Conv Internal

Overview

Internal convection describes heat transfer between a moving fluid and the wall of a confined passage such as a pipe, coil, or duct. In engineering practice, the key unknown is usually the convective coefficient h, obtained through the Nusselt number Nu and then used in equipment sizing, thermal rating, and pressure-drop/energy tradeoff studies. Internal convection correlations matter because small changes in predicted Nu can materially change exchanger area, pumping cost, and thermal margins. This category organizes widely used single-phase correlations for laminar, transitional-entry, and turbulent regimes.

The unifying framework is the dimensionless relation between Nusselt number, Reynolds number, and Prandtl number, with geometry and roughness corrections when needed. Most tools here can be interpreted as variants of Nu=f(Re,Pr,\varepsilon/D,L/D,\text{geometry}), where developing-flow effects are often represented through entry-length terms (e.g., Graetz-type behavior). In practical workflows, engineers first classify regime, then select a correlation consistent with validity ranges, wall condition assumptions, and available inputs such as friction factor. That sequence reduces model-form error before any downstream thermal design calculation.

Implementation is based on the ht Python library, specifically ht.conv_internal, a heat-transfer toolkit focused on vetted literature correlations for process and mechanical engineering analysis. The library provides both individual named correlations and dispatch utilities, making it suitable for reproducible calculator-style use and scripted sensitivity studies.

For curved and non-straight passages, HEL_TURB_NU_MORI, HEL_TURB_NU_SCHM, and HEL_TURB_NU_XIN estimate turbulent helical-coil performance with different empirical bases and curvature sensitivities. MORIMOTO_HOTTA extends the geometry-specific approach to spiral heat exchangers. Together these tools are useful when straight-pipe assumptions underpredict enhancement from secondary flows induced by curvature.

For laminar and developing internal flow, LAMINAR_T_CONST and LAMINAR_Q_CONST provide canonical fully developed limits for constant wall temperature and constant heat flux. Entry-region behavior is handled by LAM_ENTRY_BAEHR, LAM_ENTRY_HAUSEN, and LAM_ENTRY_SEIDER, which are applied when thermal and/or hydrodynamic development is significant over finite length. NU_LAM_RECT_SHAN adds rectangular-duct aspect-ratio effects for compact and non-circular channels. These functions are typically used in low-Re process lines, micro/mini channels, and startup-length calculations.

For turbulent internal convection, several classic smooth-pipe forms are available, including TURB_COLBURN, TURB_DITTUS, TURB_DREXEL, and TURB_ESDU. More general friction-factor-based forms include TURB_CHURCHILL, TURB_GNIELINSKI, TURB_GNIEL_S1, TURB_GNIEL_S2, TURB_PETUKHOV, TURB_PRANDTL, TURB_VON_KARMAN, TURB_WEBB, TURB_FRIEND, and TURB_SIEDER, while roughness-aware behavior is addressed by TURB_BHATTI_SHAH and TURB_DIPPREY. TURB_ENTRY_HAUSEN handles turbulent thermal entrance effects where x/D is not yet large. This set supports both quick estimates and more rigorous rating when friction-factor and wall-property corrections are available.

Method selection and automation are covered by NU_CONV_INT_METHODS, which lists applicable correlations for supplied inputs, and NU_CONV_INTERNAL, which evaluates a chosen method (or default heuristic) in a single call. In production engineering workflows, these two tools help enforce consistent correlation selection logic across many cases, then allow targeted overrides for standards compliance or project-specific validation.

HEL_TURB_NU_MORI

This function computes the turbulent-flow Nusselt number for a helical coil using the Mori–Nakayama correlation. It uses Reynolds number, Prandtl number, and coil geometry to estimate dimensionless internal convection performance for curved-tube flow.

Excel Usage

=HEL_TURB_NU_MORI(Re, Pr, Di, Dc)
  • Re (float, required): Reynolds number based on tube diameter (-).
  • Pr (float, required): Prandtl number (-).
  • Di (float, required): Inner tube diameter (m).
  • Dc (float, required): Coil diameter (m).

Returns (float): Nusselt number for turbulent flow in a helical coil (-).

Example 1: Mori-Nakayama example

Inputs:

Re Pr Di Dc
200000 0.7 0.01 0.2

Excel formula:

=HEL_TURB_NU_MORI(200000, 0.7, 0.01, 0.2)

Expected output:

496.252

Example 2: Moderate Reynolds number

Inputs:

Re Pr Di Dc
150000 1.2 0.008 0.15

Excel formula:

=HEL_TURB_NU_MORI(150000, 1.2, 0.008, 0.15)

Expected output:

434.88

Example 3: High Reynolds number

Inputs:

Re Pr Di Dc
500000 0.9 0.012 0.25

Excel formula:

=HEL_TURB_NU_MORI(500000, 0.9, 0.012, 0.25)

Expected output:

1096.32

Example 4: Lower Reynolds number

Inputs:

Re Pr Di Dc
80000 2 0.006 0.1

Excel formula:

=HEL_TURB_NU_MORI(80000, 2, 0.006, 0.1)

Expected output:

319.563

Python Code

Show Code 
from ht.conv_internal import helical_turbulent_Nu_Mori_Nakayama as ht_helical_turbulent_Nu_Mori_Nakayama

def hel_turb_nu_mori(Re, Pr, Di, Dc):
    """
    Calculate the turbulent helical coil Nusselt number using Mori-Nakayama.

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

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

    Args:
        Re (float): Reynolds number based on tube diameter (-).
        Pr (float): Prandtl number (-).
        Di (float): Inner tube diameter (m).
        Dc (float): Coil diameter (m).

    Returns:
        float: Nusselt number for turbulent flow in a helical coil (-).
    """
    try:
        return ht_helical_turbulent_Nu_Mori_Nakayama(Re=Re, Pr=Pr, Di=Di, Dc=Dc)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Reynolds number based on tube diameter (-).
Prandtl number (-).
Inner tube diameter (m).
Coil diameter (m).

HEL_TURB_NU_SCHM

This function computes the turbulent-flow Nusselt number for a helical coil using the Schmidt correlation. It combines Reynolds number, Prandtl number, and coil diameter ratio effects to estimate internal convection intensity in curved tubes.

Excel Usage

=HEL_TURB_NU_SCHM(Re, Pr, Di, Dc)
  • Re (float, required): Reynolds number based on tube diameter (-).
  • Pr (float, required): Prandtl number (-).
  • Di (float, required): Inner tube diameter (m).
  • Dc (float, required): Coil diameter (m).

Returns (float): Nusselt number for turbulent flow in a helical coil (-).

Example 1: Schmidt example case

Inputs:

Re Pr Di Dc
200000 0.7 0.01 0.2

Excel formula:

=HEL_TURB_NU_SCHM(200000, 0.7, 0.01, 0.2)

Expected output:

466.257

Example 2: Moderate Reynolds number

Inputs:

Re Pr Di Dc
80000 1.1 0.008 0.12

Excel formula:

=HEL_TURB_NU_SCHM(80000, 1.1, 0.008, 0.12)

Expected output:

275.073

Example 3: Larger coil diameter

Inputs:

Re Pr Di Dc
120000 0.9 0.012 0.3

Excel formula:

=HEL_TURB_NU_SCHM(120000, 0.9, 0.012, 0.3)

Expected output:

324.548

Example 4: Higher Prandtl number

Inputs:

Re Pr Di Dc
250000 1.5 0.01 0.18

Excel formula:

=HEL_TURB_NU_SCHM(250000, 1.5, 0.01, 0.18)

Expected output:

732.513

Python Code

Show Code 
from ht.conv_internal import helical_turbulent_Nu_Schmidt as ht_helical_turbulent_Nu_Schmidt

def hel_turb_nu_schm(Re, Pr, Di, Dc):
    """
    Calculate the turbulent helical coil Nusselt number using Schmidt.

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

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

    Args:
        Re (float): Reynolds number based on tube diameter (-).
        Pr (float): Prandtl number (-).
        Di (float): Inner tube diameter (m).
        Dc (float): Coil diameter (m).

    Returns:
        float: Nusselt number for turbulent flow in a helical coil (-).
    """
    try:
        return ht_helical_turbulent_Nu_Schmidt(Re=Re, Pr=Pr, Di=Di, Dc=Dc)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Reynolds number based on tube diameter (-).
Prandtl number (-).
Inner tube diameter (m).
Coil diameter (m).

