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

Calculate the Nusselt number for natural convection around a helical coil.

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

Pr *

Prandtl number at film temperature (dimensionless).

Gr *

Grashof number based on coil outer diameter (dimensionless).

horizontal

Whether the coil is horizontal (dimensionless).

---

NU_FREE_HPLATE

Calculate the Nusselt number for free convection from a horizontal plate.

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

Pr *

Prandtl number of the fluid (dimensionless).

Gr *

Grashof number for the plate (dimensionless).

buoyancy *

Whether buoyancy assists free convection (dimensionless).

L

Plate length (m).

W

Plate width (m).

hplate_method Optional VDI McAdams Rohsenow

Correlation name (string).

---

NU_FREE_HPLATE_METH

List available correlations for free convection from a horizontal plate.

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

Pr *

Prandtl number of the fluid (dimensionless).

Gr *

Grashof number for the plate (dimensionless).

buoyancy *

Whether buoyancy assists free convection (dimensionless).

L

Plate length (m).

W

Plate width (m).

check_ranges

Whether to filter methods by validity ranges (dimensionless).

---

NU_FREE_VPLATE

Calculate the Nusselt number for free convection from a vertical plate.

Excel Usage

=NU_FREE_VPLATE(Pr, Gr, buoyancy, H, W, 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).
• 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	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, 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.
        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=Method)
        if result is None:
            return "Error: Result is None"
        return float(result)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Pr *

Prandtl number of the fluid (dimensionless).

Gr *

Grashof number for the plate (dimensionless).

buoyancy

Whether buoyancy assists free convection (dimensionless).

H

Plate height (m).

W

Plate width (m).

Method

Correlation name (string).

---

NU_FREE_VPLATE_METH

List available correlations for free convection from a vertical plate.

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

Pr *

Prandtl number of the fluid (dimensionless).

Gr *

Grashof number for the plate (dimensionless).

H

Plate height (m).

W

Plate width (m).

check_ranges

Whether to filter methods by validity ranges (dimensionless).

---

NU_HCYL_CHURCHILL

Calculate the Nusselt number for a horizontal cylinder using Churchill-Chu.

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

Pr *

Prandtl number at film temperature (dimensionless).

Gr *

Grashof number based on cylinder diameter (dimensionless).

---

NU_HCYL_KUEHNGOLD

Calculate the Nusselt number for a horizontal cylinder using Kuehn-Goldstein.

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

Pr *

Prandtl number at film temperature (dimensionless).

Gr *

Grashof number based on cylinder diameter (dimensionless).

---

NU_HCYL_METHODS

List available correlations for free convection from a horizontal cylinder.

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

Pr *

Prandtl number at film temperature (dimensionless).

Gr *

Grashof number based on cylinder diameter (dimensionless).

check_ranges

Whether to filter methods by validity ranges (dimensionless).

---

NU_HCYL_MORGAN

Calculate the Nusselt number for a horizontal cylinder using Morgan.

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

Pr *

Prandtl number at film temperature (dimensionless).

Gr *

Grashof number based on cylinder diameter (dimensionless).

---

NU_HORIZ_CYL

Select and calculate a Nusselt number correlation for a horizontal cylinder.

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

Pr *

Prandtl number at film temperature (dimensionless).

Gr *

Grashof number based on cylinder diameter (dimensionless).

Nu_horiz_cyl_method Optional Morgan Churchill-Chu Kuehn & Goldstein

Correlation name (string).

---

NU_HPLATE_MCADAMS

Calculate the Nusselt number for a horizontal plate using McAdams.

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

Pr *

Prandtl number of the fluid (dimensionless).

Gr *

Grashof number for the plate (dimensionless).

buoyancy

Whether buoyancy assists free convection (dimensionless).

---

NU_HPLATE_ROHSENOW

Calculate the Nusselt number for a horizontal plate using Rohsenow.

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

Pr *

Prandtl number of the fluid (dimensionless).

Gr *

Grashof number for the plate (dimensionless).

buoyancy

Whether buoyancy assists free convection (dimensionless).

---

NU_HPLATE_VDI

Calculate the Nusselt number for a horizontal plate using VDI.

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

Pr *

Prandtl number of the fluid (dimensionless).

Gr *

Grashof number for the plate (dimensionless).

buoyancy

Whether buoyancy assists free convection (dimensionless).

---

NU_SPHERE_CHURCHILL

Calculate the Nusselt number for a sphere using Churchill.

