Condensation

Overview

Condensation is the phase-change process in which vapor becomes liquid and releases latent heat, often producing very high local heat-transfer rates. In thermal design, condensation heat transfer is central to condensers, reflux systems, refrigeration circuits, and power-plant steam cycles. The engineering challenge is that heat-transfer behavior changes strongly with flow regime, vapor quality, pressure level, and interfacial effects. This category organizes practical correlations for internal-flow and film-condensation calculations used in rating, sensitivity analysis, and preliminary sizing.

The shared foundation across these functions is the use of dimensionless transport groups (Reynolds, Prandtl, and Nusselt numbers), vapor quality x, and property-ratio corrections to represent two-phase momentum and thermal coupling. A typical structure is to estimate a liquid-only baseline and then apply a two-phase enhancement, while laminar film models instead follow gravity-viscous balance in a condensate layer. In compact form, many methods can be interpreted through Nu = hD/k and augmented by quality or reduced-pressure terms. This makes the toolset suitable for comparing model sensitivity under changing operating envelopes.

Implementation is based on the Python ht library, specifically the ht.condensation module. The module collects widely cited condensation correlations and exposes them with consistent function signatures, making it practical to reproduce handbook calculations in spreadsheet and Python workflows.

For internal condensation in tubes using empirical convective correlations, AKERS_DEANS_CROSSER, BOYKO_KRUZHILIN, and SHAH provide complementary approaches. AKERS_DEANS_CROSSER and BOYKO_KRUZHILIN both account for two-phase behavior through quality and density-ratio effects, but with different equivalent-flow constructions and coefficient forms. SHAH adds explicit reduced-pressure dependence through P_r = P/P_c, which is useful when pressure level materially shifts predicted performance. In practice, engineers often evaluate multiple members of this group to bracket uncertainty before selecting a design-point coefficient.

For Cavallini-Smith-Zecchin style internal-flow modeling, CAVALLINI_SMITH_Z and CAVALLINI_SZ expose the same underlying correlation with equivalent Reynolds-number blending of gas and liquid contributions. These functions are useful when viscosity and density asymmetry between phases is large and a dedicated equivalent-Re formulation is desired. Because both wrappers map to the same physical model, they are typically used interchangeably for compatibility with naming conventions across spreadsheets, scripts, and historical workbooks. This pair is especially handy for cross-checking against literature or legacy tools that use different shorthand labels for the same method.

For mechanism-focused limits and physical interpretation, NUSSELT_LAMINAR and H_KINETIC address two distinct resistance pictures. NUSSELT_LAMINAR represents gravity-driven laminar film condensation on a plate, including inclination effects, and is a useful baseline for external-film problems or sanity checks against tube-side correlations. H_KINETIC models interfacial molecular-transport resistance and can indicate regimes where kinetic limits are non-negligible relative to bulk convection assumptions. Together, these functions help separate bulk-flow, film, and interfacial contributions when diagnosing model disagreement.

AKERS_DEANS_CROSSER

This function estimates the condensation heat transfer coefficient for flow inside a tube using the Akers-Deans-Crosser correlation. It models convective condensation with an equivalent Reynolds number that combines liquid and vapor phase effects through quality and density ratio.

The correlation is expressed as a Nusselt-number power law:

Nu = \frac{hD}{k_l} = C Re_e^n Pr_l^{1/3}

where constants C and n depend on the equivalent Reynolds number regime. The function returns a scalar heat transfer coefficient in W/m^2/K.

Excel Usage

=AKERS_DEANS_CROSSER(m, rhog, rhol, kl, mul, Cpl, D, x)

• m (float, required): Mass flow rate (kg/s).
• rhog (float, required): Gas density (kg/m^3).
• rhol (float, required): Liquid density (kg/m^3).
• kl (float, required): Liquid thermal conductivity (W/m/K).
• mul (float, required): Liquid viscosity (Pa*s).
• Cpl (float, required): Liquid heat capacity at constant pressure (J/kg/K).
• D (float, required): Tube diameter (m).
• x (float, required): Quality at the specific interval (-).