HEL_TURB_NU_XIN

This function computes the turbulent-flow Nusselt number for a helical coil using the Xin–Ebadian correlation. It captures the influence of Reynolds number, Prandtl number, and coil curvature to estimate convective heat transfer in internal curved flow.

Excel Usage

=HEL_TURB_NU_XIN(Re, Pr, Di, Dc)
  • Re (float, required): Reynolds number based on tube diameter (-).
  • Pr (float, required): Prandtl number (-).
  • Di (float, required): Inner tube diameter (m).
  • Dc (float, required): Coil diameter (m).

Returns (float): Nusselt number for turbulent flow in a helical coil (-).

Example 1: Xin-Ebadian example

Inputs:

Re Pr Di Dc
200000 0.7 0.01 0.2

Excel formula:

=HEL_TURB_NU_XIN(200000, 0.7, 0.01, 0.2)

Expected output:

474.114

Example 2: Moderate Reynolds number

Inputs:

Re Pr Di Dc
100000 1.1 0.008 0.14

Excel formula:

=HEL_TURB_NU_XIN(100000, 1.1, 0.008, 0.14)

Expected output:

306.547

Example 3: High Reynolds number

Inputs:

Re Pr Di Dc
500000 0.9 0.012 0.25

Excel formula:

=HEL_TURB_NU_XIN(500000, 0.9, 0.012, 0.25)

Expected output:

1210.82

Example 4: Higher Prandtl number

Inputs:

Re Pr Di Dc
150000 2 0.009 0.2

Excel formula:

=HEL_TURB_NU_XIN(150000, 2, 0.009, 0.2)

Expected output:

545.591

Python Code

Show Code 
from ht.conv_internal import helical_turbulent_Nu_Xin_Ebadian as ht_helical_turbulent_Nu_Xin_Ebadian

def hel_turb_nu_xin(Re, Pr, Di, Dc):
    """
    Calculate the turbulent helical coil Nusselt number using Xin-Ebadian.

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

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

    Args:
        Re (float): Reynolds number based on tube diameter (-).
        Pr (float): Prandtl number (-).
        Di (float): Inner tube diameter (m).
        Dc (float): Coil diameter (m).

    Returns:
        float: Nusselt number for turbulent flow in a helical coil (-).
    """
    try:
        return ht_helical_turbulent_Nu_Xin_Ebadian(Re=Re, Pr=Pr, Di=Di, Dc=Dc)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Reynolds number based on tube diameter (-).
Prandtl number (-).
Inner tube diameter (m).
Coil diameter (m).

LAM_ENTRY_BAEHR

This function estimates the average laminar Nusselt number in the thermal and hydrodynamic entry region of a circular tube using the Baehr–Stephan correlation. It accounts for Reynolds number, Prandtl number, and geometry through the developing-flow length scale.

Excel Usage

=LAM_ENTRY_BAEHR(Re, Pr, L, Di)
  • Re (float, required): Reynolds number (-).
  • Pr (float, required): Prandtl number (-).
  • L (float, required): Pipe length (m).
  • Di (float, required): Pipe diameter (m).

Returns (float): Laminar entry-region Nusselt number (-).

Example 1: Baehr-Stephan example

Inputs:

Re Pr L Di
100000 1.1 5 0.5

Excel formula:

=LAM_ENTRY_BAEHR(100000, 1.1, 5, 0.5)

Expected output:

72.654

Example 2: Lower Reynolds number

Inputs:

Re Pr L Di
5000 7 1 0.05

Excel formula:

=LAM_ENTRY_BAEHR(5000, 7, 1, 0.05)

Expected output:

24.8796

Example 3: Mid Reynolds number

Inputs:

Re Pr L Di
20000 0.9 2 0.1

Excel formula:

=LAM_ENTRY_BAEHR(20000, 0.9, 2, 0.1)

Expected output:

22.9378

Example 4: Longer pipe length

Inputs:

Re Pr L Di
80000 2 3 0.2

Excel formula:

=LAM_ENTRY_BAEHR(80000, 2, 3, 0.2)

Expected output:

65.9616

Python Code

Show Code 
from ht.conv_internal import laminar_entry_Baehr_Stephan as ht_laminar_entry_Baehr_Stephan

def lam_entry_baehr(Re, Pr, L, Di):
    """
    Calculate laminar entry Nusselt number using Baehr-Stephan.

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

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

    Args:
        Re (float): Reynolds number (-).
        Pr (float): Prandtl number (-).
        L (float): Pipe length (m).
        Di (float): Pipe diameter (m).

    Returns:
        float: Laminar entry-region Nusselt number (-).
    """
    try:
        return ht_laminar_entry_Baehr_Stephan(Re=Re, Pr=Pr, L=L, Di=Di)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Reynolds number (-).
Prandtl number (-).
Pipe length (m).
Pipe diameter (m).

LAM_ENTRY_HAUSEN

This function estimates the average laminar Nusselt number in the thermal entry region of internal tube flow using the Hausen correlation. It links Reynolds number, Prandtl number, and tube length-to-diameter effects to represent developing temperature profiles.

Excel Usage

=LAM_ENTRY_HAUSEN(Re, Pr, L, Di)
  • Re (float, required): Reynolds number (-).
  • Pr (float, required): Prandtl number (-).
  • L (float, required): Pipe length (m).
  • Di (float, required): Pipe diameter (m).

Returns (float): Laminar thermal entry-region Nusselt number (-).

Example 1: Hausen example

Inputs:

Re Pr L Di
100000 1.1 5 0.5

Excel formula:

=LAM_ENTRY_HAUSEN(100000, 1.1, 5, 0.5)

Expected output:

39.0135

Example 2: Lower Reynolds number

Inputs:

Re Pr L Di
5000 7 1 0.05

Excel formula:

=LAM_ENTRY_HAUSEN(5000, 7, 1, 0.05)

Expected output:

20.829

Example 3: Mid Reynolds number

Inputs:

Re Pr L Di
20000 0.9 2 0.1

Excel formula:

=LAM_ENTRY_HAUSEN(20000, 0.9, 2, 0.1)

Expected output:

16.3739

Example 4: Short pipe length

Inputs:

Re Pr L Di
8000 2 0.6 0.03

Excel formula:

=LAM_ENTRY_HAUSEN(8000, 2, 0.6, 0.03)

Expected output:

15.6768

Python Code

Show Code 
from ht.conv_internal import laminar_entry_thermal_Hausen as ht_laminar_entry_thermal_Hausen

def lam_entry_hausen(Re, Pr, L, Di):
    """
    Calculate laminar thermal entry Nusselt number using Hausen.

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

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

    Args:
        Re (float): Reynolds number (-).
        Pr (float): Prandtl number (-).
        L (float): Pipe length (m).
        Di (float): Pipe diameter (m).

    Returns:
        float: Laminar thermal entry-region Nusselt number (-).
    """
    try:
        return ht_laminar_entry_thermal_Hausen(Re=Re, Pr=Pr, L=L, Di=Di)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Reynolds number (-).
Prandtl number (-).
Pipe length (m).
Pipe diameter (m).

LAM_ENTRY_SEIDER

This function estimates the average laminar entry-region Nusselt number using the Seider–Tate correlation. It supports optional viscosity correction through bulk and wall viscosities to improve predictions when fluid properties vary with temperature.

Excel Usage

=LAM_ENTRY_SEIDER(Re, Pr, L, Di, mu, mu_w)
  • Re (float, required): Reynolds number (-).
  • Pr (float, required): Prandtl number (-).
  • L (float, required): Pipe length (m).
  • Di (float, required): Pipe diameter (m).
  • mu (float, optional, default: null): Bulk viscosity (Pa*s).
  • mu_w (float, optional, default: null): Wall viscosity (Pa*s).

Returns (float): Laminar entry-region Nusselt number (-).

