Conv Free Immersed

Overview

Free convection for immersed bodies describes heat transfer driven by buoyancy when a solid surface exchanges heat with a quiescent surrounding fluid. In engineering terms, this category focuses on external natural-convection Nusselt-number correlations for common geometries used in thermal design, electronics cooling, vessels, and process equipment. The governing transport behavior is commonly characterized with natural convection, where density differences generate flow without forced pumping. These tools help turn dimensionless property data into practical heat-transfer coefficients for sizing, rating, and sensitivity checks.

The unifying framework is based on dimensionless analysis: Nu=\frac{hL}{k}, Gr=\frac{g\beta\Delta T L^3}{\nu^2}, and Ra=Gr\,Pr. Most correlations in this set are empirical power-law or blended forms in Ra (or Gr and Pr), with method-selection utilities that filter valid correlations by geometry and range. In practice, analysts compare multiple applicable correlations to bound uncertainty, especially around laminar-to-turbulent transitions and aspect-ratio effects for plates and cylinders.

Implementation is provided by the Python ht library, specifically ht.conv_free_immersed, which packages established heat-transfer correlations behind consistent function interfaces. This makes spreadsheet usage and scripted workflows consistent across geometries and correlation families.

For horizontal and vertical plates, NU_FREE_HPLATE and NU_FREE_VPLATE are high-level selectors, while NU_FREE_HPLATE_METH and NU_FREE_VPLATE_METH list candidate methods for a given state and geometry. The explicit horizontal-plate correlations NU_HPLATE_MCADAMS, NU_HPLATE_ROHSENOW, and NU_HPLATE_VDI are useful when a specific handbook method is required for traceability. For vertical plates, NU_VPLATE_CHURCHILL provides a standard Churchill-style formulation used widely for baseline natural-convection estimates.

For cylinders and spheres, NU_HORIZ_CYL is the horizontal-cylinder selector, supported by NU_HCYL_METHODS and the individual options NU_HCYL_CHURCHILL, NU_HCYL_KUEHNGOLD, and NU_HCYL_MORGAN. Vertical-cylinder workflows are handled by NU_VERT_CYL with discovery via NU_VCYL_METHODS, and by direct correlations NU_VCYL_ALARABI, NU_VCYL_CARNEMORGAN, NU_VCYL_EIGENSON, NU_VCYL_GRIFFITHS, NU_VCYL_HANESIAN, NU_VCYL_JAKOB, NU_VCYL_KREITH, NU_VCYL_MCADAMS, NU_VCYL_POPIEL, and NU_VCYL_TOULOUKIAN. For other immersed geometries, NU_SPHERE_CHURCHILL targets spheres and NU_COIL_XIN_EBADIAN addresses free convection around helical coils, which is useful in tank coils and compact heat-exchanger layouts.

NU_COIL_XIN_EBADIAN

This function computes the Nusselt number for natural convection around a helical coil using the Xin-Ebadian correlation from the ht library. It supports both vertical and horizontal coil orientation and uses fluid properties at film conditions.

The correlation is represented as a power-law in Rayleigh number:

Nu = C\,(Gr\,Pr)^n

where the coefficient C depends on coil orientation.

Excel Usage

=NU_COIL_XIN_EBADIAN(Pr, Gr, horizontal)
  • Pr (float, required): Prandtl number at film temperature (dimensionless).
  • Gr (float, required): Grashof number based on coil outer diameter (dimensionless).
  • horizontal (bool, optional, default: false): Whether the coil is horizontal (dimensionless).

Returns (float): Nusselt number based on coil outer diameter (dimensionless).

Example 1: Vertical coil example

Inputs:

Pr Gr horizontal
0.7 20000 false

Excel formula:

=NU_COIL_XIN_EBADIAN(0.7, 20000, FALSE)

Expected output:

4.75569

Example 2: Horizontal coil example

Inputs:

Pr Gr horizontal
0.7 20000 true

Excel formula:

=NU_COIL_XIN_EBADIAN(0.7, 20000, TRUE)

Expected output:

5.21486

Example 3: Vertical coil mid range

Inputs:

Pr Gr horizontal
1.1 80000 false

Excel formula:

=NU_COIL_XIN_EBADIAN(1.1, 80000, FALSE)

Expected output:

8.14951

Example 4: Horizontal coil low Prandtl

Inputs:

Pr Gr horizontal
0.2 60000 true

Excel formula:

=NU_COIL_XIN_EBADIAN(0.2, 60000, TRUE)

Expected output:

4.98456

Python Code

Show Code 
from ht.conv_free_immersed import Nu_coil_Xin_Ebadian as ht_Nu_coil_Xin_Ebadian

def Nu_coil_Xin_Ebadian(Pr, Gr, horizontal=False):
    """
    Calculate the Nusselt number for natural convection around a helical coil.

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

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

    Args:
        Pr (float): Prandtl number at film temperature (dimensionless).
        Gr (float): Grashof number based on coil outer diameter (dimensionless).
        horizontal (bool, optional): Whether the coil is horizontal (dimensionless). Default is False.

    Returns:
        float: Nusselt number based on coil outer diameter (dimensionless).
    """
    try:
        result = ht_Nu_coil_Xin_Ebadian(Pr, Gr, horizontal=horizontal)
        if result is None:
            return "Error: Result is None"
        return float(result)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Prandtl number at film temperature (dimensionless).
Grashof number based on coil outer diameter (dimensionless).
Whether the coil is horizontal (dimensionless).

NU_FREE_HPLATE

This function computes the Nusselt number for external free convection from a horizontal plate using selectable correlations available in ht.conv_free_immersed. Inputs are the Prandtl and Grashof numbers, buoyancy direction, and optional geometry information.

The selected model evaluates natural-convection heat transfer using a dimensionless form based on Rayleigh number:

Ra = Gr\,Pr

and returns a dimensionless Nusselt number for the plate characteristic length.

Excel Usage

=NU_FREE_HPLATE(Pr, Gr, buoyancy, L, W, hplate_method)
  • Pr (float, required): Prandtl number of the fluid (dimensionless).
  • Gr (float, required): Grashof number for the plate (dimensionless).
  • buoyancy (bool, required): Whether buoyancy assists free convection (dimensionless).
  • L (float, optional, default: null): Plate length (m).
  • W (float, optional, default: null): Plate width (m).
  • hplate_method (str, optional, default: null): Correlation name (string).

Returns (float): Nusselt number based on plate length (dimensionless).

Example 1: Horizontal plate with default VDI

Inputs:

Pr Gr buoyancy
5.54 321000000 true

Excel formula:

=NU_FREE_HPLATE(5.54, 321000000, TRUE)

Expected output:

203.897

Example 2: Horizontal plate using McAdams

Inputs:

Pr Gr buoyancy hplate_method
5.54 321000000 true McAdams

Excel formula:

=NU_FREE_HPLATE(5.54, 321000000, TRUE, "McAdams")

Expected output:

181.731

Example 3: Horizontal plate Rohsenow cold plate

Inputs:

Pr Gr buoyancy hplate_method
5.54 321000000 false Rohsenow

Excel formula:

=NU_FREE_HPLATE(5.54, 321000000, FALSE, "Rohsenow")

Expected output:

35.958

Example 4: Horizontal plate with geometry inputs

Inputs:

Pr Gr buoyancy L W
0.7 2000000 true 1.2 0.6

Excel formula:

=NU_FREE_HPLATE(0.7, 2000000, TRUE, 1.2, 0.6)

Expected output:

22.7506

Python Code

Show Code 
from ht.conv_free_immersed import Nu_free_horizontal_plate as ht_Nu_free_horizontal_plate

def Nu_free_hplate(Pr, Gr, buoyancy, L=None, W=None, hplate_method=None):
    """
    Calculate the Nusselt number for free convection from a horizontal plate.

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

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

    Args:
        Pr (float): Prandtl number of the fluid (dimensionless).
        Gr (float): Grashof number for the plate (dimensionless).
        buoyancy (bool): Whether buoyancy assists free convection (dimensionless).
        L (float, optional): Plate length (m). Default is None.
        W (float, optional): Plate width (m). Default is None.
        hplate_method (str, optional): Correlation name (string). Valid options: VDI, McAdams, Rohsenow. Default is None.

    Returns:
        float: Nusselt number based on plate length (dimensionless).
    """
    try:
        result = ht_Nu_free_horizontal_plate(Pr, Gr, buoyancy, L=L, W=W, Method=hplate_method)
        if result is None:
            return "Error: Result is None"
        return float(result)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Prandtl number of the fluid (dimensionless).
Grashof number for the plate (dimensionless).
Whether buoyancy assists free convection (dimensionless).
Plate length (m).
Plate width (m).
Correlation name (string).

NU_FREE_HPLATE_METH

This function returns the available ht correlation names for free convection from a horizontal plate for the supplied operating conditions. It can optionally filter methods based on documented applicability ranges.

The method set is determined using the same governing dimensionless groups used by the solver:

Ra = Gr\,Pr

and the output is returned as a single-column 2D array suitable for Excel spill ranges.

Excel Usage

=NU_FREE_HPLATE_METH(Pr, Gr, buoyancy, L, W, check_ranges)
  • Pr (float, required): Prandtl number of the fluid (dimensionless).
  • Gr (float, required): Grashof number for the plate (dimensionless).
  • buoyancy (bool, required): Whether buoyancy assists free convection (dimensionless).
  • L (float, optional, default: null): Plate length (m).
  • W (float, optional, default: null): Plate width (m).
  • check_ranges (bool, optional, default: true): Whether to filter methods by validity ranges (dimensionless).

Returns (list[list]): Available correlation names as a column list.