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

Example 1: Example values from reference

Inputs:

m	rhog	rhol	kl	mul	Cpl	D	x
0.35	6.36	582.9	0.098	0.000159	2520	0.03	0.85

Excel formula:

=AKERS_DEANS_CROSSER(0.35, 6.36, 582.9, 0.098, 0.000159, 2520, 0.03, 0.85)

Expected output:

7117.24

Example 2: Low quality vapor fraction

Inputs:

m	rhog	rhol	kl	mul	Cpl	D	x
0.2	10	900	0.12	0.0002	2200	0.02	0.1

Excel formula:

=AKERS_DEANS_CROSSER(0.2, 10, 900, 0.12, 0.0002, 2200, 0.02, 0.1)

Expected output:

2793.07

Example 3: Mid quality vapor fraction

Inputs:

m	rhog	rhol	kl	mul	Cpl	D	x
0.5	5	700	0.09	0.00015	2400	0.025	0.5

Excel formula:

=AKERS_DEANS_CROSSER(0.5, 5, 700, 0.09, 0.00015, 2400, 0.025, 0.5)

Expected output:

10231.3

Example 4: Higher mass flow rate

Inputs:

m	rhog	rhol	kl	mul	Cpl	D	x
1	8	650	0.11	0.00018	2100	0.04	0.7

Excel formula:

=AKERS_DEANS_CROSSER(1, 8, 650, 0.11, 0.00018, 2100, 0.04, 0.7)

Expected output:

7861.16

Python Code

Show Code

from ht.condensation import Akers_Deans_Crosser as ht_Akers_Deans_Crosser

def Akers_Deans_Crosser(m, rhog, rhol, kl, mul, Cpl, D, x):
    """
    Calculate condensation heat transfer coefficient in tubes using the Akers-Deans-Crosser correlation.

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

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

    Args:
        m (float): Mass flow rate (kg/s).
        rhog (float): Gas density (kg/m^3).
        rhol (float): Liquid density (kg/m^3).
        kl (float): Liquid thermal conductivity (W/m/K).
        mul (float): Liquid viscosity (Pa*s).
        Cpl (float): Liquid heat capacity at constant pressure (J/kg/K).
        D (float): Tube diameter (m).
        x (float): Quality at the specific interval (-).

    Returns:
        float: Heat transfer coefficient (W/m^2/K).
    """
    try:
        result = ht_Akers_Deans_Crosser(m=m, rhog=rhog, rhol=rhol, kl=kl, mul=mul, Cpl=Cpl, D=D, x=x)
        return result
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

m *

Mass flow rate (kg/s).

rhog *

Gas density (kg/m^3).

rhol *

Liquid density (kg/m^3).

kl *

Liquid thermal conductivity (W/m/K).

mul *

Liquid viscosity (Pa*s).

Cpl *

Liquid heat capacity at constant pressure (J/kg/K).

D *

Tube diameter (m).

x *

Quality at the specific interval (-).

---

BOYKO_KRUZHILIN

This function computes the condensation heat transfer coefficient in tubes using the Boyko-Kruzhilin method. The model starts from a liquid-only convective coefficient and scales it by a two-phase density/quality correction.

The core relation is:

h_{TP} = h_{LO}\left[1 + x\left(\frac{\rho_l}{\rho_g} - 1\right)\right]^{1/2}

where h_{LO} is evaluated from a turbulent single-phase style correlation. The output is a scalar heat transfer coefficient in W/m^2/K.

Excel Usage

=BOYKO_KRUZHILIN(m, rhog, rhol, kl, mul, Cpl, D, x)

• m (float, required): Mass flow rate (kg/s).
• rhog (float, required): Gas density (kg/m^3).
• rhol (float, required): Liquid density (kg/m^3).
• kl (float, required): Liquid thermal conductivity (W/m/K).
• mul (float, required): Liquid viscosity (Pa*s).
• Cpl (float, required): Liquid heat capacity at constant pressure (J/kg/K).
• D (float, required): Tube diameter (m).
• x (float, required): Quality at the specific interval (-).