Example 1: Seider-Tate example

Inputs:

Re Pr L Di
100000 1.1 5 0.5

Excel formula:

=LAM_ENTRY_SEIDER(100000, 1.1, 5, 0.5)

Expected output:

41.366

Example 2: Seider-Tate with viscosity correction

Inputs:

Re Pr L Di mu mu_w
8000 5 1 0.05 0.003 0.004

Excel formula:

=LAM_ENTRY_SEIDER(8000, 5, 1, 0.05, 0.003, 0.004)

Expected output:

22.5094

Example 3: Mid Reynolds number

Inputs:

Re Pr L Di
20000 0.9 2 0.1

Excel formula:

=LAM_ENTRY_SEIDER(20000, 0.9, 2, 0.1)

Expected output:

17.9581

Example 4: Short pipe length

Inputs:

Re Pr L Di
5000 7 0.5 0.02

Excel formula:

=LAM_ENTRY_SEIDER(5000, 7, 0.5, 0.02)

Expected output:

20.8076

Python Code

Show Code 
from ht.conv_internal import laminar_entry_Seider_Tate as ht_laminar_entry_Seider_Tate

def lam_entry_seider(Re, Pr, L, Di, mu=None, mu_w=None):
    """
    Calculate laminar entry Nusselt number using Seider-Tate.

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

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

    Args:
        Re (float): Reynolds number (-).
        Pr (float): Prandtl number (-).
        L (float): Pipe length (m).
        Di (float): Pipe diameter (m).
        mu (float, optional): Bulk viscosity (Pa*s). Default is None.
        mu_w (float, optional): Wall viscosity (Pa*s). Default is None.

    Returns:
        float: Laminar entry-region Nusselt number (-).
    """
    try:
        return ht_laminar_entry_Seider_Tate(Re=Re, Pr=Pr, L=L, Di=Di, mu=mu, mu_w=mu_w)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Reynolds number (-).
Prandtl number (-).
Pipe length (m).
Pipe diameter (m).
Bulk viscosity (Pa*s).
Wall viscosity (Pa*s).

LAMINAR_Q_CONST

This function returns the theoretical fully developed laminar Nusselt number for internal pipe flow with constant wall heat flux. It provides the standard reference value used in internal-convection analysis when thermal and velocity profiles are fully developed.

Excel Usage

=LAMINAR_Q_CONST()

Returns (float): Constant heat flux Nusselt number (-).

Example 1: Constant heat flux reference value

Inputs:

 |

|| | |

Excel formula:

=LAMINAR_Q_CONST()

Expected output:

4.36364

Example 2: Constant heat flux repeatability A

Inputs:

 |

|| | |

Excel formula:

=LAMINAR_Q_CONST()

Expected output:

4.36364

Example 3: Constant heat flux repeatability B

Inputs:

 |

|| | |

Excel formula:

=LAMINAR_Q_CONST()

Expected output:

4.36364

Example 4: Constant heat flux repeatability C

Inputs:

 |

|| | |

Excel formula:

=LAMINAR_Q_CONST()

Expected output:

4.36364

Python Code

Show Code 
from ht.conv_internal import laminar_Q_const as ht_laminar_Q_const

def laminar_q_const():
    """
    Return the laminar constant-heat-flux Nusselt number for a pipe.

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

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

    Returns:
        float: Constant heat flux Nusselt number (-).
    """
    try:
        return ht_laminar_Q_const()
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

LAMINAR_T_CONST

This function returns the theoretical fully developed laminar Nusselt number for internal pipe flow with constant wall temperature. It provides the canonical baseline value for laminar internal-convection calculations under isothermal wall conditions.

Excel Usage

=LAMINAR_T_CONST()

Returns (float): Constant wall temperature Nusselt number (-).

Example 1: Constant wall temperature reference value

Inputs:

 |

|| | |

Excel formula:

=LAMINAR_T_CONST()

Expected output:

3.66

Example 2: Constant wall temperature repeatability A

Inputs:

 |

|| | |

Excel formula:

=LAMINAR_T_CONST()

Expected output:

3.66

Example 3: Constant wall temperature repeatability B

Inputs:

 |

|| | |

Excel formula:

=LAMINAR_T_CONST()

Expected output:

3.66

Example 4: Constant wall temperature repeatability C

Inputs:

 |

|| | |

Excel formula:

=LAMINAR_T_CONST()

Expected output:

3.66

Python Code

Show Code 
from ht.conv_internal import laminar_T_const as ht_laminar_T_const

def laminar_t_const():
    """
    Return the laminar constant-wall-temperature Nusselt number for a pipe.

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

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

    Returns:
        float: Constant wall temperature Nusselt number (-).
    """
    try:
        return ht_laminar_T_const()
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

MORIMOTO_HOTTA

This function computes the internal-flow Nusselt number for spiral heat exchangers using the Morimoto–Hotta correlation. It relates convection performance to Reynolds and Prandtl numbers and the ratio of hydraulic diameter to spiral radius.

Excel Usage

=MORIMOTO_HOTTA(Re, Pr, Dh, Rm)
  • Re (float, required): Reynolds number (-).
  • Pr (float, required): Prandtl number (-).
  • Dh (float, required): Average hydraulic diameter (m).
  • Rm (float, required): Average spiral radius (m).

Returns (float): Nusselt number with respect to hydraulic diameter (-).

Example 1: Spiral exchanger example

Inputs:

Re Pr Dh Rm
100000 5.7 0.05 0.5

Excel formula:

=MORIMOTO_HOTTA(100000, 5.7, 0.05, 0.5)

Expected output:

634.488

Example 2: Moderate Reynolds number

Inputs:

Re Pr Dh Rm
50000 2 0.03 0.4

Excel formula:

=MORIMOTO_HOTTA(50000, 2, 0.03, 0.4)

Expected output:

249.663

Example 3: Higher Reynolds number case

Inputs:

Re Pr Dh Rm
200000 1.1 0.08 0.6

Excel formula:

=MORIMOTO_HOTTA(200000, 1.1, 0.08, 0.6)

Expected output:

798.615

Example 4: Compact spiral geometry

Inputs:

Re Pr Dh Rm
80000 0.8 0.04 0.35

Excel formula:

=MORIMOTO_HOTTA(80000, 0.8, 0.04, 0.35)

Expected output:

329.11

Python Code

Show Code 
from ht.conv_internal import Morimoto_Hotta as ht_Morimoto_Hotta

def morimoto_hotta(Re, Pr, Dh, Rm):
    """
    Calculate the Nusselt number for flow in a spiral heat exchanger.

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

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

    Args:
        Re (float): Reynolds number (-).
        Pr (float): Prandtl number (-).
        Dh (float): Average hydraulic diameter (m).
        Rm (float): Average spiral radius (m).

    Returns:
        float: Nusselt number with respect to hydraulic diameter (-).
    """
    try:
        return ht_Morimoto_Hotta(Re=Re, Pr=Pr, Dh=Dh, Rm=Rm)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Reynolds number (-).
Prandtl number (-).
Average hydraulic diameter (m).
Average spiral radius (m).

NU_CONV_INT_METHODS

This function returns the available internal-convection method names for a given pipe-flow condition. It can optionally filter to only range-appropriate correlations based on Reynolds number, Prandtl number, roughness, and entry-region inputs.

Excel Usage

=NU_CONV_INT_METHODS(Re, Pr, eD, Di, x, fd, check_ranges)
  • Re (float, required): Reynolds number (-).
  • Pr (float, required): Prandtl number (-).
  • eD (float, optional, default: 0): Relative roughness (-).
  • Di (float, optional, default: null): Inside diameter of the pipe (m).
  • x (float, optional, default: null): Axial distance from the inlet (m).
  • fd (float, optional, default: null): Darcy friction factor (-).
  • check_ranges (bool, optional, default: true): Whether to return only applicable correlations (-).

Returns (list[list]): 2D array of available correlation method names.