Example 1: Horizontal plate methods default

Inputs:

Pr Gr buoyancy
0.69 2630000000 true

Excel formula:

=NU_FREE_HPLATE_METH(0.69, 2630000000, TRUE)

Expected output:

VDI
McAdams
Rohsenow
Example 2: Horizontal plate methods without range checks

Inputs:

Pr Gr buoyancy check_ranges
0.69 2630000000 true false

Excel formula:

=NU_FREE_HPLATE_METH(0.69, 2630000000, TRUE, FALSE)

Expected output:

VDI
McAdams
Rohsenow
Example 3: Horizontal plate methods for cold plate

Inputs:

Pr Gr buoyancy
0.7 1000000 false

Excel formula:

=NU_FREE_HPLATE_METH(0.7, 1000000, FALSE)

Expected output:

VDI
McAdams
Rohsenow
Example 4: Horizontal plate methods with geometry inputs

Inputs:

Pr Gr buoyancy L W
2 5000000 true 1 0.5

Excel formula:

=NU_FREE_HPLATE_METH(2, 5000000, TRUE, 1, 0.5)

Expected output:

VDI
McAdams
Rohsenow

Python Code

Show Code 
from ht.conv_free_immersed import Nu_free_horizontal_plate_methods as ht_Nu_free_horizontal_plate_methods

def Nu_free_hplate_meth(Pr, Gr, buoyancy, L=None, W=None, check_ranges=True):
    """
    List available correlations for free convection from a horizontal plate.

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

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

    Args:
        Pr (float): Prandtl number of the fluid (dimensionless).
        Gr (float): Grashof number for the plate (dimensionless).
        buoyancy (bool): Whether buoyancy assists free convection (dimensionless).
        L (float, optional): Plate length (m). Default is None.
        W (float, optional): Plate width (m). Default is None.
        check_ranges (bool, optional): Whether to filter methods by validity ranges (dimensionless). Default is True.

    Returns:
        list[list]: Available correlation names as a column list.
    """
    try:
        methods = ht_Nu_free_horizontal_plate_methods(Pr, Gr, buoyancy, L=L, W=W, check_ranges=check_ranges)
        if methods is None:
            return "Error: No methods returned"
        return [[method] for method in methods]
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Prandtl number of the fluid (dimensionless).
Grashof number for the plate (dimensionless).
Whether buoyancy assists free convection (dimensionless).
Plate length (m).
Plate width (m).
Whether to filter methods by validity ranges (dimensionless).

NU_FREE_VPLATE

This function computes the Nusselt number for external free convection from a vertical plate using the ht implementation and optional method selection. It uses Prandtl number, Grashof number, and optional geometry inputs.

Free-convection correlation selection is based on dimensionless groups, primarily the Rayleigh number:

Ra = Gr\,Pr

and returns a dimensionless Nusselt number referenced to plate height.

Excel Usage

=NU_FREE_VPLATE(Pr, Gr, buoyancy, H, W, vplate_method)
  • Pr (float, required): Prandtl number of the fluid (dimensionless).
  • Gr (float, required): Grashof number for the plate (dimensionless).
  • buoyancy (bool, optional, default: null): Whether buoyancy assists free convection (dimensionless).
  • H (float, optional, default: null): Plate height (m).
  • W (float, optional, default: null): Plate width (m).
  • vplate_method (str, optional, default: null): Correlation name (string).

Returns (float): Nusselt number based on plate height (dimensionless).

Example 1: Vertical plate default method

Inputs:

Pr Gr
0.69 2630000000

Excel formula:

=NU_FREE_VPLATE(0.69, 2630000000)

Expected output:

147.162

Example 2: Vertical plate with buoyancy flag

Inputs:

Pr Gr buoyancy
0.69 2630000000 false

Excel formula:

=NU_FREE_VPLATE(0.69, 2630000000, FALSE)

Expected output:

147.162

Example 3: Vertical plate with explicit method

Inputs:

Pr Gr vplate_method
0.69 2630000000 Churchill

Excel formula:

=NU_FREE_VPLATE(0.69, 2630000000, "Churchill")

Expected output:

147.162

Example 4: Vertical plate with geometry inputs

Inputs:

Pr Gr buoyancy H W
0.9 2000000 true 1.5 0.4

Excel formula:

=NU_FREE_VPLATE(0.9, 2000000, TRUE, 1.5, 0.4)

Expected output:

19.934

Python Code

Show Code 
from ht.conv_free_immersed import Nu_free_vertical_plate as ht_Nu_free_vertical_plate

def Nu_free_vplate(Pr, Gr, buoyancy=None, H=None, W=None, vplate_method=None):
    """
    Calculate the Nusselt number for free convection from a vertical plate.

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

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

    Args:
        Pr (float): Prandtl number of the fluid (dimensionless).
        Gr (float): Grashof number for the plate (dimensionless).
        buoyancy (bool, optional): Whether buoyancy assists free convection (dimensionless). Default is None.
        H (float, optional): Plate height (m). Default is None.
        W (float, optional): Plate width (m). Default is None.
        vplate_method (str, optional): Correlation name (string). Default is None.

    Returns:
        float: Nusselt number based on plate height (dimensionless).
    """
    try:
        result = ht_Nu_free_vertical_plate(Pr, Gr, buoyancy=buoyancy, H=H, W=W, Method=vplate_method)
        if result is None:
            return "Error: Result is None"
        return float(result)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Prandtl number of the fluid (dimensionless).
Grashof number for the plate (dimensionless).
Whether buoyancy assists free convection (dimensionless).
Plate height (m).
Plate width (m).
Correlation name (string).

NU_FREE_VPLATE_METH

This function returns available correlation names for vertical-plate free convection from the ht library for the given conditions. It supports optional geometry inputs and optional range filtering.

Correlation applicability is evaluated using standard dimensionless groups, chiefly:

Ra = Gr\,Pr

and the result is emitted as a one-column 2D array for Excel compatibility.

Excel Usage

=NU_FREE_VPLATE_METH(Pr, Gr, H, W, check_ranges)
  • Pr (float, required): Prandtl number of the fluid (dimensionless).
  • Gr (float, required): Grashof number for the plate (dimensionless).
  • H (float, optional, default: null): Plate height (m).
  • W (float, optional, default: null): Plate width (m).
  • check_ranges (bool, optional, default: true): Whether to filter methods by validity ranges (dimensionless).

Returns (list[list]): Available correlation names as a column list.

Example 1: Vertical plate methods default

Inputs:

Pr Gr
0.69 2630000000

Excel formula:

=NU_FREE_VPLATE_METH(0.69, 2630000000)

Expected output:

"Churchill"

Example 2: Vertical plate methods without range checks

Inputs:

Pr Gr check_ranges
0.69 2630000000 false

Excel formula:

=NU_FREE_VPLATE_METH(0.69, 2630000000, FALSE)

Expected output:

"Churchill"

Example 3: Vertical plate methods with geometry inputs

Inputs:

Pr Gr H W
1 1000000 1.2 0.3

Excel formula:

=NU_FREE_VPLATE_METH(1, 1000000, 1.2, 0.3)

Expected output:

"Churchill"

Example 4: Vertical plate methods low Grashof

Inputs:

Pr Gr
0.8 500000

Excel formula:

=NU_FREE_VPLATE_METH(0.8, 500000)

Expected output:

"Churchill"

Python Code

Show Code 
from ht.conv_free_immersed import Nu_free_vertical_plate_methods as ht_Nu_free_vertical_plate_methods

def Nu_free_vplate_meth(Pr, Gr, H=None, W=None, check_ranges=True):
    """
    List available correlations for free convection from a vertical plate.

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

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

    Args:
        Pr (float): Prandtl number of the fluid (dimensionless).
        Gr (float): Grashof number for the plate (dimensionless).
        H (float, optional): Plate height (m). Default is None.
        W (float, optional): Plate width (m). Default is None.
        check_ranges (bool, optional): Whether to filter methods by validity ranges (dimensionless). Default is True.

    Returns:
        list[list]: Available correlation names as a column list.
    """
    try:
        methods = ht_Nu_free_vertical_plate_methods(Pr, Gr, H=H, W=W, check_ranges=check_ranges)
        if methods is None:
            return "Error: No methods returned"
        return [[method] for method in methods]
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Prandtl number of the fluid (dimensionless).
Grashof number for the plate (dimensionless).
Plate height (m).
Plate width (m).
Whether to filter methods by validity ranges (dimensionless).

NU_HCYL_CHURCHILL

This function applies the Churchill-Chu free-convection correlation for an isothermal horizontal cylinder from the ht library. It uses Prandtl and Grashof numbers evaluated at film conditions.

The model is expressed in terms of Rayleigh number with a smooth laminar-to-turbulent transition:

Ra = Gr\,Pr

and returns a diameter-based dimensionless Nusselt number.

Excel Usage

=NU_HCYL_CHURCHILL(Pr, Gr)
  • Pr (float, required): Prandtl number at film temperature (dimensionless).
  • Gr (float, required): Grashof number based on cylinder diameter (dimensionless).

Returns (float): Nusselt number based on cylinder diameter (dimensionless).

Example 1: Churchill-Chu example

Inputs:

Pr Gr
0.69 2630000000

Excel formula:

=NU_HCYL_CHURCHILL(0.69, 2630000000)

Expected output:

139.135

Example 2: Churchill-Chu low Grashof

Inputs:

Pr Gr
0.7 100000

Excel formula:

=NU_HCYL_CHURCHILL(0.7, 100000)

Expected output:

7.07684

Example 3: Churchill-Chu mid Grashof

Inputs:

Pr Gr
1.2 5000000

Excel formula:

=NU_HCYL_CHURCHILL(1.2, 5000000)

Expected output:

25.9779

Example 4: Churchill-Chu high Grashof

Inputs:

Pr Gr
0.9 1000000000

Excel formula:

=NU_HCYL_CHURCHILL(0.9, 1000000000)

Expected output:

115.819

Python Code

Show Code 
from ht.conv_free_immersed import Nu_horizontal_cylinder_Churchill_Chu as ht_Nu_horizontal_cylinder_Churchill_Chu

def Nu_hcyl_Churchill(Pr, Gr):
    """
    Calculate the Nusselt number for a horizontal cylinder using Churchill-Chu.