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

Example 1: Example values from reference

Inputs:

m	rhog	rhol	kl	mul	Cpl	D	x
0.3534291735	6.36	582.9	0.098	0.000159	2520	0.03	0.85

Excel formula:

=BOYKO_KRUZHILIN(0.3534291735, 6.36, 582.9, 0.098, 0.000159, 2520, 0.03, 0.85)

Expected output:

10598.7

Example 2: Low quality vapor fraction

Inputs:

m	rhog	rhol	kl	mul	Cpl	D	x
0.15	9	900	0.12	0.00021	2300	0.02	0.1

Excel formula:

=BOYKO_KRUZHILIN(0.15, 9, 900, 0.12, 0.00021, 2300, 0.02, 0.1)

Expected output:

4030.28

Example 3: Mid quality vapor fraction

Inputs:

m	rhog	rhol	kl	mul	Cpl	D	x
0.6	4.5	700	0.095	0.00017	2400	0.025	0.5

Excel formula:

=BOYKO_KRUZHILIN(0.6, 4.5, 700, 0.095, 0.00017, 2400, 0.025, 0.5)

Expected output:

21121.4

Example 4: Higher mass flow rate

Inputs:

m	rhog	rhol	kl	mul	Cpl	D	x
1.2	7.5	650	0.11	0.00019	2150	0.04	0.7

Excel formula:

=BOYKO_KRUZHILIN(1.2, 7.5, 650, 0.11, 0.00019, 2150, 0.04, 0.7)

Expected output:

13859.1

Python Code

Show Code

from ht.condensation import Boyko_Kruzhilin as ht_Boyko_Kruzhilin

def Boyko_Kruzhilin(m, rhog, rhol, kl, mul, Cpl, D, x):
    """
    Calculate condensation heat transfer coefficient using the Boyko-Kruzhilin correlation.

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

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

    Args:
        m (float): Mass flow rate (kg/s).
        rhog (float): Gas density (kg/m^3).
        rhol (float): Liquid density (kg/m^3).
        kl (float): Liquid thermal conductivity (W/m/K).
        mul (float): Liquid viscosity (Pa*s).
        Cpl (float): Liquid heat capacity at constant pressure (J/kg/K).
        D (float): Tube diameter (m).
        x (float): Quality at the specific interval (-).

    Returns:
        float: Heat transfer coefficient (W/m^2/K).
    """
    try:
        result = ht_Boyko_Kruzhilin(m=m, rhog=rhog, rhol=rhol, kl=kl, mul=mul, Cpl=Cpl, D=D, x=x)
        return result
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

m *

Mass flow rate (kg/s).

rhog *

Gas density (kg/m^3).

rhol *

Liquid density (kg/m^3).

kl *

Liquid thermal conductivity (W/m/K).

mul *

Liquid viscosity (Pa*s).

Cpl *

Liquid heat capacity at constant pressure (J/kg/K).

D *

Tube diameter (m).

x *

Quality at the specific interval (-).

---

CAVALLINI_SMITH_Z

This function evaluates the Cavallini-Smith-Zecchin condensation correlation for internal two-phase flow in tubes. It computes a two-phase heat transfer coefficient from an equivalent Reynolds number that blends gas and liquid flow contributions.

The Nusselt-number form is:

Nu = \frac{hD}{k_l} = 0.05 Re_{eq}^{0.8} Pr_l^{0.33}

where Re_{eq} is based on liquid and gas superficial flow terms with viscosity and density corrections. The output is a scalar heat transfer coefficient in W/m^2/K.