Example 1: Methods for turbulent flow

Inputs:

Re Pr
100000 0.7

Excel formula:

=NU_CONV_INT_METHODS(100000, 0.7)

Expected output:

Churchill-Zajic
Petukhov-Kirillov-Popov
Gnielinski
Bhatti-Shah
Dipprey-Sabersky
Sandall
Webb
Friend-Metzner
Prandtl
von-Karman
Gowen-Smith
Kawase-Ulbrecht
Kawase-De
Nunner
Dittus-Boelter
Sieder-Tate
Drexel-McAdams
Colburn
ESDU
Gnielinski smooth low Pr
Gnielinski smooth high Pr
Example 2: Methods for laminar entry flow

Inputs:

Re Pr x Di
100 0.7 0.01 0.1

Excel formula:

=NU_CONV_INT_METHODS(100, 0.7, 0.01, 0.1)

Expected output:

Baehr-Stephan laminar thermal/velocity entry
Hausen laminar thermal entry
Seider-Tate laminar thermal entry
Laminar - constant T
Laminar - constant Q
Example 3: Methods for rough pipe

Inputs:

Re Pr eD
50000 2 0.001

Excel formula:

=NU_CONV_INT_METHODS(50000, 2, 0.001)

Expected output:

Churchill-Zajic
Petukhov-Kirillov-Popov
Gnielinski
Bhatti-Shah
Dipprey-Sabersky
Sandall
Webb
Friend-Metzner
Prandtl
von-Karman
Gowen-Smith
Kawase-Ulbrecht
Kawase-De
Nunner
Dittus-Boelter
Sieder-Tate
Drexel-McAdams
Colburn
ESDU
Gnielinski smooth low Pr
Gnielinski smooth high Pr
Example 4: Methods without range checking

Inputs:

Re Pr check_ranges
200000 1 false

Excel formula:

=NU_CONV_INT_METHODS(200000, 1, FALSE)

Expected output:

Laminar - constant T
Laminar - constant Q
Martinelli
Hausen
Churchill-Zajic
Petukhov-Kirillov-Popov
Gnielinski
Bhatti-Shah
Dipprey-Sabersky
Sandall
Webb
Friend-Metzner
Prandtl
von-Karman
Gowen-Smith
Kawase-Ulbrecht
Kawase-De
Nunner
Dittus-Boelter
Sieder-Tate
Drexel-McAdams
Colburn
ESDU
Gnielinski smooth low Pr
Gnielinski smooth high Pr

Python Code

Show Code 
from ht.conv_internal import Nu_conv_internal_methods as ht_Nu_conv_internal_methods

def nu_conv_int_methods(Re, Pr, eD=0, Di=None, x=None, fd=None, check_ranges=True):
    """
    List available internal convection correlations for a pipe.

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

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

    Args:
        Re (float): Reynolds number (-).
        Pr (float): Prandtl number (-).
        eD (float, optional): Relative roughness (-). Default is 0.
        Di (float, optional): Inside diameter of the pipe (m). Default is None.
        x (float, optional): Axial distance from the inlet (m). Default is None.
        fd (float, optional): Darcy friction factor (-). Default is None.
        check_ranges (bool, optional): Whether to return only applicable correlations (-). Default is True.

    Returns:
        list[list]: 2D array of available correlation method names.
    """
    try:
        methods = ht_Nu_conv_internal_methods(
            Re=Re,
            Pr=Pr,
            eD=eD,
            Di=Di,
            x=x,
            fd=fd,
            check_ranges=check_ranges,
        )
        return [[method] for method in methods]
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Reynolds number (-).
Prandtl number (-).
Relative roughness (-).
Inside diameter of the pipe (m).
Axial distance from the inlet (m).
Darcy friction factor (-).
Whether to return only applicable correlations (-).

NU_CONV_INTERNAL

This function selects and applies an internal-convection correlation to compute pipe-flow Nusselt number from Reynolds and Prandtl numbers, with optional roughness, entry-length, friction-factor, and explicit method controls. It serves as a high-level dispatcher for laminar and turbulent regimes.

Excel Usage

=NU_CONV_INTERNAL(Re, Pr, eD, Di, x, fd, Method)
  • Re (float, required): Reynolds number (-).
  • Pr (float, required): Prandtl number (-).
  • eD (float, optional, default: 0): Relative roughness (-).
  • Di (float, optional, default: null): Inside diameter of the pipe (m).
  • x (float, optional, default: null): Axial distance from the inlet (m).
  • fd (float, optional, default: null): Darcy friction factor (-).
  • Method (str, optional, default: null): Correlation method name (-).

Returns (float): Nusselt number for internal pipe flow (-).

Example 1: Turbulent flow default method

Inputs:

Re Pr
100000 0.7

Excel formula:

=NU_CONV_INTERNAL(100000, 0.7)

Expected output:

183.711

Example 2: Laminar entry length case

Inputs:

Re Pr x Di
100 0.7 0.01 0.1

Excel formula:

=NU_CONV_INTERNAL(100, 0.7, 0.01, 0.1)

Expected output:

14.918

Example 3: Rough pipe with higher Prandtl number

Inputs:

Re Pr eD
50000 2 0.001

Excel formula:

=NU_CONV_INTERNAL(50000, 2, 0.001)

Expected output:

209.914

Example 4: Turbulent entry length case

Inputs:

Re Pr Di x
200000 1 0.05 0.5

Excel formula:

=NU_CONV_INTERNAL(200000, 1, 0.05, 0.5)

Expected output:

417.218

Python Code

Show Code 
from ht.conv_internal import Nu_conv_internal as ht_Nu_conv_internal

def nu_conv_internal(Re, Pr, eD=0, Di=None, x=None, fd=None, Method=None):
    """
    Compute the Nusselt number for internal pipe convection.

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

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

    Args:
        Re (float): Reynolds number (-).
        Pr (float): Prandtl number (-).
        eD (float, optional): Relative roughness (-). Default is 0.
        Di (float, optional): Inside diameter of the pipe (m). Default is None.
        x (float, optional): Axial distance from the inlet (m). Default is None.
        fd (float, optional): Darcy friction factor (-). Default is None.
        Method (str, optional): Correlation method name (-). Default is None.

    Returns:
        float: Nusselt number for internal pipe flow (-).
    """
    try:
        return ht_Nu_conv_internal(
            Re=Re,
            Pr=Pr,
            eD=eD,
            Di=Di,
            x=x,
            fd=fd,
            Method=Method,
        )
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Reynolds number (-).
Prandtl number (-).
Relative roughness (-).
Inside diameter of the pipe (m).
Axial distance from the inlet (m).
Darcy friction factor (-).
Correlation method name (-).

NU_LAM_RECT_SHAN

This function computes the fully developed laminar Nusselt number for internal flow in a rectangular duct using the Shah–London polynomial correlation. The result depends on aspect ratio and assumes constant wall heat flux boundary conditions.

Excel Usage

=NU_LAM_RECT_SHAN(a_r)
  • a_r (float, required): Aspect ratio of the channel (0 to 1) (-).

Returns (float): Nusselt number for laminar rectangular duct flow (-).

Example 1: Aspect ratio 0.7

Inputs:

a_r
0.7

Excel formula:

=NU_LAM_RECT_SHAN(0.7)

Expected output:

3.75176

Example 2: Square duct aspect ratio

Inputs:

a_r
1

Excel formula:

=NU_LAM_RECT_SHAN(1)

Expected output:

3.61022

Example 3: Low aspect ratio

Inputs:

a_r
0.2

Excel formula:

=NU_LAM_RECT_SHAN(0.2)

Expected output:

5.73825

Example 4: Mid aspect ratio

Inputs:

a_r
0.5

Excel formula:

=NU_LAM_RECT_SHAN(0.5)

Expected output:

4.12581

Python Code

Show Code 
from ht.conv_internal import Nu_laminar_rectangular_Shan_London as ht_Nu_laminar_rectangular_Shan_London

def nu_lam_rect_shan(a_r):
    """
    Calculate the laminar Nusselt number for a rectangular duct.

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

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

    Args:
        a_r (float): Aspect ratio of the channel (0 to 1) (-).

    Returns:
        float: Nusselt number for laminar rectangular duct flow (-).
    """
    try:
        return ht_Nu_laminar_rectangular_Shan_London(a_r=a_r)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Aspect ratio of the channel (0 to 1) (-).

TURB_BHATTI_SHAH

This function computes turbulent internal-flow Nusselt number in rough pipes using the Bhatti–Shah correlation. It requires Reynolds number, Prandtl number, Darcy friction factor, and relative roughness to model roughness-enhanced convection.

Excel Usage

=TURB_BHATTI_SHAH(Re, Pr, fd, eD)
  • Re (float, required): Reynolds number (-).
  • Pr (float, required): Prandtl number (-).
  • fd (float, required): Darcy friction factor (-).
  • eD (float, required): Relative roughness (-).

Returns (float): Turbulent Nusselt number for rough pipes (-).