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

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

    Args:
        Pr (float): Prandtl number at film temperature (dimensionless).
        Gr (float): Grashof number based on cylinder diameter (dimensionless).

    Returns:
        float: Nusselt number based on cylinder diameter (dimensionless).
    """
    try:
        result = ht_Nu_horizontal_cylinder_Churchill_Chu(Pr, Gr)
        if result is None:
            return "Error: Result is None"
        return float(result)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Prandtl number at film temperature (dimensionless).
Grashof number based on cylinder diameter (dimensionless).

NU_HCYL_KUEHNGOLD

This function evaluates natural-convection Nusselt number for a horizontal isothermal cylinder using the Kuehn-Goldstein correlation from ht. It is intended for dimensionless inputs at film conditions.

The correlation is Rayleigh-based with Prandtl dependence:

Ra = Gr\,Pr

and outputs a dimensionless Nusselt number referenced to cylinder diameter.

Excel Usage

=NU_HCYL_KUEHNGOLD(Pr, Gr)
  • Pr (float, required): Prandtl number at film temperature (dimensionless).
  • Gr (float, required): Grashof number based on cylinder diameter (dimensionless).

Returns (float): Nusselt number based on cylinder diameter (dimensionless).

Example 1: Kuehn-Goldstein example

Inputs:

Pr Gr
0.69 2630000000

Excel formula:

=NU_HCYL_KUEHNGOLD(0.69, 2630000000)

Expected output:

122.993

Example 2: Kuehn-Goldstein low Grashof

Inputs:

Pr Gr
0.7 100000

Excel formula:

=NU_HCYL_KUEHNGOLD(0.7, 100000)

Expected output:

7.4417

Example 3: Kuehn-Goldstein mid Grashof

Inputs:

Pr Gr
1.2 5000000

Excel formula:

=NU_HCYL_KUEHNGOLD(1.2, 5000000)

Expected output:

22.0489

Example 4: Kuehn-Goldstein high Grashof

Inputs:

Pr Gr
0.9 1000000000

Excel formula:

=NU_HCYL_KUEHNGOLD(0.9, 1000000000)

Expected output:

97.6097

Python Code

Show Code 
from ht.conv_free_immersed import Nu_horizontal_cylinder_Kuehn_Goldstein as ht_Nu_horizontal_cylinder_Kuehn_Goldstein

def Nu_hcyl_KuehnGold(Pr, Gr):
    """
    Calculate the Nusselt number for a horizontal cylinder using Kuehn-Goldstein.

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

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

    Args:
        Pr (float): Prandtl number at film temperature (dimensionless).
        Gr (float): Grashof number based on cylinder diameter (dimensionless).

    Returns:
        float: Nusselt number based on cylinder diameter (dimensionless).
    """
    try:
        result = ht_Nu_horizontal_cylinder_Kuehn_Goldstein(Pr, Gr)
        if result is None:
            return "Error: Result is None"
        return float(result)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Prandtl number at film temperature (dimensionless).
Grashof number based on cylinder diameter (dimensionless).

NU_HCYL_METHODS

This function returns available ht method names for horizontal-cylinder natural convection under the provided Prandtl and Grashof conditions. It can either filter by validity range or return all candidate methods.

Method availability is determined from standard free-convection groups:

Ra = Gr\,Pr

and the output is formatted as a one-column 2D array for Excel.

Excel Usage

=NU_HCYL_METHODS(Pr, Gr, check_ranges)
  • Pr (float, required): Prandtl number at film temperature (dimensionless).
  • Gr (float, required): Grashof number based on cylinder diameter (dimensionless).
  • check_ranges (bool, optional, default: true): Whether to filter methods by validity ranges (dimensionless).

Returns (list[list]): Available correlation names as a column list.

Example 1: Horizontal cylinder methods default

Inputs:

Pr Gr
0.72 10000000

Excel formula:

=NU_HCYL_METHODS(0.72, 10000000)

Expected output:

Morgan
Churchill-Chu
Kuehn & Goldstein
Example 2: Horizontal cylinder methods without range checks

Inputs:

Pr Gr check_ranges
0.72 10000000 false

Excel formula:

=NU_HCYL_METHODS(0.72, 10000000, FALSE)

Expected output:

Morgan
Churchill-Chu
Kuehn & Goldstein
Example 3: Horizontal cylinder methods mid Grashof

Inputs:

Pr Gr
1.1 5000000

Excel formula:

=NU_HCYL_METHODS(1.1, 5000000)

Expected output:

Morgan
Churchill-Chu
Kuehn & Goldstein
Example 4: Horizontal cylinder methods high Grashof

Inputs:

Pr Gr
0.9 1000000000

Excel formula:

=NU_HCYL_METHODS(0.9, 1000000000)

Expected output:

Morgan
Churchill-Chu
Kuehn & Goldstein

Python Code

Show Code 
from ht.conv_free_immersed import Nu_horizontal_cylinder_methods as ht_Nu_horizontal_cylinder_methods

def Nu_hcyl_methods(Pr, Gr, check_ranges=True):
    """
    List available correlations for free convection from a horizontal cylinder.

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

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

    Args:
        Pr (float): Prandtl number at film temperature (dimensionless).
        Gr (float): Grashof number based on cylinder diameter (dimensionless).
        check_ranges (bool, optional): Whether to filter methods by validity ranges (dimensionless). Default is True.

    Returns:
        list[list]: Available correlation names as a column list.
    """
    try:
        methods = ht_Nu_horizontal_cylinder_methods(Pr, Gr, check_ranges=check_ranges)
        if methods is None:
            return "Error: No methods returned"
        return [[method] for method in methods]
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Prandtl number at film temperature (dimensionless).
Grashof number based on cylinder diameter (dimensionless).
Whether to filter methods by validity ranges (dimensionless).

NU_HCYL_MORGAN

This function computes the Morgan free-convection correlation for an isothermal horizontal cylinder using the ht library implementation. It accepts Prandtl and Grashof numbers as dimensionless inputs.

The relation is piecewise power-law in Rayleigh number:

Nu = C\,Ra^n,\qquad Ra = Gr\,Pr

and returns a diameter-based dimensionless Nusselt number.

Excel Usage

=NU_HCYL_MORGAN(Pr, Gr)
  • Pr (float, required): Prandtl number at film temperature (dimensionless).
  • Gr (float, required): Grashof number based on cylinder diameter (dimensionless).

Returns (float): Nusselt number based on cylinder diameter (dimensionless).

Example 1: Morgan example

Inputs:

Pr Gr
0.69 2630000000

Excel formula:

=NU_HCYL_MORGAN(0.69, 2630000000)

Expected output:

151.388

Example 2: Morgan low Grashof

Inputs:

Pr Gr
0.7 100

Excel formula:

=NU_HCYL_MORGAN(0.7, 100)

Expected output:

1.91282

Example 3: Morgan mid Grashof

Inputs:

Pr Gr
1.2 1000000

Excel formula:

=NU_HCYL_MORGAN(1.2, 1000000)

Expected output:

15.8868

Example 4: Morgan high Grashof

Inputs:

Pr Gr
0.9 10000000000

Excel formula:

=NU_HCYL_MORGAN(0.9, 10000000000)

Expected output:

258.032

Python Code

Show Code 
from ht.conv_free_immersed import Nu_horizontal_cylinder_Morgan as ht_Nu_horizontal_cylinder_Morgan

def Nu_hcyl_Morgan(Pr, Gr):
    """
    Calculate the Nusselt number for a horizontal cylinder using Morgan.

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

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

    Args:
        Pr (float): Prandtl number at film temperature (dimensionless).
        Gr (float): Grashof number based on cylinder diameter (dimensionless).

    Returns:
        float: Nusselt number based on cylinder diameter (dimensionless).
    """
    try:
        result = ht_Nu_horizontal_cylinder_Morgan(Pr, Gr)
        if result is None:
            return "Error: Result is None"
        return float(result)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Prandtl number at film temperature (dimensionless).
Grashof number based on cylinder diameter (dimensionless).

NU_HORIZ_CYL

This function computes natural-convection Nusselt number for a horizontal cylinder using a selectable ht correlation. If no method is specified, the underlying library default selection logic is used.

The calculation uses Prandtl and Grashof numbers through Rayleigh number behavior:

Ra = Gr\,Pr

and returns a dimensionless Nusselt number based on cylinder diameter.

Excel Usage

=NU_HORIZ_CYL(Pr, Gr, Nu_horiz_cyl_method)
  • Pr (float, required): Prandtl number at film temperature (dimensionless).
  • Gr (float, required): Grashof number based on cylinder diameter (dimensionless).
  • Nu_horiz_cyl_method (str, optional, default: null): Correlation name (string).

Returns (float): Nusselt number based on cylinder diameter (dimensionless).