Excel Usage

=CAVALLINI_SMITH_Z(m, x, D, rhol, rhog, mul, mug, kl, Cpl)

• m (float, required): Mass flow rate (kg/s).
• x (float, required): Quality at the specific interval (-).
• D (float, required): Channel diameter (m).
• rhol (float, required): Liquid density (kg/m^3).
• rhog (float, required): Gas density (kg/m^3).
• mul (float, required): Liquid viscosity (Pa*s).
• mug (float, required): Gas viscosity (Pa*s).
• kl (float, required): Liquid thermal conductivity (W/m/K).
• Cpl (float, required): Liquid heat capacity at constant pressure (J/kg/K).

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

Example 1: Example values from reference

Inputs:

m	x	D	rhol	rhog	mul	mug	kl	Cpl
1	0.4	0.3	800	2.5	0.00001	0.001	0.6	2300

Excel formula:

=CAVALLINI_SMITH_Z(1, 0.4, 0.3, 800, 2.5, 0.00001, 0.001, 0.6, 2300)

Expected output:

5578.22

Example 2: Low quality vapor fraction

Inputs:

m	x	D	rhol	rhog	mul	mug	kl	Cpl
0.5	0.1	0.05	900	6	0.0002	0.00002	0.12	2000

Excel formula:

=CAVALLINI_SMITH_Z(0.5, 0.1, 0.05, 900, 6, 0.0002, 0.00002, 0.12, 2000)

Expected output:

2273.43

Example 3: Mid quality vapor fraction

Inputs:

m	x	D	rhol	rhog	mul	mug	kl	Cpl
0.8	0.6	0.08	700	3	0.00015	0.00003	0.1	2400

Excel formula:

=CAVALLINI_SMITH_Z(0.8, 0.6, 0.08, 700, 3, 0.00015, 0.00003, 0.1, 2400)

Expected output:

5094.11

Example 4: Higher mass flow rate

Inputs:

m	x	D	rhol	rhog	mul	mug	kl	Cpl
2	0.7	0.12	650	4	0.00018	0.00004	0.11	2100

Excel formula:

=CAVALLINI_SMITH_Z(2, 0.7, 0.12, 650, 4, 0.00018, 0.00004, 0.11, 2100)

Expected output:

4647.2

Python Code

Show Code

from ht.condensation import Cavallini_Smith_Zecchin as ht_Cavallini_Smith_Zecchin

def Cavallini_Smith_Z(m, x, D, rhol, rhog, mul, mug, kl, Cpl):
    """
    Calculate condensation heat transfer coefficient using the Cavallini-Smith-Zecchin correlation.

    See: https://ht.readthedocs.io/en/latest/ht.condensation.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 interval (-).
        D (float): Channel diameter (m).
        rhol (float): Liquid density (kg/m^3).
        rhog (float): Gas density (kg/m^3).
        mul (float): Liquid viscosity (Pa*s).
        mug (float): Gas viscosity (Pa*s).
        kl (float): Liquid thermal conductivity (W/m/K).
        Cpl (float): Liquid heat capacity at constant pressure (J/kg/K).

    Returns:
        float: Heat transfer coefficient (W/m^2/K).
    """
    try:
        result = ht_Cavallini_Smith_Zecchin(m=m, x=x, D=D, rhol=rhol, rhog=rhog, mul=mul, mug=mug, kl=kl, Cpl=Cpl)
        return result
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

m *

Mass flow rate (kg/s).

x *

Quality at the specific interval (-).

D *

Channel diameter (m).

rhol *

Liquid density (kg/m^3).

rhog *

Gas density (kg/m^3).

mul *

Liquid viscosity (Pa*s).

mug *

Gas viscosity (Pa*s).

kl *

Liquid thermal conductivity (W/m/K).

Cpl *

Liquid heat capacity at constant pressure (J/kg/K).

---

CAVALLINI_SZ

This function evaluates the Cavallini-Smith-Zecchin condensation correlation for internal two-phase flow in tubes. It computes a two-phase heat transfer coefficient from an equivalent Reynolds number that blends gas and liquid flow contributions.

The Nusselt-number form is:

Nu = \frac{hD}{k_l} = 0.05 Re_{eq}^{0.8} Pr_l^{0.33}

where Re_{eq} is based on liquid and gas superficial flow terms with viscosity and density corrections. The output is a scalar heat transfer coefficient in W/m^2/K.