Example 1: Bhatti-Shah example

Inputs:

Re Pr fd eD
100000 1.2 0.0185 0.001

Excel formula:

=TURB_BHATTI_SHAH(100000, 1.2, 0.0185, 0.001)

Expected output:

302.704

Example 2: Higher Reynolds number

Inputs:

Re Pr fd eD
200000 0.8 0.02 0.0005

Excel formula:

=TURB_BHATTI_SHAH(200000, 0.8, 0.02, 0.0005)

Expected output:

468.568

Example 3: Mid Reynolds number

Inputs:

Re Pr fd eD
50000 2 0.022 0.002

Excel formula:

=TURB_BHATTI_SHAH(50000, 2, 0.022, 0.002)

Expected output:

269.563

Example 4: Lower Reynolds number

Inputs:

Re Pr fd eD
150000 1 0.017 0.0008

Excel formula:

=TURB_BHATTI_SHAH(150000, 1, 0.017, 0.0008)

Expected output:

353.716

Python Code

Show Code 
from ht.conv_internal import turbulent_Bhatti_Shah as ht_turbulent_Bhatti_Shah

def turb_bhatti_shah(Re, Pr, fd, eD):
    """
    Calculate turbulent Nusselt number using the Bhatti-Shah correlation.

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

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

    Args:
        Re (float): Reynolds number (-).
        Pr (float): Prandtl number (-).
        fd (float): Darcy friction factor (-).
        eD (float): Relative roughness (-).

    Returns:
        float: Turbulent Nusselt number for rough pipes (-).
    """
    try:
        return ht_turbulent_Bhatti_Shah(Re=Re, Pr=Pr, fd=fd, eD=eD)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Reynolds number (-).
Prandtl number (-).
Darcy friction factor (-).
Relative roughness (-).

TURB_CHURCHILL

This function computes turbulent internal-flow Nusselt number using the Churchill–Zajic correlation. It combines Reynolds number, Prandtl number, and Darcy friction factor in a broadly applicable model for fully developed turbulent pipe convection.

Excel Usage

=TURB_CHURCHILL(Re, Pr, fd)
  • Re (float, required): Reynolds number (-).
  • Pr (float, required): Prandtl number (-).
  • fd (float, required): Darcy friction factor (-).

Returns (float): Turbulent Nusselt number for pipe flow (-).

Example 1: Churchill-Zajic example

Inputs:

Re Pr fd
100000 1.2 0.0185

Excel formula:

=TURB_CHURCHILL(100000, 1.2, 0.0185)

Expected output:

260.556

Example 2: Higher Reynolds number

Inputs:

Re Pr fd
200000 0.8 0.02

Excel formula:

=TURB_CHURCHILL(200000, 0.8, 0.02)

Expected output:

440.755

Example 3: Mid Reynolds number

Inputs:

Re Pr fd
50000 2 0.022

Excel formula:

=TURB_CHURCHILL(50000, 2, 0.022)

Expected output:

196.368

Example 4: Lower Reynolds number

Inputs:

Re Pr fd
150000 1 0.017

Excel formula:

=TURB_CHURCHILL(150000, 1, 0.017)

Expected output:

326.138

Python Code

Show Code 
from ht.conv_internal import turbulent_Churchill_Zajic as ht_turbulent_Churchill_Zajic

def turb_churchill(Re, Pr, fd):
    """
    Calculate turbulent Nusselt number using Churchill-Zajic.

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

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

    Args:
        Re (float): Reynolds number (-).
        Pr (float): Prandtl number (-).
        fd (float): Darcy friction factor (-).

    Returns:
        float: Turbulent Nusselt number for pipe flow (-).
    """
    try:
        return ht_turbulent_Churchill_Zajic(Re=Re, Pr=Pr, fd=fd)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Reynolds number (-).
Prandtl number (-).
Darcy friction factor (-).

TURB_COLBURN

This function computes turbulent pipe-flow Nusselt number using the Colburn correlation. It provides a simple Reynolds–Prandtl power-law estimate for internal forced convection in smooth-tube conditions.

Excel Usage

=TURB_COLBURN(Re, Pr)
  • Re (float, required): Reynolds number (-).
  • Pr (float, required): Prandtl number (-).

Returns (float): Turbulent Nusselt number for pipe flow (-).

Example 1: Colburn example

Inputs:

Re Pr
100000 1.2

Excel formula:

=TURB_COLBURN(100000, 1.2)

Expected output:

244.411

Example 2: Lower Prandtl number

Inputs:

Re Pr
50000 0.8

Excel formula:

=TURB_COLBURN(50000, 0.8)

Expected output:

122.631

Example 3: Higher Prandtl number

Inputs:

Re Pr
200000 2

Excel formula:

=TURB_COLBURN(200000, 2)

Expected output:

504.539

Example 4: Mid Reynolds number

Inputs:

Re Pr
150000 1

Excel formula:

=TURB_COLBURN(150000, 1)

Expected output:

318.127

Python Code

Show Code 
from ht.conv_internal import turbulent_Colburn as ht_turbulent_Colburn

def turb_colburn(Re, Pr):
    """
    Calculate turbulent Nusselt number using the Colburn correlation.

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

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

    Args:
        Re (float): Reynolds number (-).
        Pr (float): Prandtl number (-).

    Returns:
        float: Turbulent Nusselt number for pipe flow (-).
    """
    try:
        return ht_turbulent_Colburn(Re=Re, Pr=Pr)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Reynolds number (-).
Prandtl number (-).

TURB_DIPPREY

This function computes turbulent Nusselt number for rough internal pipe flow using the Dipprey–Sabersky correlation. It uses Reynolds number, Prandtl number, friction factor, and roughness to estimate convective transfer with rough-wall effects.

Excel Usage

=TURB_DIPPREY(Re, Pr, fd, eD)
  • Re (float, required): Reynolds number (-).
  • Pr (float, required): Prandtl number (-).
  • fd (float, required): Darcy friction factor (-).
  • eD (float, required): Relative roughness (-).

Returns (float): Turbulent Nusselt number for rough pipes (-).

Example 1: Dipprey-Sabersky example

Inputs:

Re Pr fd eD
100000 1.2 0.0185 0.001

Excel formula:

=TURB_DIPPREY(100000, 1.2, 0.0185, 0.001)

Expected output:

288.334

Example 2: Higher Reynolds number

Inputs:

Re Pr fd eD
200000 0.9 0.02 0.0005

Excel formula:

=TURB_DIPPREY(200000, 0.9, 0.02, 0.0005)

Expected output:

490.292

Example 3: Mid Reynolds number

Inputs:

Re Pr fd eD
60000 2 0.022 0.002

Excel formula:

=TURB_DIPPREY(60000, 2, 0.022, 0.002)

Expected output:

303.111

Example 4: Lower Reynolds number

Inputs:

Re Pr fd eD
150000 1 0.017 0.0008

Excel formula:

=TURB_DIPPREY(150000, 1, 0.017, 0.0008)

Expected output:

336.971

Python Code

Show Code 
from ht.conv_internal import turbulent_Dipprey_Sabersky as ht_turbulent_Dipprey_Sabersky

def turb_dipprey(Re, Pr, fd, eD):
    """
    Calculate turbulent Nusselt number using Dipprey-Sabersky.

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

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

    Args:
        Re (float): Reynolds number (-).
        Pr (float): Prandtl number (-).
        fd (float): Darcy friction factor (-).
        eD (float): Relative roughness (-).

    Returns:
        float: Turbulent Nusselt number for rough pipes (-).
    """
    try:
        return ht_turbulent_Dipprey_Sabersky(Re=Re, Pr=Pr, fd=fd, eD=eD)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Reynolds number (-).
Prandtl number (-).
Darcy friction factor (-).
Relative roughness (-).

TURB_DITTUS

This function computes turbulent internal-flow Nusselt number using the Dittus–Boelter correlation. Optional flags select heating versus cooling exponent behavior and revised versus original coefficient forms.

Excel Usage

=TURB_DITTUS(Re, Pr, heating, revised)
  • Re (float, required): Reynolds number (-).
  • Pr (float, required): Prandtl number (-).
  • heating (bool, optional, default: true): Whether the flow is being heated (-).
  • revised (bool, optional, default: true): Whether to use the revised coefficients (-).

Returns (float): Turbulent Nusselt number for pipe flow (-).

