (float): Heat of vaporization (J/kg).
        Cpl (float): Heat capacity of liquid (J/kg/K).
        q (float): Heat flux (W/m^2).
        A_channel_flow (float): Channel flow area (m^2).

    Returns:
        float: Boiling heat transfer coefficient (W/m^2/K).
    """
    try:
        result = ht_h_boiling_Yan_Lin(m, x, Dh, rhol, rhog, mul, kl, Hvap, Cpl, q, A_channel_flow)
        return result
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Mass flow rate (kg/s).
Quality at the specific point (-).
Hydraulic diameter of the plate (m).
Density of the liquid (kg/m^3).
Density of the gas (kg/m^3).
Viscosity of the liquid (Pa*s).
Thermal conductivity of liquid (W/m/K).
Heat of vaporization (J/kg).
Heat capacity of liquid (J/kg/K).
Heat flux (W/m^2).
Channel flow area (m^2).

THERMAL_DIFFUSIVITY

This function calculates thermal diffusivity, which measures how quickly heat spreads through a material relative to its ability to store thermal energy.

Thermal diffusivity is defined as:

\alpha = \frac{k}{\rho C_p}

where k is thermal conductivity, \rho is density, and C_p is specific heat capacity. The result is returned in m^2/s.

Excel Usage

=THERMAL_DIFFUSIVITY(k, rho, Cp)
  • k (float, required): Thermal conductivity (W/m/K).
  • rho (float, required): Density (kg/m^3).
  • Cp (float, required): Heat capacity (J/kg/K).

Returns (float): Thermal diffusivity (m^2/s).

Example 1: Thermal diffusivity example case

Inputs:

k rho Cp
0.02 1 1000

Excel formula:

=THERMAL_DIFFUSIVITY(0.02, 1, 1000)

Expected output:

0.00002

Example 2: Thermal diffusivity for water like properties

Inputs:

k rho Cp
0.6 1000 4180

Excel formula:

=THERMAL_DIFFUSIVITY(0.6, 1000, 4180)

Expected output:

1.43541e-7

Example 3: Thermal diffusivity for air like properties

Inputs:

k rho Cp
0.026 1.2 1005

Excel formula:

=THERMAL_DIFFUSIVITY(0.026, 1.2, 1005)

Expected output:

0.0000215589

Example 4: Thermal diffusivity for oil like properties

Inputs:

k rho Cp
0.13 850 2000

Excel formula:

=THERMAL_DIFFUSIVITY(0.13, 850, 2000)

Expected output:

7.64706e-8

Python Code

Show Code 
from ht.boiling_plate import thermal_diffusivity as ht_thermal_diffusivity

def thermal_diffusivity(k, rho, Cp):
    """
    Calculate thermal diffusivity for a fluid.

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

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

    Args:
        k (float): Thermal conductivity (W/m/K).
        rho (float): Density (kg/m^3).
        Cp (float): Heat capacity (J/kg/K).

    Returns:
        float: Thermal diffusivity (m^2/s).
    """
    try:
        result = ht_thermal_diffusivity(k, rho, Cp)
        return result
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Thermal conductivity (W/m/K).
Density (kg/m^3).
Heat capacity (J/kg/K).