Excel Usage

=CAVALLINI_SZ(m, x, D, rhol, rhog, mul, mug, kl, Cpl)

• m (float, required): Mass flow rate (kg/s).
• x (float, required): Quality at the specific interval (-).
• D (float, required): Channel diameter (m).
• rhol (float, required): Liquid density (kg/m^3).
• rhog (float, required): Gas density (kg/m^3).
• mul (float, required): Liquid viscosity (Pa*s).
• mug (float, required): Gas viscosity (Pa*s).
• kl (float, required): Liquid thermal conductivity (W/m/K).
• Cpl (float, required): Liquid heat capacity at constant pressure (J/kg/K).

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

Example 1: Example values from reference

Inputs:

m	x	D	rhol	rhog	mul	mug	kl	Cpl
1	0.4	0.3	800	2.5	0.00001	0.001	0.6	2300

Excel formula:

=CAVALLINI_SZ(1, 0.4, 0.3, 800, 2.5, 0.00001, 0.001, 0.6, 2300)

Expected output:

5578.22

Example 2: Low quality vapor fraction

Inputs:

m	x	D	rhol	rhog	mul	mug	kl	Cpl
0.5	0.1	0.05	900	6	0.0002	0.00002	0.12	2000

Excel formula:

=CAVALLINI_SZ(0.5, 0.1, 0.05, 900, 6, 0.0002, 0.00002, 0.12, 2000)

Expected output:

2273.43

Example 3: Mid quality vapor fraction

Inputs:

m	x	D	rhol	rhog	mul	mug	kl	Cpl
0.8	0.6	0.08	700	3	0.00015	0.00003	0.1	2400

Excel formula:

=CAVALLINI_SZ(0.8, 0.6, 0.08, 700, 3, 0.00015, 0.00003, 0.1, 2400)

Expected output:

5094.11

Example 4: Higher mass flow rate

Inputs:

m	x	D	rhol	rhog	mul	mug	kl	Cpl
2	0.7	0.12	650	4	0.00018	0.00004	0.11	2100

Excel formula:

=CAVALLINI_SZ(2, 0.7, 0.12, 650, 4, 0.00018, 0.00004, 0.11, 2100)

Expected output:

4647.2

Python Code

Show Code

from ht.condensation import Cavallini_Smith_Zecchin as ht_Cavallini_Smith_Zecchin

def Cavallini_SZ(m, x, D, rhol, rhog, mul, mug, kl, Cpl):
    """
    Calculate condensation heat transfer coefficient using the Cavallini-Smith-Zecchin correlation.

    See: https://ht.readthedocs.io/en/latest/ht.condensation.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 interval (-).
        D (float): Channel diameter (m).
        rhol (float): Liquid density (kg/m^3).
        rhog (float): Gas density (kg/m^3).
        mul (float): Liquid viscosity (Pa*s).
        mug (float): Gas viscosity (Pa*s).
        kl (float): Liquid thermal conductivity (W/m/K).
        Cpl (float): Liquid heat capacity at constant pressure (J/kg/K).

    Returns:
        float: Heat transfer coefficient (W/m^2/K).
    """
    try:
        result = ht_Cavallini_Smith_Zecchin(m=m, x=x, D=D, rhol=rhol, rhog=rhog, mul=mul, mug=mug, kl=kl, Cpl=Cpl)
        return result
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

m *

Mass flow rate (kg/s).

x *

Quality at the specific interval (-).

D *

Channel diameter (m).

rhol *

Liquid density (kg/m^3).

rhog *

Gas density (kg/m^3).

mul *

Liquid viscosity (Pa*s).

mug *

Gas viscosity (Pa*s).

kl *

Liquid thermal conductivity (W/m/K).

Cpl *

Liquid heat capacity at constant pressure (J/kg/K).