Example 1: Dittus-Boelter default coefficients

Inputs:

Re Pr
100000 1.2

Excel formula:

=TURB_DITTUS(100000, 1.2)

Expected output:

247.4

Example 2: Dittus-Boelter cooling case

Inputs:

Re Pr heating
100000 1.2 false

Excel formula:

=TURB_DITTUS(100000, 1.2, FALSE)

Expected output:

242.931

Example 3: Dittus-Boelter original coefficients

Inputs:

Re Pr revised
200000 0.7 false

Excel formula:

=TURB_DITTUS(200000, 0.7, FALSE)

Expected output:

366.834

Example 4: Dittus-Boelter cooling original

Inputs:

Re Pr heating revised
50000 2 false false

Excel formula:

=TURB_DITTUS(50000, 2, FALSE, FALSE)

Expected output:

187.383

Python Code

Show Code 
from ht.conv_internal import turbulent_Dittus_Boelter as ht_turbulent_Dittus_Boelter

def turb_dittus(Re, Pr, heating=True, revised=True):
    """
    Calculate turbulent Nusselt number using Dittus-Boelter.

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

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

    Args:
        Re (float): Reynolds number (-).
        Pr (float): Prandtl number (-).
        heating (bool, optional): Whether the flow is being heated (-). Default is True.
        revised (bool, optional): Whether to use the revised coefficients (-). Default is True.

    Returns:
        float: Turbulent Nusselt number for pipe flow (-).
    """
    try:
        return ht_turbulent_Dittus_Boelter(Re=Re, Pr=Pr, heating=heating, revised=revised)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Reynolds number (-).
Prandtl number (-).
Whether the flow is being heated (-).
Whether to use the revised coefficients (-).

TURB_DREXEL

This function computes turbulent pipe-flow Nusselt number using the Drexel–McAdams correlation. It provides a compact Reynolds–Prandtl relation commonly applied to low-Prandtl-number gas-flow heat transfer.

Excel Usage

=TURB_DREXEL(Re, Pr)
  • Re (float, required): Reynolds number (-).
  • Pr (float, required): Prandtl number (-).

Returns (float): Turbulent Nusselt number for pipe flow (-).

Example 1: Drexel-McAdams example

Inputs:

Re Pr
100000 0.6

Excel formula:

=TURB_DREXEL(100000, 0.6)

Expected output:

171.191

Example 2: Lower Prandtl number

Inputs:

Re Pr
80000 0.5

Excel formula:

=TURB_DREXEL(80000, 0.5)

Expected output:

133.131

Example 3: Higher Reynolds number

Inputs:

Re Pr
300000 0.7

Excel formula:

=TURB_DREXEL(300000, 0.7)

Expected output:

438.486

Example 4: Mid Reynolds number

Inputs:

Re Pr
150000 0.65

Excel formula:

=TURB_DREXEL(150000, 0.65)

Expected output:

244.488

Python Code

Show Code 
from ht.conv_internal import turbulent_Drexel_McAdams as ht_turbulent_Drexel_McAdams

def turb_drexel(Re, Pr):
    """
    Calculate turbulent Nusselt number using Drexel-McAdams.

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

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

    Args:
        Re (float): Reynolds number (-).
        Pr (float): Prandtl number (-).

    Returns:
        float: Turbulent Nusselt number for pipe flow (-).
    """
    try:
        return ht_turbulent_Drexel_McAdams(Re=Re, Pr=Pr)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Reynolds number (-).
Prandtl number (-).

TURB_ENTRY_HAUSEN

This function estimates the turbulent entry-region Nusselt number for internal pipe flow using Hausen’s relation. It incorporates Reynolds and Prandtl numbers together with the axial position-to-diameter ratio to represent developing thermal behavior.

Excel Usage

=TURB_ENTRY_HAUSEN(Re, Pr, Di, x)
  • Re (float, required): Reynolds number (-).
  • Pr (float, required): Prandtl number (-).
  • Di (float, required): Pipe inside diameter (m).
  • x (float, required): Axial distance from the inlet (m).

Returns (float): Turbulent entry-region Nusselt number (-).

Example 1: Hausen turbulent entry example

Inputs:

Re Pr Di x
100000 1.2 0.154 0.05

Excel formula:

=TURB_ENTRY_HAUSEN(100000, 1.2, 0.154, 0.05)

Expected output:

677.723

Example 2: Longer entry length

Inputs:

Re Pr Di x
150000 0.9 0.1 0.2

Excel formula:

=TURB_ENTRY_HAUSEN(150000, 0.9, 0.1, 0.2)

Expected output:

429.388

Example 3: Short entry length

Inputs:

Re Pr Di x
80000 1.5 0.08 0.02

Excel formula:

=TURB_ENTRY_HAUSEN(80000, 1.5, 0.08, 0.02)

Expected output:

706.721

Example 4: Higher Reynolds number

Inputs:

Re Pr Di x
200000 1 0.12 0.1

Excel formula:

=TURB_ENTRY_HAUSEN(200000, 1, 0.12, 0.1)

Expected output:

730.893

Python Code

Show Code 
from ht.conv_internal import turbulent_entry_Hausen as ht_turbulent_entry_Hausen

def turb_entry_hausen(Re, Pr, Di, x):
    """
    Calculate turbulent entry-region Nusselt number using Hausen.

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

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

    Args:
        Re (float): Reynolds number (-).
        Pr (float): Prandtl number (-).
        Di (float): Pipe inside diameter (m).
        x (float): Axial distance from the inlet (m).

    Returns:
        float: Turbulent entry-region Nusselt number (-).
    """
    try:
        return ht_turbulent_entry_Hausen(Re=Re, Pr=Pr, Di=Di, x=x)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Reynolds number (-).
Prandtl number (-).
Pipe inside diameter (m).
Axial distance from the inlet (m).

TURB_ESDU

This function computes turbulent internal convection Nusselt number using the ESDU correlation. It expresses heat transfer as a Reynolds–Prandtl relation with an additional logarithmic Prandtl-number correction.

Excel Usage

=TURB_ESDU(Re, Pr)
  • Re (float, required): Reynolds number (-).
  • Pr (float, required): Prandtl number (-).

Returns (float): Turbulent Nusselt number for pipe flow (-).

Example 1: ESDU example

Inputs:

Re Pr
100000 1.2

Excel formula:

=TURB_ESDU(100000, 1.2)

Expected output:

232.302

Example 2: Lower Prandtl number

Inputs:

Re Pr
60000 0.7

Excel formula:

=TURB_ESDU(60000, 0.7)

Expected output:

118.275

Example 3: Higher Prandtl number

Inputs:

Re Pr
200000 5

Excel formula:

=TURB_ESDU(200000, 5)

Expected output:

771.223

Example 4: Mid Reynolds number

Inputs:

Re Pr
150000 1

Excel formula:

=TURB_ESDU(150000, 1)

Expected output:

293.207

Python Code

Show Code 
from ht.conv_internal import turbulent_ESDU as ht_turbulent_ESDU

def turb_esdu(Re, Pr):
    """
    Calculate turbulent Nusselt number using the ESDU correlation.

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

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

    Args:
        Re (float): Reynolds number (-).
        Pr (float): Prandtl number (-).

    Returns:
        float: Turbulent Nusselt number for pipe flow (-).
    """
    try:
        return ht_turbulent_ESDU(Re=Re, Pr=Pr)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Reynolds number (-).
Prandtl number (-).

TURB_FRIEND

This function computes turbulent Nusselt number in internal pipe flow using the Friend–Metzner correlation. It requires Reynolds number, Prandtl number, and Darcy friction factor and is primarily used for high-Prandtl-number applications.

Excel Usage

=TURB_FRIEND(Re, Pr, fd)
  • Re (float, required): Reynolds number (-).
  • Pr (float, required): Prandtl number (-).
  • fd (float, required): Darcy friction factor (-).

Returns (float): Turbulent Nusselt number for pipe flow (-).

Example 1: Friend-Metzner example

Inputs:

Re Pr fd
100000 100 0.0185

Excel formula:

=TURB_FRIEND(100000, 100, 0.0185)

Expected output:

1738.34

Example 2: Higher Prandtl number

Inputs:

Re Pr fd
200000 200 0.02

Excel formula:

=TURB_FRIEND(200000, 200, 0.02)

Expected output:

4699.95

Example 3: Mid Prandtl number

Inputs:

Re Pr fd
50000 50 0.022

Excel formula:

=TURB_FRIEND(50000, 50, 0.022)

Expected output:

729.025

Example 4: Lower Reynolds number

Inputs:

Re Pr fd
150000 80 0.017

Excel formula:

=TURB_FRIEND(150000, 80, 0.017)

Expected output:

2282.29

Python Code

Show Code 
from ht.conv_internal import turbulent_Friend_Metzner as ht_turbulent_Friend_Metzner

def turb_friend(Re, Pr, fd):
    """
    Calculate turbulent Nusselt number using Friend-Metzner.