Example 1: Horizontal cylinder default method

Inputs:

Pr Gr
0.72 10000000

Excel formula:

=NU_HORIZ_CYL(0.72, 10000000)

Expected output:

24.8642

Example 2: Horizontal cylinder Morgan method

Inputs:

Pr Gr Nu_horiz_cyl_method
0.69 2630000000 Morgan

Excel formula:

=NU_HORIZ_CYL(0.69, 2630000000, "Morgan")

Expected output:

151.388

Example 3: Horizontal cylinder Churchill-Chu method

Inputs:

Pr Gr Nu_horiz_cyl_method
0.69 2630000000 Churchill-Chu

Excel formula:

=NU_HORIZ_CYL(0.69, 2630000000, "Churchill-Chu")

Expected output:

139.135

Example 4: Horizontal cylinder Kuehn-Goldstein method

Inputs:

Pr Gr Nu_horiz_cyl_method
0.69 2630000000 Kuehn & Goldstein

Excel formula:

=NU_HORIZ_CYL(0.69, 2630000000, "Kuehn & Goldstein")

Expected output:

122.993

Python Code

Show Code 
from ht.conv_free_immersed import Nu_horizontal_cylinder as ht_Nu_horizontal_cylinder

def Nu_horiz_cyl(Pr, Gr, Nu_horiz_cyl_method=None):
    """
    Select and calculate a Nusselt number correlation for a horizontal cylinder.

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

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

    Args:
        Pr (float): Prandtl number at film temperature (dimensionless).
        Gr (float): Grashof number based on cylinder diameter (dimensionless).
        Nu_horiz_cyl_method (str, optional): Correlation name (string). Valid options: Morgan, Churchill-Chu, Kuehn & Goldstein. Default is None.

    Returns:
        float: Nusselt number based on cylinder diameter (dimensionless).
    """
    try:
        result = ht_Nu_horizontal_cylinder(Pr, Gr, Method=Nu_horiz_cyl_method)
        if result is None:
            return "Error: Result is None"
        return float(result)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Prandtl number at film temperature (dimensionless).
Grashof number based on cylinder diameter (dimensionless).
Correlation name (string).

NU_HPLATE_MCADAMS

This function computes natural-convection Nusselt number for an isothermal horizontal plate with the McAdams correlation from ht. It accounts for buoyancy-assisted (hot upper surface) or opposing (cold upper surface) orientation.

The correlation is based on Rayleigh number behavior:

Ra = Gr\,Pr

and returns a dimensionless plate-length Nusselt number.

Excel Usage

=NU_HPLATE_MCADAMS(Pr, Gr, buoyancy)
  • Pr (float, required): Prandtl number of the fluid (dimensionless).
  • Gr (float, required): Grashof number for the plate (dimensionless).
  • buoyancy (bool, optional, default: true): Whether buoyancy assists free convection (dimensionless).

Returns (float): Nusselt number based on plate length (dimensionless).

Example 1: McAdams hot plate example

Inputs:

Pr Gr buoyancy
5.54 321000000 true

Excel formula:

=NU_HPLATE_MCADAMS(5.54, 321000000, TRUE)

Expected output:

181.731

Example 2: McAdams cold plate example

Inputs:

Pr Gr buoyancy
5.54 321000000 false

Excel formula:

=NU_HPLATE_MCADAMS(5.54, 321000000, FALSE)

Expected output:

55.4456

Example 3: McAdams low Pr hot plate

Inputs:

Pr Gr buoyancy
0.01 321000000 true

Excel formula:

=NU_HPLATE_MCADAMS(0.01, 321000000, TRUE)

Expected output:

22.857

Example 4: McAdams low Pr cold plate

Inputs:

Pr Gr buoyancy
0.01 321000000 false

Excel formula:

=NU_HPLATE_MCADAMS(0.01, 321000000, FALSE)

Expected output:

11.4285

Python Code

Show Code 
from ht.conv_free_immersed import Nu_horizontal_plate_McAdams as ht_Nu_horizontal_plate_McAdams

def Nu_hplate_McAdams(Pr, Gr, buoyancy=True):
    """
    Calculate the Nusselt number for a horizontal plate using McAdams.

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

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

    Args:
        Pr (float): Prandtl number of the fluid (dimensionless).
        Gr (float): Grashof number for the plate (dimensionless).
        buoyancy (bool, optional): Whether buoyancy assists free convection (dimensionless). Default is True.

    Returns:
        float: Nusselt number based on plate length (dimensionless).
    """
    try:
        result = ht_Nu_horizontal_plate_McAdams(Pr, Gr, buoyancy=buoyancy)
        if result is None:
            return "Error: Result is None"
        return float(result)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Prandtl number of the fluid (dimensionless).
Grashof number for the plate (dimensionless).
Whether buoyancy assists free convection (dimensionless).

NU_HPLATE_ROHSENOW

This function computes free-convection Nusselt number for a horizontal isothermal plate using the Rohsenow-family correlation in ht. It supports buoyancy-assisted and buoyancy-opposed orientations.

Inputs are interpreted through Rayleigh-number scaling:

Ra = Gr\,Pr

and the output is a dimensionless Nusselt number referenced to plate length.

Excel Usage

=NU_HPLATE_ROHSENOW(Pr, Gr, buoyancy)
  • Pr (float, required): Prandtl number of the fluid (dimensionless).
  • Gr (float, required): Grashof number for the plate (dimensionless).
  • buoyancy (bool, optional, default: true): Whether buoyancy assists free convection (dimensionless).

Returns (float): Nusselt number based on plate length (dimensionless).

Example 1: Rohsenow hot plate example

Inputs:

Pr Gr buoyancy
5.54 321000000 true

Excel formula:

=NU_HPLATE_ROHSENOW(5.54, 321000000, TRUE)

Expected output:

175.911

Example 2: Rohsenow cold plate example

Inputs:

Pr Gr buoyancy
5.54 321000000 false

Excel formula:

=NU_HPLATE_ROHSENOW(5.54, 321000000, FALSE)

Expected output:

35.958

Example 3: Rohsenow mid Grashof

Inputs:

Pr Gr buoyancy
0.9 2000000 true

Excel formula:

=NU_HPLATE_ROHSENOW(0.9, 2000000, TRUE)

Expected output:

17.1376

Example 4: Rohsenow low Grashof

Inputs:

Pr Gr buoyancy
0.7 200000 false

Excel formula:

=NU_HPLATE_ROHSENOW(0.7, 200000, FALSE)

Expected output:

5.43349

Python Code

Show Code 
from ht.conv_free_immersed import Nu_horizontal_plate_Rohsenow as ht_Nu_horizontal_plate_Rohsenow

def Nu_hplate_Rohsenow(Pr, Gr, buoyancy=True):
    """
    Calculate the Nusselt number for a horizontal plate using Rohsenow.

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

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

    Args:
        Pr (float): Prandtl number of the fluid (dimensionless).
        Gr (float): Grashof number for the plate (dimensionless).
        buoyancy (bool, optional): Whether buoyancy assists free convection (dimensionless). Default is True.

    Returns:
        float: Nusselt number based on plate length (dimensionless).
    """
    try:
        result = ht_Nu_horizontal_plate_Rohsenow(Pr, Gr, buoyancy=buoyancy)
        if result is None:
            return "Error: Result is None"
        return float(result)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Prandtl number of the fluid (dimensionless).
Grashof number for the plate (dimensionless).
Whether buoyancy assists free convection (dimensionless).

NU_HPLATE_VDI

This function computes natural-convection Nusselt number for an isothermal horizontal plate using the VDI-based ht correlation. It handles both buoyancy-assisted and buoyancy-opposed configurations.

The calculation follows Rayleigh-number scaling with:

Ra = Gr\,Pr

and returns a dimensionless Nusselt number based on plate length.

Excel Usage

=NU_HPLATE_VDI(Pr, Gr, buoyancy)
  • Pr (float, required): Prandtl number of the fluid (dimensionless).
  • Gr (float, required): Grashof number for the plate (dimensionless).
  • buoyancy (bool, optional, default: true): Whether buoyancy assists free convection (dimensionless).

Returns (float): Nusselt number based on plate length (dimensionless).

Example 1: VDI hot plate example

Inputs:

Pr Gr buoyancy
5.54 321000000 true

Excel formula:

=NU_HPLATE_VDI(5.54, 321000000, TRUE)

Expected output:

203.897

Example 2: VDI cold plate example

Inputs:

Pr Gr buoyancy
5.54 321000000 false

Excel formula:

=NU_HPLATE_VDI(5.54, 321000000, FALSE)

Expected output:

39.1686

Example 3: VDI mid Grashof

Inputs:

Pr Gr buoyancy
0.9 2000000 true

Excel formula:

=NU_HPLATE_VDI(0.9, 2000000, TRUE)

Expected output:

23.9665

Example 4: VDI low Grashof

Inputs:

Pr Gr buoyancy
0.7 200000 false

Excel formula:

=NU_HPLATE_VDI(0.7, 200000, FALSE)

Expected output:

5.1868

Python Code

Show Code 
from ht.conv_free_immersed import Nu_horizontal_plate_VDI as ht_Nu_horizontal_plate_VDI

def Nu_hplate_VDI(Pr, Gr, buoyancy=True):
    """
    Calculate the Nusselt number for a horizontal plate using VDI.

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

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

    Args:
        Pr (float): Prandtl number of the fluid (dimensionless).
        Gr (float): Grashof number for the plate (dimensionless).
        buoyancy (bool, optional): Whether buoyancy assists free convection (dimensionless). Default is True.

    Returns:
        float: Nusselt number based on plate length (dimensionless).
    """
    try:
        result = ht_Nu_horizontal_plate_VDI(Pr, Gr, buoyancy=buoyancy)
        if result is None:
            return "Error: Result is None"
        return float(result)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Prandtl number of the fluid (dimensionless).
Grashof number for the plate (dimensionless).
Whether buoyancy assists free convection (dimensionless).

NU_SPHERE_CHURCHILL

This function computes natural-convection Nusselt number for an isothermal sphere using the Churchill correlation from ht. It uses Prandtl and Grashof numbers as dimensionless inputs.

The model is evaluated from Rayleigh-number dependence:

Ra = Gr\,Pr

and returns a dimensionless Nusselt number referenced to sphere diameter.

Excel Usage

=NU_SPHERE_CHURCHILL(Pr, Gr)
  • Pr (float, required): Prandtl number of the fluid (dimensionless).
  • Gr (float, required): Grashof number based on sphere diameter (dimensionless).

