Conv Free Enclosed

Overview

Natural convection in enclosed spaces describes buoyancy-driven heat transfer where fluid motion arises from density differences inside bounded geometries, rather than from pumps or fans. This regime underpins thermal behavior in cavities, double-pane structures, tanks, and compact process equipment where boundary conditions strongly influence stability and transport. In engineering analysis, the key transition is from pure conduction to convection cells as buoyancy overcomes viscous and diffusive damping. The broader physical framework is captured by Rayleigh-Bénard convection, a canonical model for thermally driven instability.

The unifying concepts in this category are the Nusselt number (Nu), Rayleigh number (Ra), and critical Rayleigh number (Ra_c). In enclosed free convection, Nu quantifies effective heat-transfer enhancement relative to conduction, while Ra measures buoyancy strength through property and geometry scaling. Onset criteria are governed by stability thresholds: when Ra < Ra_c, conduction dominates; when Ra exceeds Ra_c, organized convective motion develops and Nu increases. This makes both forward prediction (Nu from operating conditions) and threshold estimation (Ra_c from geometry and boundaries) essential to practical design.

Implementation is provided by the Python ht library, specifically ht.conv_free_enclosed, which compiles established enclosure-convection correlations into consistent callable forms. The module is used for rapid screening, spreadsheet engineering workflows, and preliminary sizing where transparent empirical models are preferred before higher-fidelity CFD.

For horizontal enclosed layers, NU_RA_HOLLANDS, NU_RA_HOLLINGHERWIG, and NU_RA_PROBERT estimate Nu from Ra=Pr\,Gr under different assumptions and calibration ranges. Hollands is commonly used when finite-geometry effects and customizable Ra_c handling are needed, while Holling-Herwig targets idealized infinite-plate Rayleigh-Bénard conditions. Probert provides a piecewise regime form that is convenient for quick laminar-to-higher-Ra scaling studies. Together, these three functions support correlation comparison, sensitivity checks, and conservative-versus-aggressive heat-transfer bracketing in horizontal enclosure problems.

For non-horizontal enclosed configurations, NU_VERT_THESS models natural convection between vertical plates and can include explicit geometry terms (height and length) when available. In curved heat-exchanger geometries, NU_VHELIX_ALI and NU_VHELIX_PRR target external free convection around vertical helical coils in surrounding fluid volumes. These coil correlations are especially relevant in tank heating/cooling and process vessels where coil pitch and curvature alter boundary-layer development compared with straight surfaces. Using both functions in parallel is useful for method cross-checking when project standards do not mandate a single published correlation.

For instability thresholds, RAC_RAYLEIGH and RAC_RAYLEIGH_DISK compute Ra_c for enclosed parallel plates and parallel disks, respectively, including insulated versus uninsulated boundary-condition effects. These functions are complementary to the Nu correlations because they identify whether convection should be expected at all before applying enhancement formulas. In feasibility studies, they help prevent nonphysical overprediction by enforcing onset logic and clarifying when conduction-only assumptions remain appropriate. This threshold-first workflow is particularly valuable in narrow gaps, low temperature differences, and geometries near marginal stability.

NU_RA_HOLLANDS

This function computes the natural-convection Nusselt number between horizontal plates using the Hollands correlation for enclosed layers. It uses the Rayleigh number formed from Grashof and Prandtl numbers, with a critical Rayleigh threshold to account for finite-geometry effects.

With \mathrm{Ra} = \mathrm{Pr}\,\mathrm{Gr}, the model applies a buoyancy-dependent relation that transitions from conduction-dominated behavior to convection-enhanced heat transfer. For stable configurations or subcritical Rayleigh number, the result returns to the conduction limit.

\mathrm{Nu} = 1 \quad \text{for } \mathrm{Ra} < \mathrm{Ra}_c \text{ or when buoyancy is not assisting convection}

Excel Usage

=NU_RA_HOLLANDS(Pr, Gr, buoyancy, Rac)

Pr (float, required): Prandtl number with respect to fluid properties (-).
Gr (float, required): Grashof number with respect to fluid properties and plate temperature difference (-).
buoyancy (bool, optional, default: true): Whether convection is buoyancy assisted (hot plate) (-).
Rac (float, optional, default: 1708): Critical Rayleigh number (-).

Returns (float): Nusselt number between plates, or error message if invalid.