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

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

    Args:
        Re (float): Reynolds number (-).
        Pr (float): Prandtl number (-).
        fd (float): Darcy friction factor (-).

    Returns:
        float: Turbulent Nusselt number for pipe flow (-).
    """
    try:
        return ht_turbulent_Friend_Metzner(Re=Re, Pr=Pr, fd=fd)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Reynolds number (-).
Prandtl number (-).
Darcy friction factor (-).

TURB_GNIEL_S1

This function computes turbulent Nusselt number for smooth internal pipe flow using the first simplified Gnielinski correlation. It is intended for lower-Prandtl-number smooth-pipe conditions.

Excel Usage

=TURB_GNIEL_S1(Re, Pr)
  • Re (float, required): Reynolds number (-).
  • Pr (float, required): Prandtl number (-).

Returns (float): Turbulent Nusselt number for smooth pipes (-).

Example 1: Gnielinski smooth 1 example

Inputs:

Re Pr
100000 1.2

Excel formula:

=TURB_GNIEL_S1(100000, 1.2)

Expected output:

227.888

Example 2: Lower Prandtl number

Inputs:

Re Pr
80000 0.8

Excel formula:

=TURB_GNIEL_S1(80000, 0.8)

Expected output:

161.77

Example 3: Higher Reynolds number

Inputs:

Re Pr
200000 1

Excel formula:

=TURB_GNIEL_S1(200000, 1)

Expected output:

370.456

Example 4: Mid Reynolds number

Inputs:

Re Pr
150000 1.4

Excel formula:

=TURB_GNIEL_S1(150000, 1.4)

Expected output:

336.191

Python Code

Show Code 
from ht.conv_internal import turbulent_Gnielinski_smooth_1 as ht_turbulent_Gnielinski_smooth_1

def turb_gniel_s1(Re, Pr):
    """
    Calculate turbulent Nusselt number using Gnielinski smooth pipe case 1.

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

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

    Args:
        Re (float): Reynolds number (-).
        Pr (float): Prandtl number (-).

    Returns:
        float: Turbulent Nusselt number for smooth pipes (-).
    """
    try:
        return ht_turbulent_Gnielinski_smooth_1(Re=Re, Pr=Pr)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Reynolds number (-).
Prandtl number (-).

TURB_GNIEL_S2

This function computes turbulent Nusselt number for smooth internal pipe flow using the second simplified Gnielinski correlation. It is intended for higher-Prandtl-number smooth-pipe operating ranges.

Excel Usage

=TURB_GNIEL_S2(Re, Pr)
  • Re (float, required): Reynolds number (-).
  • Pr (float, required): Prandtl number (-).

Returns (float): Turbulent Nusselt number for smooth pipes (-).

Example 1: Gnielinski smooth 2 example

Inputs:

Re Pr
100000 7

Excel formula:

=TURB_GNIEL_S2(100000, 7)

Expected output:

577.769

Example 2: Lower Prandtl number

Inputs:

Re Pr
50000 2

Excel formula:

=TURB_GNIEL_S2(50000, 2)

Expected output:

189.52

Example 3: Higher Prandtl number

Inputs:

Re Pr
200000 20

Excel formula:

=TURB_GNIEL_S2(200000, 20)

Expected output:

1616.24

Example 4: Mid Reynolds number

Inputs:

Re Pr
150000 10

Excel formula:

=TURB_GNIEL_S2(150000, 10)

Expected output:

951.802

Python Code

Show Code 
from ht.conv_internal import turbulent_Gnielinski_smooth_2 as ht_turbulent_Gnielinski_smooth_2

def turb_gniel_s2(Re, Pr):
    """
    Calculate turbulent Nusselt number using Gnielinski smooth pipe case 2.

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

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

    Args:
        Re (float): Reynolds number (-).
        Pr (float): Prandtl number (-).

    Returns:
        float: Turbulent Nusselt number for smooth pipes (-).
    """
    try:
        return ht_turbulent_Gnielinski_smooth_2(Re=Re, Pr=Pr)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Reynolds number (-).
Prandtl number (-).

TURB_GNIELINSKI

This function computes turbulent internal-flow Nusselt number using the Gnielinski correlation. It combines Reynolds number, Prandtl number, and friction factor to provide a widely used general-purpose turbulent pipe heat-transfer estimate.

Excel Usage

=TURB_GNIELINSKI(Re, Pr, fd)
  • Re (float, required): Reynolds number (-).
  • Pr (float, required): Prandtl number (-).
  • fd (float, required): Darcy friction factor (-).

Returns (float): Turbulent Nusselt number for pipe flow (-).

Example 1: Gnielinski example

Inputs:

Re Pr fd
100000 1.2 0.0185

Excel formula:

=TURB_GNIELINSKI(100000, 1.2, 0.0185)

Expected output:

254.627

Example 2: Higher Reynolds number

Inputs:

Re Pr fd
200000 0.8 0.02

Excel formula:

=TURB_GNIELINSKI(200000, 0.8, 0.02)

Expected output:

436.295

Example 3: Mid Reynolds number

Inputs:

Re Pr fd
50000 2 0.022

Excel formula:

=TURB_GNIELINSKI(50000, 2, 0.022)

Expected output:

193.717

Example 4: Lower Reynolds number

Inputs:

Re Pr fd
150000 1 0.017

Excel formula:

=TURB_GNIELINSKI(150000, 1, 0.017)

Expected output:

316.625

Python Code

Show Code 
from ht.conv_internal import turbulent_Gnielinski as ht_turbulent_Gnielinski

def turb_gnielinski(Re, Pr, fd):
    """
    Calculate turbulent Nusselt number using the Gnielinski correlation.

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

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

    Args:
        Re (float): Reynolds number (-).
        Pr (float): Prandtl number (-).
        fd (float): Darcy friction factor (-).

    Returns:
        float: Turbulent Nusselt number for pipe flow (-).
    """
    try:
        return ht_turbulent_Gnielinski(Re=Re, Pr=Pr, fd=fd)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Reynolds number (-).
Prandtl number (-).
Darcy friction factor (-).

TURB_PETUKHOV

This function computes turbulent internal-flow Nusselt number using the Petukhov–Kirillov–Popov correlation. It uses Reynolds number, Prandtl number, and friction factor to estimate convective transfer in turbulent pipe flow.

Excel Usage

=TURB_PETUKHOV(Re, Pr, fd)
  • Re (float, required): Reynolds number (-).
  • Pr (float, required): Prandtl number (-).
  • fd (float, required): Darcy friction factor (-).

Returns (float): Turbulent Nusselt number for pipe flow (-).

Example 1: Petukhov-Kirillov-Popov example

Inputs:

Re Pr fd
100000 1.2 0.0185

Excel formula:

=TURB_PETUKHOV(100000, 1.2, 0.0185)

Expected output:

250.119

Example 2: Higher Reynolds number

Inputs:

Re Pr fd
200000 0.8 0.02

Excel formula:

=TURB_PETUKHOV(200000, 0.8, 0.02)

Expected output:

436.335

Example 3: Mid Reynolds number

Inputs:

Re Pr fd
50000 2 0.022

Excel formula:

=TURB_PETUKHOV(50000, 2, 0.022)

Expected output:

189.759

Example 4: Lower Reynolds number

Inputs:

Re Pr fd
150000 1 0.017

Excel formula:

=TURB_PETUKHOV(150000, 1, 0.017)

Expected output:

312.89

Python Code

Show Code 
from ht.conv_internal import turbulent_Petukhov_Kirillov_Popov as ht_turbulent_Petukhov_Kirillov_Popov

def turb_petukhov(Re, Pr, fd):
    """
    Calculate turbulent Nusselt number using Petukhov-Kirillov-Popov.

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

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

    Args:
        Re (float): Reynolds number (-).
        Pr (float): Prandtl number (-).
        fd (float): Darcy friction factor (-).