Returns (float): Nusselt number based on sphere diameter (dimensionless).

Example 1: Churchill sphere example

Inputs:

Pr Gr
0.7 10000000

Excel formula:

=NU_SPHERE_CHURCHILL(0.7, 10000000)

Expected output:

25.6709

Example 2: Churchill sphere low Grashof

Inputs:

Pr Gr
0.8 100000

Excel formula:

=NU_SPHERE_CHURCHILL(0.8, 100000)

Expected output:

9.74458

Example 3: Churchill sphere mid Grashof

Inputs:

Pr Gr
1.1 5000000

Excel formula:

=NU_SPHERE_CHURCHILL(1.1, 5000000)

Expected output:

25.3343

Example 4: Churchill sphere high Grashof

Inputs:

Pr Gr
0.9 1000000000

Excel formula:

=NU_SPHERE_CHURCHILL(0.9, 1000000000)

Expected output:

108.333

Python Code

Show Code 
from ht.conv_free_immersed import Nu_sphere_Churchill as ht_Nu_sphere_Churchill

def Nu_sphere_Churchill(Pr, Gr):
    """
    Calculate the Nusselt number for a sphere using Churchill.

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

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

    Args:
        Pr (float): Prandtl number of the fluid (dimensionless).
        Gr (float): Grashof number based on sphere diameter (dimensionless).

    Returns:
        float: Nusselt number based on sphere diameter (dimensionless).
    """
    try:
        result = ht_Nu_sphere_Churchill(Pr, Gr)
        if result is None:
            return "Error: Result is None"
        return float(result)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Prandtl number of the fluid (dimensionless).
Grashof number based on sphere diameter (dimensionless).

NU_VCYL_ALARABI

This function evaluates the Al-Arabi and Khamis free-convection correlation for a vertical isothermal cylinder using the ht implementation. It requires Prandtl number, Grashof number, and cylinder geometry.

The piecewise formulation is based on Rayleigh scaling and geometric correction:

Ra = Gr\,Pr

and returns a dimensionless Nusselt number based on cylinder height.

Excel Usage

=NU_VCYL_ALARABI(Pr, Gr, L, D, turbulent)
  • Pr (float, required): Prandtl number of the fluid (dimensionless).
  • Gr (float, required): Grashof number based on cylinder height (dimensionless).
  • L (float, required): Cylinder length (m).
  • D (float, required): Cylinder diameter (m).
  • turbulent (bool, optional, default: null): Whether to force turbulent or laminar regime (dimensionless).

Returns (float): Nusselt number based on cylinder height (dimensionless).

Example 1: Al-Arabi Khamis example

Inputs:

Pr Gr L D
0.71 20000000000 10 1

Excel formula:

=NU_VCYL_ALARABI(0.71, 20000000000, 10, 1)

Expected output:

280.398

Example 2: Al-Arabi Khamis forced laminar

Inputs:

Pr Gr L D turbulent
0.71 800000000 8 0.8 false

Excel formula:

=NU_VCYL_ALARABI(0.71, 800000000, 8, 0.8, FALSE)

Expected output:

144.232

Example 3: Al-Arabi Khamis forced turbulent

Inputs:

Pr Gr L D turbulent
0.71 3000000000 12 1.2 true

Excel formula:

=NU_VCYL_ALARABI(0.71, 3000000000, 12, 1.2, TRUE)

Expected output:

174.501

Example 4: Al-Arabi Khamis mid range

Inputs:

Pr Gr L D
1.2 1200000000 6 0.6

Excel formula:

=NU_VCYL_ALARABI(1.2, 1200000000, 6, 0.6)

Expected output:

175.95

Python Code

Show Code 
from ht.conv_free_immersed import Nu_vertical_cylinder_Al_Arabi_Khamis as ht_Nu_vertical_cylinder_Al_Arabi_Khamis

def Nu_vcyl_AlArabi(Pr, Gr, L, D, turbulent=None):
    """
    Calculate the Nusselt number for a vertical cylinder using Al-Arabi and Khamis.

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

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

    Args:
        Pr (float): Prandtl number of the fluid (dimensionless).
        Gr (float): Grashof number based on cylinder height (dimensionless).
        L (float): Cylinder length (m).
        D (float): Cylinder diameter (m).
        turbulent (bool, optional): Whether to force turbulent or laminar regime (dimensionless). Default is None.

    Returns:
        float: Nusselt number based on cylinder height (dimensionless).
    """
    try:
        result = ht_Nu_vertical_cylinder_Al_Arabi_Khamis(Pr, Gr, L, D, turbulent=turbulent)
        if result is None:
            return "Error: Result is None"
        return float(result)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Prandtl number of the fluid (dimensionless).
Grashof number based on cylinder height (dimensionless).
Cylinder length (m).
Cylinder diameter (m).
Whether to force turbulent or laminar regime (dimensionless).

NU_VCYL_CARNEMORGAN

This function computes vertical-cylinder natural-convection Nusselt number using the Carne-Morgan correlation available in ht. It supports automatic, forced laminar, or forced turbulent branch selection.

The correlation is defined as piecewise power-law behavior in Rayleigh number:

Nu = C\,Ra^n,\qquad Ra = Gr\,Pr

and returns a dimensionless Nusselt number referenced to cylinder height.

Excel Usage

=NU_VCYL_CARNEMORGAN(Pr, Gr, turbulent)
  • Pr (float, required): Prandtl number of the fluid (dimensionless).
  • Gr (float, required): Grashof number based on cylinder height (dimensionless).
  • turbulent (bool, optional, default: null): Whether to force turbulent or laminar regime (dimensionless).

Returns (float): Nusselt number based on cylinder height (dimensionless).

Example 1: Carne Morgan example

Inputs:

Pr Gr
0.7 200000000

Excel formula:

=NU_VCYL_CARNEMORGAN(0.7, 200000000)

Expected output:

204.315

Example 2: Carne Morgan forced laminar

Inputs:

Pr Gr turbulent
0.7 50000000 false

Excel formula:

=NU_VCYL_CARNEMORGAN(0.7, 50000000, FALSE)

Expected output:

138.587

Example 3: Carne Morgan forced turbulent

Inputs:

Pr Gr turbulent
0.7 5000000000 true

Excel formula:

=NU_VCYL_CARNEMORGAN(0.7, 5000000000, TRUE)

Expected output:

643.561

Example 4: Carne Morgan mid range

Inputs:

Pr Gr
1.1 800000000

Excel formula:

=NU_VCYL_CARNEMORGAN(1.1, 800000000)

Expected output:

380.844

Python Code

Show Code 
from ht.conv_free_immersed import Nu_vertical_cylinder_Carne_Morgan as ht_Nu_vertical_cylinder_Carne_Morgan

def Nu_vcyl_CarneMorgan(Pr, Gr, turbulent=None):
    """
    Calculate the Nusselt number for a vertical cylinder using Carne-Morgan.

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

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

    Args:
        Pr (float): Prandtl number of the fluid (dimensionless).
        Gr (float): Grashof number based on cylinder height (dimensionless).
        turbulent (bool, optional): Whether to force turbulent or laminar regime (dimensionless). Default is None.

    Returns:
        float: Nusselt number based on cylinder height (dimensionless).
    """
    try:
        result = ht_Nu_vertical_cylinder_Carne_Morgan(Pr, Gr, turbulent=turbulent)
        if result is None:
            return "Error: Result is None"
        return float(result)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Prandtl number of the fluid (dimensionless).
Grashof number based on cylinder height (dimensionless).
Whether to force turbulent or laminar regime (dimensionless).

NU_VCYL_EIGENSON

This function computes natural-convection Nusselt number for a vertical isothermal cylinder using the Eigenson-Morgan model in ht. It allows automatic or forced regime selection through the turbulent argument.

The implementation uses piecewise relations in Rayleigh number:

Ra = Gr\,Pr

and returns a dimensionless Nusselt number referenced to cylinder height.

Excel Usage

=NU_VCYL_EIGENSON(Pr, Gr, turbulent)
  • Pr (float, required): Prandtl number of the fluid (dimensionless).
  • Gr (float, required): Grashof number based on cylinder height (dimensionless).
  • turbulent (bool, optional, default: null): Whether to force turbulent or laminar regime (dimensionless).

Returns (float): Nusselt number based on cylinder height (dimensionless).

Example 1: Eigenson Morgan example

Inputs:

Pr Gr
0.7 20000000000

Excel formula:

=NU_VCYL_EIGENSON(0.7, 20000000000)

Expected output:

230.559

Example 2: Eigenson Morgan forced laminar

Inputs:

Pr Gr turbulent
0.7 2000000000 false

Excel formula:

=NU_VCYL_EIGENSON(0.7, 2000000000, FALSE)

Expected output:

92.8481

Example 3: Eigenson Morgan forced turbulent

Inputs:

Pr Gr turbulent
0.7 50000000000 true

Excel formula:

=NU_VCYL_EIGENSON(0.7, 50000000000, TRUE)

Expected output:

356.518

Example 4: Eigenson Morgan mid range

Inputs:

Pr Gr
1 8000000000

Excel formula:

=NU_VCYL_EIGENSON(1, 8000000000)

Expected output:

177.359

Python Code

Show Code 
from ht.conv_free_immersed import Nu_vertical_cylinder_Eigenson_Morgan as ht_Nu_vertical_cylinder_Eigenson_Morgan

def Nu_vcyl_Eigenson(Pr, Gr, turbulent=None):
    """
    Calculate the Nusselt number for a vertical cylinder using Eigenson-Morgan.

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

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

    Args:
        Pr (float): Prandtl number of the fluid (dimensionless).
        Gr (float): Grashof number based on cylinder height (dimensionless).
        turbulent (bool, optional): Whether to force turbulent or laminar regime (dimensionless). Default is None.