---

H_KINETIC

This function estimates condensation heat transfer using a kinetic-theory resistance model rather than a bulk convective correlation. It is useful when interfacial molecular transport contributes significantly to condensation resistance.

The model follows:

h = \left(\frac{2f}{2-f}\right)\left(\frac{MW}{1000\cdot 2\pi RT}\right)^{1/2}\left(\frac{H_{vap}^2 P\cdot MW}{1000\cdot RT^2}\right)

where f is an accommodation-style correction factor. The result is a scalar heat transfer coefficient in W/m^2/K.

Excel Usage

=H_KINETIC(T, P, MW, Hvap, f)

• T (float, required): Vapor temperature (K).
• P (float, required): Vapor pressure (Pa).
• MW (float, required): Molecular weight (g/mol).
• Hvap (float, required): Heat of vaporization (J/kg).
• f (float, optional, default: 1): Correction factor (-).

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

Example 1: Example values from reference

Inputs:

T	P	MW	Hvap	f
300	100000	18.02	2441674	1

Excel formula:

=H_KINETIC(300, 100000, 18.02, 2441674, 1)

Expected output:

30788800

Example 2: Higher vapor pressure

Inputs:

T	P	MW	Hvap	f
320	200000	18.02	2300000	1

Excel formula:

=H_KINETIC(320, 200000, 18.02, 2300000, 1)

Expected output:

46497700

Example 3: Heavier molecule

Inputs:

T	P	MW	Hvap	f
350	150000	44.01	2000000	1

Excel formula:

=H_KINETIC(350, 150000, 44.01, 2000000, 1)

Expected output:

80444600

Example 4: Non unity correction factor

Inputs:

T	P	MW	Hvap	f
300	100000	18.02	2441674	0.9

Excel formula:

=H_KINETIC(300, 100000, 18.02, 2441674, 0.9)

Expected output:

25190900

Python Code

Show Code

from ht.condensation import h_kinetic as ht_h_kinetic

def h_kinetic(T, P, MW, Hvap, f=1):
    """
    Calculate kinetic theory condensation heat transfer coefficient.

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

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

    Args:
        T (float): Vapor temperature (K).
        P (float): Vapor pressure (Pa).
        MW (float): Molecular weight (g/mol).
        Hvap (float): Heat of vaporization (J/kg).
        f (float, optional): Correction factor (-). Default is 1.

    Returns:
        float: Heat transfer coefficient (W/m^2/K).
    """
    try:
        result = ht_h_kinetic(T=T, P=P, MW=MW, Hvap=Hvap, f=f)
        return result
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

T *

Vapor temperature (K).

P *

Vapor pressure (Pa).

MW *

Molecular weight (g/mol).

Hvap *

Heat of vaporization (J/kg).

f

Correction factor (-).

---

NUSSELT_LAMINAR

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

The form is:

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

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

Excel Usage

=NUSSELT_LAMINAR(Tsat, Tw, rhog, rhol, kl, mul, Hvap, L, angle)

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

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

Example 1: Example values from reference

Inputs:

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

Excel formula:

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

Expected output:

1482.21

Example 2: Inclined plate at 45 degrees

Inputs:

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

Excel formula:

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

Expected output:

1252.37

Example 3: Short plate length

Inputs:

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

Excel formula:

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

Expected output:

1595.77

Example 4: Small temperature difference

Inputs:

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

Excel formula:

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

Expected output:

2086.01

Python Code

Show Code

from ht.condensation import Nusselt_laminar as ht_Nusselt_laminar

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

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

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

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

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

Online Calculator

Tsat *

Saturation temperature (K).

Tw *

Wall temperature (K).

rhog *

Gas density (kg/m^3).

rhol *

Liquid density (kg/m^3).

kl *

Liquid thermal conductivity (W/m/K).

mul *

Liquid viscosity (Pa*s).

Hvap *

Heat of vaporization (J/kg).

L *

Plate length (m).

angle

Plate inclination angle (degrees).