    Returns:
        float: Turbulent Nusselt number for pipe flow (-).
    """
    try:
        return ht_turbulent_Petukhov_Kirillov_Popov(Re=Re, Pr=Pr, fd=fd)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Reynolds number (-).
Prandtl number (-).
Darcy friction factor (-).

TURB_PRANDTL

This function computes turbulent internal-flow Nusselt number using the Prandtl correlation. It applies Reynolds number, Prandtl number, and Darcy friction factor through a compact semi-empirical formulation.

Excel Usage

=TURB_PRANDTL(Re, Pr, fd)
  • Re (float, required): Reynolds number (-).
  • Pr (float, required): Prandtl number (-).
  • fd (float, required): Darcy friction factor (-).

Returns (float): Turbulent Nusselt number for pipe flow (-).

Example 1: Prandtl example

Inputs:

Re Pr fd
100000 1.2 0.0185

Excel formula:

=TURB_PRANDTL(100000, 1.2, 0.0185)

Expected output:

256.073

Example 2: Higher Reynolds number

Inputs:

Re Pr fd
200000 0.8 0.02

Excel formula:

=TURB_PRANDTL(200000, 0.8, 0.02)

Expected output:

438.116

Example 3: Mid Reynolds number

Inputs:

Re Pr fd
50000 2 0.022

Excel formula:

=TURB_PRANDTL(50000, 2, 0.022)

Expected output:

188.844

Example 4: Lower Reynolds number

Inputs:

Re Pr fd
150000 1 0.017

Excel formula:

=TURB_PRANDTL(150000, 1, 0.017)

Expected output:

318.75

Python Code

Show Code 
from ht.conv_internal import turbulent_Prandtl as ht_turbulent_Prandtl

def turb_prandtl(Re, Pr, fd):
    """
    Calculate turbulent Nusselt number using the Prandtl correlation.

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

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

    Args:
        Re (float): Reynolds number (-).
        Pr (float): Prandtl number (-).
        fd (float): Darcy friction factor (-).

    Returns:
        float: Turbulent Nusselt number for pipe flow (-).
    """
    try:
        return ht_turbulent_Prandtl(Re=Re, Pr=Pr, fd=fd)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Reynolds number (-).
Prandtl number (-).
Darcy friction factor (-).

TURB_SIEDER

This function computes turbulent internal-flow Nusselt number using the Sieder–Tate correlation. It accepts optional bulk and wall viscosities to apply viscosity-ratio correction when fluid-property variation is significant.

Excel Usage

=TURB_SIEDER(Re, Pr, mu, mu_w)
  • Re (float, required): Reynolds number (-).
  • Pr (float, required): Prandtl number (-).
  • mu (float, optional, default: null): Bulk viscosity (Pa*s).
  • mu_w (float, optional, default: null): Wall viscosity (Pa*s).

Returns (float): Turbulent Nusselt number for pipe flow (-).

Example 1: Sieder-Tate example

Inputs:

Re Pr
100000 1.2

Excel formula:

=TURB_SIEDER(100000, 1.2)

Expected output:

286.918

Example 2: Sieder-Tate with viscosity correction

Inputs:

Re Pr mu mu_w
100000 1.2 0.01 0.067

Excel formula:

=TURB_SIEDER(100000, 1.2, 0.01, 0.067)

Expected output:

219.84

Example 3: Higher Reynolds number

Inputs:

Re Pr
200000 0.7

Excel formula:

=TURB_SIEDER(200000, 0.7)

Expected output:

417.401

Example 4: Mid Reynolds number

Inputs:

Re Pr mu mu_w
50000 2 0.002 0.0015

Excel formula:

=TURB_SIEDER(50000, 2, 0.002, 0.0015)

Expected output:

203.411

Python Code

Show Code 
from ht.conv_internal import turbulent_Sieder_Tate as ht_turbulent_Sieder_Tate

def turb_sieder(Re, Pr, mu=None, mu_w=None):
    """
    Calculate turbulent Nusselt number using the Sieder-Tate correlation.

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

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

    Args:
        Re (float): Reynolds number (-).
        Pr (float): Prandtl number (-).
        mu (float, optional): Bulk viscosity (Pa*s). Default is None.
        mu_w (float, optional): Wall viscosity (Pa*s). Default is None.

    Returns:
        float: Turbulent Nusselt number for pipe flow (-).
    """
    try:
        return ht_turbulent_Sieder_Tate(Re=Re, Pr=Pr, mu=mu, mu_w=mu_w)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Reynolds number (-).
Prandtl number (-).
Bulk viscosity (Pa*s).
Wall viscosity (Pa*s).

TURB_VON_KARMAN

This function computes turbulent internal-flow Nusselt number using the von Kármán correlation. It uses Reynolds number, Prandtl number, and friction factor to estimate convective transfer in fully developed turbulent pipe flow.

Excel Usage

=TURB_VON_KARMAN(Re, Pr, fd)
  • Re (float, required): Reynolds number (-).
  • Pr (float, required): Prandtl number (-).
  • fd (float, required): Darcy friction factor (-).

Returns (float): Turbulent Nusselt number for pipe flow (-).

Example 1: von Karman example

Inputs:

Re Pr fd
100000 1.2 0.0185

Excel formula:

=TURB_VON_KARMAN(100000, 1.2, 0.0185)

Expected output:

255.724

Example 2: Higher Reynolds number

Inputs:

Re Pr fd
200000 0.8 0.02

Excel formula:

=TURB_VON_KARMAN(200000, 0.8, 0.02)

Expected output:

442.273

Example 3: Mid Reynolds number

Inputs:

Re Pr fd
50000 2 0.022

Excel formula:

=TURB_VON_KARMAN(50000, 2, 0.022)

Expected output:

193.508

Example 4: Lower Reynolds number

Inputs:

Re Pr fd
150000 1 0.017

Excel formula:

=TURB_VON_KARMAN(150000, 1, 0.017)

Expected output:

318.75

Python Code

Show Code 
from ht.conv_internal import turbulent_von_Karman as ht_turbulent_von_Karman

def turb_von_karman(Re, Pr, fd):
    """
    Calculate turbulent Nusselt number using the von Karman correlation.

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

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

    Args:
        Re (float): Reynolds number (-).
        Pr (float): Prandtl number (-).
        fd (float): Darcy friction factor (-).

    Returns:
        float: Turbulent Nusselt number for pipe flow (-).
    """
    try:
        return ht_turbulent_von_Karman(Re=Re, Pr=Pr, fd=fd)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Reynolds number (-).
Prandtl number (-).
Darcy friction factor (-).

TURB_WEBB

This function computes turbulent internal-flow Nusselt number using the Webb correlation. It incorporates Reynolds number, Prandtl number, and friction factor to model forced convection in turbulent pipe flow.

Excel Usage

=TURB_WEBB(Re, Pr, fd)
  • Re (float, required): Reynolds number (-).
  • Pr (float, required): Prandtl number (-).
  • fd (float, required): Darcy friction factor (-).

Returns (float): Turbulent Nusselt number for pipe flow (-).

Example 1: Webb example

Inputs:

Re Pr fd
100000 1.2 0.0185

Excel formula:

=TURB_WEBB(100000, 1.2, 0.0185)

Expected output:

239.101

Example 2: Higher Reynolds number

Inputs:

Re Pr fd
200000 0.8 0.02

Excel formula:

=TURB_WEBB(200000, 0.8, 0.02)

Expected output:

406.14

Example 3: Mid Reynolds number

Inputs:

Re Pr fd
50000 2 0.022

Excel formula:

=TURB_WEBB(50000, 2, 0.022)

Expected output:

168.581

Example 4: Lower Reynolds number

Inputs:

Re Pr fd
150000 1 0.017

Excel formula:

=TURB_WEBB(150000, 1, 0.017)

Expected output:

297.897

Python Code

Show Code 
from ht.conv_internal import turbulent_Webb as ht_turbulent_Webb

def turb_webb(Re, Pr, fd):
    """
    Calculate turbulent Nusselt number using the Webb correlation.

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

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

    Args:
        Re (float): Reynolds number (-).
        Pr (float): Prandtl number (-).
        fd (float): Darcy friction factor (-).

    Returns:
        float: Turbulent Nusselt number for pipe flow (-).
    """
    try:
        return ht_turbulent_Webb(Re=Re, Pr=Pr, fd=fd)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Reynolds number (-).
Prandtl number (-).
Darcy friction factor (-).