    Returns:
        float: Nusselt number based on cylinder height (dimensionless).
    """
    try:
        result = ht_Nu_vertical_cylinder_Eigenson_Morgan(Pr, Gr, turbulent=turbulent)
        if result is None:
            return "Error: Result is None"
        return float(result)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Prandtl number of the fluid (dimensionless).
Grashof number based on cylinder height (dimensionless).
Whether to force turbulent or laminar regime (dimensionless).

NU_VCYL_GRIFFITHS

This function evaluates natural-convection heat transfer for a vertical isothermal cylinder using the Griffiths-Davis-Morgan correlation in ht. It supports automatic or forced branch selection via the turbulence flag.

The correlation uses piecewise Rayleigh-number scaling:

Nu = C\,Ra^n,\qquad Ra = Gr\,Pr

and returns a dimensionless Nusselt number referenced to cylinder height.

Excel Usage

=NU_VCYL_GRIFFITHS(Pr, Gr, turbulent)
  • Pr (float, required): Prandtl number of the fluid (dimensionless).
  • Gr (float, required): Grashof number based on cylinder height (dimensionless).
  • turbulent (bool, optional, default: null): Whether to force turbulent or laminar regime (dimensionless).

Returns (float): Nusselt number based on cylinder height (dimensionless).

Example 1: Griffiths Davis Morgan example

Inputs:

Pr Gr
0.7 20000000000

Excel formula:

=NU_VCYL_GRIFFITHS(0.7, 20000000000)

Expected output:

327.623

Example 2: Griffiths Davis Morgan forced laminar

Inputs:

Pr Gr turbulent
0.7 500000000 false

Excel formula:

=NU_VCYL_GRIFFITHS(0.7, 500000000, FALSE)

Expected output:

91.6414

Example 3: Griffiths Davis Morgan forced turbulent

Inputs:

Pr Gr turbulent
0.7 50000000000 true

Excel formula:

=NU_VCYL_GRIFFITHS(0.7, 50000000000, TRUE)

Expected output:

454.401

Example 4: Griffiths Davis Morgan mid range

Inputs:

Pr Gr
1 8000000000

Excel formula:

=NU_VCYL_GRIFFITHS(1, 8000000000)

Expected output:

268.293

Python Code

Show Code 
from ht.conv_free_immersed import Nu_vertical_cylinder_Griffiths_Davis_Morgan as ht_Nu_vertical_cylinder_Griffiths_Davis_Morgan

def Nu_vcyl_Griffiths(Pr, Gr, turbulent=None):
    """
    Calculate the Nusselt number for a vertical cylinder using Griffiths-Davis-Morgan.

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

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

    Args:
        Pr (float): Prandtl number of the fluid (dimensionless).
        Gr (float): Grashof number based on cylinder height (dimensionless).
        turbulent (bool, optional): Whether to force turbulent or laminar regime (dimensionless). Default is None.

    Returns:
        float: Nusselt number based on cylinder height (dimensionless).
    """
    try:
        result = ht_Nu_vertical_cylinder_Griffiths_Davis_Morgan(Pr, Gr, turbulent=turbulent)
        if result is None:
            return "Error: Result is None"
        return float(result)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Prandtl number of the fluid (dimensionless).
Grashof number based on cylinder height (dimensionless).
Whether to force turbulent or laminar regime (dimensionless).

NU_VCYL_HANESIAN

This function computes natural-convection Nusselt number for a vertical isothermal cylinder using the Hanesian-Kalish-Morgan correlation from ht. It takes Prandtl and Grashof numbers and evaluates the laminar-range relation.

The expression is represented through Rayleigh-number scaling:

Nu = C\,Ra^n,\qquad Ra = Gr\,Pr

and returns a dimensionless Nusselt number based on cylinder height.

Excel Usage

=NU_VCYL_HANESIAN(Pr, Gr)
  • Pr (float, required): Prandtl number of the fluid (dimensionless).
  • Gr (float, required): Grashof number based on cylinder height (dimensionless).

Returns (float): Nusselt number based on cylinder height (dimensionless).

Example 1: Hanesian Kalish Morgan example

Inputs:

Pr Gr
0.7 10000000

Excel formula:

=NU_VCYL_HANESIAN(0.7, 10000000)

Expected output:

18.0142

Example 2: Hanesian Kalish Morgan low Grashof

Inputs:

Pr Gr
0.9 1000000

Excel formula:

=NU_VCYL_HANESIAN(0.9, 1000000)

Expected output:

11.2387

Example 3: Hanesian Kalish Morgan mid Grashof

Inputs:

Pr Gr
1.2 5000000

Excel formula:

=NU_VCYL_HANESIAN(1.2, 5000000)

Expected output:

17.3867

Example 4: Hanesian Kalish Morgan high Grashof

Inputs:

Pr Gr
0.8 50000000

Excel formula:

=NU_VCYL_HANESIAN(0.8, 50000000)

Expected output:

26.8977

Python Code

Show Code 
from ht.conv_free_immersed import Nu_vertical_cylinder_Hanesian_Kalish_Morgan as ht_Nu_vertical_cylinder_Hanesian_Kalish_Morgan

def Nu_vcyl_Hanesian(Pr, Gr):
    """
    Calculate the Nusselt number for a vertical cylinder using Hanesian-Kalish-Morgan.

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

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

    Args:
        Pr (float): Prandtl number of the fluid (dimensionless).
        Gr (float): Grashof number based on cylinder height (dimensionless).

    Returns:
        float: Nusselt number based on cylinder height (dimensionless).
    """
    try:
        result = ht_Nu_vertical_cylinder_Hanesian_Kalish_Morgan(Pr, Gr)
        if result is None:
            return "Error: Result is None"
        return float(result)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Prandtl number of the fluid (dimensionless).
Grashof number based on cylinder height (dimensionless).

NU_VCYL_JAKOB

This function computes free-convection Nusselt number for a vertical isothermal cylinder using the Jakob-Linke-Morgan correlation in ht. It supports optional forcing of laminar or turbulent branch selection.

The model is piecewise in Rayleigh number:

Nu = C\,Ra^n,\qquad Ra = Gr\,Pr

and returns a dimensionless Nusselt number referenced to cylinder height.

Excel Usage

=NU_VCYL_JAKOB(Pr, Gr, turbulent)
  • Pr (float, required): Prandtl number of the fluid (dimensionless).
  • Gr (float, required): Grashof number based on cylinder height (dimensionless).
  • turbulent (bool, optional, default: null): Whether to force turbulent or laminar regime (dimensionless).

Returns (float): Nusselt number based on cylinder height (dimensionless).

Example 1: Jakob Linke Morgan example

Inputs:

Pr Gr
0.7 20000000000

Excel formula:

=NU_VCYL_JAKOB(0.7, 20000000000)

Expected output:

310.908

Example 2: Jakob Linke Morgan forced laminar

Inputs:

Pr Gr turbulent
0.7 500000000 false

Excel formula:

=NU_VCYL_JAKOB(0.7, 500000000, FALSE)

Expected output:

75.9119

Example 3: Jakob Linke Morgan forced turbulent

Inputs:

Pr Gr turbulent
0.7 50000000000 true

Excel formula:

=NU_VCYL_JAKOB(0.7, 50000000000, TRUE)

Expected output:

421.968

Example 4: Jakob Linke Morgan mid range

Inputs:

Pr Gr
1 8000000000

Excel formula:

=NU_VCYL_JAKOB(1, 8000000000)

Expected output:

258

Python Code

Show Code 
from ht.conv_free_immersed import Nu_vertical_cylinder_Jakob_Linke_Morgan as ht_Nu_vertical_cylinder_Jakob_Linke_Morgan

def Nu_vcyl_Jakob(Pr, Gr, turbulent=None):
    """
    Calculate the Nusselt number for a vertical cylinder using Jakob-Linke-Morgan.

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

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

    Args:
        Pr (float): Prandtl number of the fluid (dimensionless).
        Gr (float): Grashof number based on cylinder height (dimensionless).
        turbulent (bool, optional): Whether to force turbulent or laminar regime (dimensionless). Default is None.

    Returns:
        float: Nusselt number based on cylinder height (dimensionless).
    """
    try:
        result = ht_Nu_vertical_cylinder_Jakob_Linke_Morgan(Pr, Gr, turbulent=turbulent)
        if result is None:
            return "Error: Result is None"
        return float(result)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Prandtl number of the fluid (dimensionless).
Grashof number based on cylinder height (dimensionless).
Whether to force turbulent or laminar regime (dimensionless).

NU_VCYL_KREITH

This function computes vertical-cylinder natural-convection Nusselt number with the Kreith-Eckert correlation implemented in ht. It uses Prandtl and Grashof numbers and supports optional branch control.

The relation is piecewise in Rayleigh number:

Nu = C\,Ra^n,\qquad Ra = Gr\,Pr

and returns a dimensionless Nusselt number based on cylinder height.

Excel Usage

=NU_VCYL_KREITH(Pr, Gr, turbulent)
  • Pr (float, required): Prandtl number of the fluid (dimensionless).
  • Gr (float, required): Grashof number based on cylinder height (dimensionless).
  • turbulent (bool, optional, default: null): Whether to force turbulent or laminar regime (dimensionless).

Returns (float): Nusselt number based on cylinder height (dimensionless).