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

Pr *

Prandtl number of the fluid (dimensionless).

Gr *

Grashof number based on sphere diameter (dimensionless).

---

NU_VCYL_ALARABI

Calculate the Nusselt number for a vertical cylinder using Al-Arabi and Khamis.

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

Pr *

Prandtl number of the fluid (dimensionless).

Gr *

Grashof number based on cylinder height (dimensionless).

L *

Cylinder length (m).

D *

Cylinder diameter (m).

turbulent

Whether to force turbulent or laminar regime (dimensionless).

---

NU_VCYL_CARNEMORGAN

Calculate the Nusselt number for a vertical cylinder using Carne-Morgan.

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

Pr *

Prandtl number of the fluid (dimensionless).

Gr *

Grashof number based on cylinder height (dimensionless).

turbulent

Whether to force turbulent or laminar regime (dimensionless).

---

NU_VCYL_EIGENSON

Calculate the Nusselt number for a vertical cylinder using Eigenson-Morgan.

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

Pr *

Prandtl number of the fluid (dimensionless).

Gr *

Grashof number based on cylinder height (dimensionless).

turbulent

Whether to force turbulent or laminar regime (dimensionless).

---

NU_VCYL_GRIFFITHS

Calculate the Nusselt number for a vertical cylinder using Griffiths-Davis-Morgan.

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

Pr *

Prandtl number of the fluid (dimensionless).

Gr *

Grashof number based on cylinder height (dimensionless).

turbulent

Whether to force turbulent or laminar regime (dimensionless).

---

NU_VCYL_HANESIAN

Calculate the Nusselt number for a vertical cylinder using Hanesian-Kalish-Morgan.

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

Pr *

Prandtl number of the fluid (dimensionless).

Gr *

Grashof number based on cylinder height (dimensionless).

---

NU_VCYL_JAKOB

Calculate the Nusselt number for a vertical cylinder using Jakob-Linke-Morgan.

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

Pr *

Prandtl number of the fluid (dimensionless).

Gr *

Grashof number based on cylinder height (dimensionless).

turbulent

Whether to force turbulent or laminar regime (dimensionless).

---

NU_VCYL_KREITH

Calculate the Nusselt number for a vertical cylinder using Kreith-Eckert.

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

Pr *

Prandtl number of the fluid (dimensionless).

Gr *

Grashof number based on cylinder height (dimensionless).

turbulent

Whether to force turbulent or laminar regime (dimensionless).

---

NU_VCYL_MCADAMS

Calculate the Nusselt number for a vertical cylinder using McAdams-Weiss-Saunders.

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

Pr *

Prandtl number of the fluid (dimensionless).

Gr *

Grashof number based on cylinder height (dimensionless).

turbulent

Whether to force turbulent or laminar regime (dimensionless).

---

NU_VCYL_METHODS

List available correlations for free convection from a vertical cylinder.

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

Pr *

Prandtl number of the fluid (dimensionless).

Gr *

Grashof number based on cylinder height (dimensionless).

L

Cylinder length (m).

D

Cylinder diameter (m).

check_ranges

Whether to filter methods by validity ranges (dimensionless).

---

NU_VCYL_POPIEL

Calculate the Nusselt number for a vertical cylinder using Popiel-Churchill.

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

Pr *

Prandtl number of the fluid (dimensionless).

Gr *

Grashof number based on cylinder height (dimensionless).

L *

Cylinder length (m).

D *

Cylinder diameter (m).

---

NU_VCYL_TOULOUKIAN

Calculate the Nusselt number for a vertical cylinder using Touloukian-Morgan.

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

Pr *

Prandtl number of the fluid (dimensionless).

Gr *

Grashof number based on cylinder height (dimensionless).

turbulent

Whether to force turbulent or laminar regime (dimensionless).

---

NU_VERT_CYL

Select and calculate a Nusselt number correlation for a vertical cylinder.

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, McAdams. 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

Pr *

Prandtl number of the fluid (dimensionless).

Gr *

Grashof number based on cylinder height (dimensionless).

L

Cylinder length (m).

D

Cylinder diameter (m).

Nu_vert_cyl_method Optional Popiel & Churchill McAdams

Correlation name (string).

---

NU_VPLATE_CHURCHILL

Calculate the Nusselt number for a vertical plate using Churchill-Chu.

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

Pr *

Prandtl number of the fluid (dimensionless).

Gr *

Grashof number for the plate (dimensionless).