---

SHAH

This function calculates internal-flow condensation heat transfer using the Shah correlation. It combines a liquid-only convective baseline with a quality- and reduced-pressure-dependent enhancement term.

The two-phase coefficient is estimated as:

h_{TP} = h_L\left[(1-x)^{0.8} + \frac{3.8x^{0.76}(1-x)^{0.04}}{P_r^{0.38}}\right]

where P_r = P/P_c is reduced pressure and h_L is a liquid-only turbulent correlation value. The output is a scalar heat transfer coefficient in W/m^2/K.

Excel Usage

=SHAH(m, x, D, rhol, mul, kl, Cpl, P, Pc)

• m (float, required): Mass flow rate (kg/s).
• x (float, required): Quality at the specific interval (-).
• D (float, required): Channel diameter (m).
• rhol (float, required): Liquid density (kg/m^3).
• mul (float, required): Liquid viscosity (Pa*s).
• kl (float, required): Liquid thermal conductivity (W/m/K).
• Cpl (float, required): Liquid heat capacity at constant pressure (J/kg/K).
• P (float, required): Pressure (Pa).
• Pc (float, required): Critical pressure (Pa).

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

Example 1: Example values from reference

Inputs:

m	x	D	rhol	mul	kl	Cpl	P	Pc
1	0.4	0.3	800	0.00001	0.6	2300	1000000	20000000

Excel formula:

=SHAH(1, 0.4, 0.3, 800, 0.00001, 0.6, 2300, 1000000, 20000000)

Expected output:

2561.26

Example 2: Low quality vapor fraction

Inputs:

m	x	D	rhol	mul	kl	Cpl	P	Pc
0.6	0.1	0.05	900	0.0002	0.12	2000	800000	22000000

Excel formula:

=SHAH(0.6, 0.1, 0.05, 900, 0.0002, 0.12, 2000, 800000, 22000000)

Expected output:

2331.05

Example 3: Mid quality vapor fraction

Inputs:

m	x	D	rhol	mul	kl	Cpl	P	Pc
0.9	0.6	0.08	700	0.00015	0.1	2400	1500000	25000000

Excel formula:

=SHAH(0.9, 0.6, 0.08, 700, 0.00015, 0.1, 2400, 1500000, 25000000)

Expected output:

3569.56

Example 4: Higher mass flow rate

Inputs:

m	x	D	rhol	mul	kl	Cpl	P	Pc
2	0.7	0.12	650	0.00018	0.11	2100	2000000	30000000

Excel formula:

=SHAH(2, 0.7, 0.12, 650, 0.00018, 0.11, 2100, 2000000, 30000000)

Expected output:

3195.67

Python Code

Show Code

from ht.condensation import Shah as ht_Shah

def Shah(m, x, D, rhol, mul, kl, Cpl, P, Pc):
    """
    Calculate condensation heat transfer coefficient using the Shah correlation.

    See: https://ht.readthedocs.io/en/latest/ht.condensation.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 interval (-).
        D (float): Channel diameter (m).
        rhol (float): Liquid density (kg/m^3).
        mul (float): Liquid viscosity (Pa*s).
        kl (float): Liquid thermal conductivity (W/m/K).
        Cpl (float): Liquid heat capacity at constant pressure (J/kg/K).
        P (float): Pressure (Pa).
        Pc (float): Critical pressure (Pa).

    Returns:
        float: Heat transfer coefficient (W/m^2/K).
    """
    try:
        result = ht_Shah(m=m, x=x, D=D, rhol=rhol, mul=mul, kl=kl, Cpl=Cpl, P=P, Pc=Pc)
        return result
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

m *

Mass flow rate (kg/s).

x *

Quality at the specific interval (-).

D *

Channel diameter (m).

rhol *

Liquid density (kg/m^3).

mul *

Liquid viscosity (Pa*s).

kl *

Liquid thermal conductivity (W/m/K).

Cpl *

Liquid heat capacity at constant pressure (J/kg/K).

P *

Pressure (Pa).

Pc *

Critical pressure (Pa).