Example 1: Kreith Eckert example

Inputs:

Pr Gr
0.7 20000000000

Excel formula:

=NU_VCYL_KREITH(0.7, 20000000000)

Expected output:

240.254

Example 2: Kreith Eckert forced laminar

Inputs:

Pr Gr turbulent
0.7 500000000 false

Excel formula:

=NU_VCYL_KREITH(0.7, 500000000, FALSE)

Expected output:

75.9119

Example 3: Kreith Eckert forced turbulent

Inputs:

Pr Gr turbulent
0.7 50000000000 true

Excel formula:

=NU_VCYL_KREITH(0.7, 50000000000, TRUE)

Expected output:

346.614

Example 4: Kreith Eckert mid range

Inputs:

Pr Gr
1 8000000000

Excel formula:

=NU_VCYL_KREITH(1, 8000000000)

Expected output:

192.068

Python Code

Show Code 
from ht.conv_free_immersed import Nu_vertical_cylinder_Kreith_Eckert as ht_Nu_vertical_cylinder_Kreith_Eckert

def Nu_vcyl_Kreith(Pr, Gr, turbulent=None):
    """
    Calculate the Nusselt number for a vertical cylinder using Kreith-Eckert.

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

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

    Args:
        Pr (float): Prandtl number of the fluid (dimensionless).
        Gr (float): Grashof number based on cylinder height (dimensionless).
        turbulent (bool, optional): Whether to force turbulent or laminar regime (dimensionless). Default is None.

    Returns:
        float: Nusselt number based on cylinder height (dimensionless).
    """
    try:
        result = ht_Nu_vertical_cylinder_Kreith_Eckert(Pr, Gr, turbulent=turbulent)
        if result is None:
            return "Error: Result is None"
        return float(result)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Prandtl number of the fluid (dimensionless).
Grashof number based on cylinder height (dimensionless).
Whether to force turbulent or laminar regime (dimensionless).

NU_VCYL_MCADAMS

This function computes natural-convection Nusselt number for a vertical isothermal cylinder using the McAdams-Weiss-Saunders correlation in ht. It accepts optional laminar/turbulent branch forcing.

The formulation is piecewise with Rayleigh-number dependence:

Nu = C\,Ra^n,\qquad Ra = Gr\,Pr

and returns a dimensionless Nusselt number referenced to cylinder height.

Excel Usage

=NU_VCYL_MCADAMS(Pr, Gr, turbulent)
  • Pr (float, required): Prandtl number of the fluid (dimensionless).
  • Gr (float, required): Grashof number based on cylinder height (dimensionless).
  • turbulent (bool, optional, default: null): Whether to force turbulent or laminar regime (dimensionless).

Returns (float): Nusselt number based on cylinder height (dimensionless).

Example 1: McAdams Weiss Saunders example

Inputs:

Pr Gr
0.7 20000000000

Excel formula:

=NU_VCYL_MCADAMS(0.7, 20000000000)

Expected output:

313.318

Example 2: McAdams Weiss Saunders forced laminar

Inputs:

Pr Gr turbulent
0.7 500000000 false

Excel formula:

=NU_VCYL_MCADAMS(0.7, 500000000, FALSE)

Expected output:

80.6992

Example 3: McAdams Weiss Saunders forced turbulent

Inputs:

Pr Gr turbulent
0.7 50000000000 true

Excel formula:

=NU_VCYL_MCADAMS(0.7, 50000000000, TRUE)

Expected output:

425.239

Example 4: McAdams Weiss Saunders mid range

Inputs:

Pr Gr
1 8000000000

Excel formula:

=NU_VCYL_MCADAMS(1, 8000000000)

Expected output:

260

Python Code

Show Code 
from ht.conv_free_immersed import Nu_vertical_cylinder_McAdams_Weiss_Saunders as ht_Nu_vertical_cylinder_McAdams_Weiss_Saunders

def Nu_vcyl_McAdams(Pr, Gr, turbulent=None):
    """
    Calculate the Nusselt number for a vertical cylinder using McAdams-Weiss-Saunders.

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

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

    Args:
        Pr (float): Prandtl number of the fluid (dimensionless).
        Gr (float): Grashof number based on cylinder height (dimensionless).
        turbulent (bool, optional): Whether to force turbulent or laminar regime (dimensionless). Default is None.

    Returns:
        float: Nusselt number based on cylinder height (dimensionless).
    """
    try:
        result = ht_Nu_vertical_cylinder_McAdams_Weiss_Saunders(Pr, Gr, turbulent=turbulent)
        if result is None:
            return "Error: Result is None"
        return float(result)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Prandtl number of the fluid (dimensionless).
Grashof number based on cylinder height (dimensionless).
Whether to force turbulent or laminar regime (dimensionless).

NU_VCYL_METHODS

This function returns available ht correlation names for free convection from a vertical cylinder at the specified conditions. It can use optional geometric inputs and optionally restrict methods to valid ranges.

Method filtering is based on standard free-convection dimensionless groups:

Ra = Gr\,Pr

and output is returned as a one-column 2D array for Excel spill compatibility.

Excel Usage

=NU_VCYL_METHODS(Pr, Gr, L, D, check_ranges)
  • Pr (float, required): Prandtl number of the fluid (dimensionless).
  • Gr (float, required): Grashof number based on cylinder height (dimensionless).
  • L (float, optional, default: null): Cylinder length (m).
  • D (float, optional, default: null): Cylinder diameter (m).
  • check_ranges (bool, optional, default: true): Whether to filter methods by validity ranges (dimensionless).

Returns (list[list]): Available correlation names as a column list.

Example 1: Vertical cylinder methods default

Inputs:

Pr Gr
0.72 10000000

Excel formula:

=NU_VCYL_METHODS(0.72, 10000000)

Expected output:

McAdams, Weiss & Saunders
Churchill Vertical Plate
Griffiths, Davis, & Morgan
Jakob, Linke, & Morgan
Carne & Morgan
Eigenson & Morgan
Touloukian & Morgan
Kreith & Eckert
Hanesian, Kalish & Morgan
Example 2: Vertical cylinder methods without range checks

Inputs:

Pr Gr check_ranges
0.72 10000000 false

Excel formula:

=NU_VCYL_METHODS(0.72, 10000000, FALSE)

Expected output:

McAdams, Weiss & Saunders
Churchill Vertical Plate
Griffiths, Davis, & Morgan
Jakob, Linke, & Morgan
Carne & Morgan
Eigenson & Morgan
Touloukian & Morgan
Kreith & Eckert
Hanesian, Kalish & Morgan
Example 3: Vertical cylinder methods with geometry inputs

Inputs:

Pr Gr L D
0.7 10000000000 2.5 1

Excel formula:

=NU_VCYL_METHODS(0.7, 10000000000, 2.5, 1)

Expected output:

Popiel & Churchill
Churchill Vertical Plate
Griffiths, Davis, & Morgan
Jakob, Linke, & Morgan
Carne & Morgan
Eigenson & Morgan
Touloukian & Morgan
McAdams, Weiss & Saunders
Kreith & Eckert
Hanesian, Kalish & Morgan
Al-Arabi & Khamis
Example 4: Vertical cylinder methods mid Grashof

Inputs:

Pr Gr
1.1 5000000

Excel formula:

=NU_VCYL_METHODS(1.1, 5000000)

Expected output:

McAdams, Weiss & Saunders
Churchill Vertical Plate
Griffiths, Davis, & Morgan
Jakob, Linke, & Morgan
Carne & Morgan
Eigenson & Morgan
Touloukian & Morgan
Kreith & Eckert
Hanesian, Kalish & Morgan

Python Code

Show Code 
from ht.conv_free_immersed import Nu_vertical_cylinder_methods as ht_Nu_vertical_cylinder_methods

def Nu_vcyl_methods(Pr, Gr, L=None, D=None, check_ranges=True):
    """
    List available correlations for free convection from a vertical cylinder.

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

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

    Args:
        Pr (float): Prandtl number of the fluid (dimensionless).
        Gr (float): Grashof number based on cylinder height (dimensionless).
        L (float, optional): Cylinder length (m). Default is None.
        D (float, optional): Cylinder diameter (m). Default is None.
        check_ranges (bool, optional): Whether to filter methods by validity ranges (dimensionless). Default is True.

    Returns:
        list[list]: Available correlation names as a column list.
    """
    try:
        methods = ht_Nu_vertical_cylinder_methods(Pr, Gr, L=L, D=D, check_ranges=check_ranges)
        if methods is None:
            return "Error: No methods returned"
        return [[method] for method in methods]
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Prandtl number of the fluid (dimensionless).
Grashof number based on cylinder height (dimensionless).
Cylinder length (m).
Cylinder diameter (m).
Whether to filter methods by validity ranges (dimensionless).

NU_VCYL_POPIEL

This function evaluates natural-convection Nusselt number for a vertical slender cylinder with the Popiel-Churchill correction in ht. It requires Prandtl and Grashof numbers plus explicit cylinder length and diameter.

The method applies a vertical-plate baseline with a geometric correction governed by dimensionless groups including:

Ra = Gr\,Pr

and returns a dimensionless Nusselt number based on cylinder height.

Excel Usage

=NU_VCYL_POPIEL(Pr, Gr, L, D)
  • Pr (float, required): Prandtl number of the fluid (dimensionless).
  • Gr (float, required): Grashof number based on cylinder height (dimensionless).
  • L (float, required): Cylinder length (m).
  • D (float, required): Cylinder diameter (m).

Returns (float): Nusselt number based on cylinder height (dimensionless).

Example 1: Popiel Churchill example

Inputs:

Pr Gr L D
0.7 10000000000 2.5 1

Excel formula:

=NU_VCYL_POPIEL(0.7, 10000000000, 2.5, 1)

Expected output:

228.898

Example 2: Popiel Churchill short cylinder

Inputs:

Pr Gr L D
1.2 3000000000 1 0.4

Excel formula:

=NU_VCYL_POPIEL(1.2, 3000000000, 1, 0.4)

Expected output:

199.467

Example 3: Popiel Churchill slender cylinder

Inputs:

Pr Gr L D
0.9 8000000000 4 0.6

Excel formula:

=NU_VCYL_POPIEL(0.9, 8000000000, 4, 0.6)

Expected output:

244.494

Example 4: Popiel Churchill low Prandtl

Inputs:

Pr Gr L D
0.1 1000000000 3 0.5

Excel formula:

=NU_VCYL_POPIEL(0.1, 1000000000, 3, 0.5)

Expected output:

49.6141

Python Code

Show Code 
from ht.conv_free_immersed import Nu_vertical_cylinder_Popiel_Churchill as ht_Nu_vertical_cylinder_Popiel_Churchill

def Nu_vcyl_Popiel(Pr, Gr, L, D):
    """
    Calculate the Nusselt number for a vertical cylinder using Popiel-Churchill.

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

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

    Args:
        Pr (float): Prandtl number of the fluid (dimensionless).
        Gr (float): Grashof number based on cylinder height (dimensionless).
        L (float): Cylinder length (m).
        D (float): Cylinder diameter (m).

    Returns:
        float: Nusselt number based on cylinder height (dimensionless).
    """
    try:
        result = ht_Nu_vertical_cylinder_Popiel_Churchill(Pr, Gr, L, D)
        if result is None:
            return "Error: Result is None"
        return float(result)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Prandtl number of the fluid (dimensionless).
Grashof number based on cylinder height (dimensionless).
Cylinder length (m).
Cylinder diameter (m).

NU_VCYL_TOULOUKIAN

This function computes natural-convection Nusselt number for a vertical isothermal cylinder using the Touloukian-Morgan correlation in ht. It supports automatic or forced branch selection between available regimes.

The correlation is represented through Rayleigh-based scaling:

Ra = Gr\,Pr

and returns a dimensionless Nusselt number referenced to cylinder height.

Excel Usage

=NU_VCYL_TOULOUKIAN(Pr, Gr, turbulent)
  • Pr (float, required): Prandtl number of the fluid (dimensionless).
  • Gr (float, required): Grashof number based on cylinder height (dimensionless).
  • turbulent (bool, optional, default: null): Whether to force turbulent or laminar regime (dimensionless).

Returns (float): Nusselt number based on cylinder height (dimensionless).

Example 1: Touloukian Morgan example

Inputs:

Pr Gr
0.7 20000000000

Excel formula:

=NU_VCYL_TOULOUKIAN(0.7, 20000000000)

Expected output:

249.729

Example 2: Touloukian Morgan forced laminar

Inputs:

Pr Gr turbulent
0.7 500000000 false

Excel formula:

=NU_VCYL_TOULOUKIAN(0.7, 500000000, FALSE)

Expected output:

99.301

Example 3: Touloukian Morgan forced turbulent

Inputs:

Pr Gr turbulent
0.7 50000000000 true

Excel formula:

=NU_VCYL_TOULOUKIAN(0.7, 50000000000, TRUE)

Expected output:

212.998

Example 4: Touloukian Morgan mid range

Inputs:

Pr Gr
1 8000000000

Excel formula:

=NU_VCYL_TOULOUKIAN(1, 8000000000)

Expected output:

217.125

Python Code

Show Code 
from ht.conv_free_immersed import Nu_vertical_cylinder_Touloukian_Morgan as ht_Nu_vertical_cylinder_Touloukian_Morgan

def Nu_vcyl_Touloukian(Pr, Gr, turbulent=None):
    """
    Calculate the Nusselt number for a vertical cylinder using Touloukian-Morgan.

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

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

    Args:
        Pr (float): Prandtl number of the fluid (dimensionless).
        Gr (float): Grashof number based on cylinder height (dimensionless).
        turbulent (bool, optional): Whether to force turbulent or laminar regime (dimensionless). Default is None.

    Returns:
        float: Nusselt number based on cylinder height (dimensionless).
    """
    try:
        result = ht_Nu_vertical_cylinder_Touloukian_Morgan(Pr, Gr, turbulent=turbulent)
        if result is None:
            return "Error: Result is None"
        return float(result)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Prandtl number of the fluid (dimensionless).
Grashof number based on cylinder height (dimensionless).
Whether to force turbulent or laminar regime (dimensionless).

NU_VERT_CYL

This function computes natural-convection Nusselt number for a vertical cylinder using selectable correlations from ht. It accepts Prandtl and Grashof numbers and optional geometric parameters for methods that require cylinder aspect information.

The selection and evaluation are based on free-convection dimensionless groups:

Ra = Gr\,Pr

and returns a dimensionless Nusselt number associated with cylinder height.

Excel Usage

=NU_VERT_CYL(Pr, Gr, L, D, Nu_vert_cyl_method)
  • Pr (float, required): Prandtl number of the fluid (dimensionless).
  • Gr (float, required): Grashof number based on cylinder height (dimensionless).
  • L (float, optional, default: null): Cylinder length (m).
  • D (float, optional, default: null): Cylinder diameter (m).
  • Nu_vert_cyl_method (str, optional, default: null): Correlation name (string).

Returns (float): Nusselt number based on cylinder height (dimensionless).

Example 1: Vertical cylinder default method

Inputs:

Pr Gr
0.72 10000000

Excel formula:

=NU_VERT_CYL(0.72, 10000000)

Expected output:

30.5622

Example 2: Vertical cylinder Popiel and Churchill

Inputs:

Pr Gr L D Nu_vert_cyl_method
0.7 10000000000 2.5 1 Popiel & Churchill

Excel formula:

=NU_VERT_CYL(0.7, 10000000000, 2.5, 1, "Popiel & Churchill")

Expected output:

228.898

Example 3: Vertical cylinder McAdams Weiss Saunders

Inputs:

Pr Gr Nu_vert_cyl_method
0.7 20000000000 McAdams, Weiss & Saunders

Excel formula:

=NU_VERT_CYL(0.7, 20000000000, "McAdams, Weiss & Saunders")

Expected output:

313.318

Example 4: Vertical cylinder with geometry inputs

Inputs:

Pr Gr L D
1.1 5000000 3 0.5

Excel formula:

=NU_VERT_CYL(1.1, 5000000, 3, 0.5)

Expected output:

32.9289

Python Code

Show Code 
from ht.conv_free_immersed import Nu_vertical_cylinder as ht_Nu_vertical_cylinder

def Nu_vert_cyl(Pr, Gr, L=None, D=None, Nu_vert_cyl_method=None):
    """
    Select and calculate a Nusselt number correlation for a vertical cylinder.

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

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

    Args:
        Pr (float): Prandtl number of the fluid (dimensionless).
        Gr (float): Grashof number based on cylinder height (dimensionless).
        L (float, optional): Cylinder length (m). Default is None.
        D (float, optional): Cylinder diameter (m). Default is None.
        Nu_vert_cyl_method (str, optional): Correlation name (string). Valid options: Popiel & Churchill, Churchill Vertical Plate, Griffiths, Davis, & Morgan, Jakob, Linke, & Morgan, Carne & Morgan, Eigenson & Morgan, Touloukian & Morgan, McAdams, Weiss & Saunders, Kreith & Eckert, Hanesian, Kalish & Morgan, Al-Arabi & Khamis. Default is None.

    Returns:
        float: Nusselt number based on cylinder height (dimensionless).
    """
    try:
        result = ht_Nu_vertical_cylinder(Pr, Gr, L=L, D=D, Method=Nu_vert_cyl_method)
        if result is None:
            return "Error: Result is None"
        return float(result)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Prandtl number of the fluid (dimensionless).
Grashof number based on cylinder height (dimensionless).
Cylinder length (m).
Cylinder diameter (m).
Correlation name (string).

NU_VPLATE_CHURCHILL

This function computes natural-convection Nusselt number for an isothermal vertical plate using the Churchill-Chu correlation from ht. It accepts Prandtl and Grashof numbers evaluated at film conditions.

The correlation is expressed using Rayleigh-number dependence:

Ra = Gr\,Pr

and returns a dimensionless Nusselt number based on plate height.

Excel Usage

=NU_VPLATE_CHURCHILL(Pr, Gr)
  • Pr (float, required): Prandtl number of the fluid (dimensionless).
  • Gr (float, required): Grashof number for the plate (dimensionless).

Returns (float): Nusselt number based on plate height (dimensionless).

Example 1: Churchill vertical plate example

Inputs:

Pr Gr
0.69 2630000000

Excel formula:

=NU_VPLATE_CHURCHILL(0.69, 2630000000)

Expected output:

147.162

Example 2: Churchill vertical plate low Grashof

Inputs:

Pr Gr
0.7 100000

Excel formula:

=NU_VPLATE_CHURCHILL(0.7, 100000)

Expected output:

8.44179

Example 3: Churchill vertical plate mid Grashof

Inputs:

Pr Gr
1.2 5000000

Excel formula:

=NU_VPLATE_CHURCHILL(1.2, 5000000)

Expected output:

28.7179

Example 4: Churchill vertical plate high Grashof

Inputs:

Pr Gr
0.9 1000000000

Excel formula:

=NU_VPLATE_CHURCHILL(0.9, 1000000000)

Expected output:

122.748

Python Code

Show Code 
from ht.conv_free_immersed import Nu_vertical_plate_Churchill as ht_Nu_vertical_plate_Churchill

def Nu_vplate_Churchill(Pr, Gr):
    """
    Calculate the Nusselt number for a vertical plate using Churchill-Chu.

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

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

    Args:
        Pr (float): Prandtl number of the fluid (dimensionless).
        Gr (float): Grashof number for the plate (dimensionless).

    Returns:
        float: Nusselt number based on plate height (dimensionless).
    """
    try:
        result = ht_Nu_vertical_plate_Churchill(Pr, Gr)
        if result is None:
            return "Error: Result is None"
        return float(result)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Prandtl number of the fluid (dimensionless).
Grashof number for the plate (dimensionless).