Example 1: Hollands correlation at high Rayleigh

Inputs:

Pr	Gr	buoyancy
5.54	321000000	true

Excel formula:

=NU_RA_HOLLANDS(5.54, 321000000, TRUE)

Expected output:

69.0267

Example 2: Hollands correlation with custom critical Rayleigh

Inputs:

Pr	Gr	buoyancy	Rac
0.7	3210000	true	2530.5

Excel formula:

=NU_RA_HOLLANDS(0.7, 3210000, TRUE, 2530.5)

Expected output:

8.81176

Example 3: Hollands correlation with buoyancy opposed

Inputs:

Pr	Gr	buoyancy
0.7	1000000	false

Excel formula:

=NU_RA_HOLLANDS(0.7, 1000000, FALSE)

Expected output:

1

Example 4: Hollands correlation with insulated critical Rayleigh

Inputs:

Pr	Gr	buoyancy	Rac
7	10000000	true	2071.0089443385655

Excel formula:

=NU_RA_HOLLANDS(7, 10000000, TRUE, 2071.0089443385655)

Expected output:

26.082

Python Code

Show Code

from ht.conv_free_enclosed import Nu_Nusselt_Rayleigh_Hollands as ht_Nu_Nusselt_Rayleigh_Hollands

def Nu_Ra_Hollands(Pr, Gr, buoyancy=True, Rac=1708):
    """
    Calculate the Nusselt number between horizontal plates using the Hollands correlation.

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

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

    Args:
        Pr (float): Prandtl number with respect to fluid properties (-).
        Gr (float): Grashof number with respect to fluid properties and plate temperature difference (-).
        buoyancy (bool, optional): Whether convection is buoyancy assisted (hot plate) (-). Default is True.
        Rac (float, optional): Critical Rayleigh number (-). Default is 1708.

    Returns:
        float: Nusselt number between plates, or error message if invalid.
    """
    try:
        return ht_Nu_Nusselt_Rayleigh_Hollands(Pr=Pr, Gr=Gr, buoyancy=buoyancy, Rac=Rac)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Pr *

Prandtl number with respect to fluid properties (-).

Gr *

Grashof number with respect to fluid properties and plate temperature difference (-).

buoyancy

Whether convection is buoyancy assisted (hot plate) (-).

Rac

Critical Rayleigh number (-).

NU_RA_HOLLINGHERWIG

This function evaluates the Holling-Herwig correlation for natural convection between effectively infinite horizontal plates in a Rayleigh-Bénard configuration. It is intended for idealized geometry where one plate dimension is much larger than the other.

The correlation uses \mathrm{Ra} = \mathrm{Pr}\,\mathrm{Gr} in a nonlinear expression that captures turbulent free-convection scaling over high Rayleigh numbers. At low Rayleigh number or when buoyancy does not assist motion, the result falls back to the conduction baseline.

\mathrm{Nu} = 1 \quad \text{for } \mathrm{Ra} < 1708 \text{ or when buoyancy is not assisting convection}

Excel Usage

=NU_RA_HOLLINGHERWIG(Pr, Gr, buoyancy)

Pr (float, required): Prandtl number with respect to fluid properties (-).
Gr (float, required): Grashof number with respect to fluid properties and plate temperature difference (-).
buoyancy (bool, optional, default: true): Whether convection is buoyancy assisted (hot plate) (-).

Returns (float): Nusselt number between plates, or error message if invalid.

Example 1: Holling-Herwig correlation at high Rayleigh

Inputs:

Pr	Gr	buoyancy
5.54	321000000	true

Excel formula:

=NU_RA_HOLLINGHERWIG(5.54, 321000000, TRUE)

Expected output:

77.5466

Example 2: Holling-Herwig correlation at medium Rayleigh

Inputs:

Pr	Gr	buoyancy
0.71	10000000	true

Excel formula:

=NU_RA_HOLLINGHERWIG(0.71, 10000000, TRUE)

Expected output:

14.1806

Example 3: Holling-Herwig correlation near onset

Inputs:

Pr	Gr	buoyancy
1	50000	true

Excel formula:

=NU_RA_HOLLINGHERWIG(1, 50000, TRUE)

Expected output:

3.95402

Example 4: Holling-Herwig correlation with buoyancy opposed

Inputs:

Pr	Gr	buoyancy
0.9	2000000	false

Excel formula:

=NU_RA_HOLLINGHERWIG(0.9, 2000000, FALSE)

Expected output:

1

Python Code

Show Code

from ht.conv_free_enclosed import Nu_Nusselt_Rayleigh_Holling_Herwig as ht_Nu_Nusselt_Rayleigh_Holling_Herwig

def Nu_Ra_HollingHerwig(Pr, Gr, buoyancy=True):
    """
    Calculate the Nusselt number between infinite horizontal plates using the Holling-Herwig correlation.

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

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

    Args:
        Pr (float): Prandtl number with respect to fluid properties (-).
        Gr (float): Grashof number with respect to fluid properties and plate temperature difference (-).
        buoyancy (bool, optional): Whether convection is buoyancy assisted (hot plate) (-). Default is True.

    Returns:
        float: Nusselt number between plates, or error message if invalid.
    """
    try:
        return ht_Nu_Nusselt_Rayleigh_Holling_Herwig(Pr=Pr, Gr=Gr, buoyancy=buoyancy)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Pr *

Prandtl number with respect to fluid properties (-).

Gr *

Grashof number with respect to fluid properties and plate temperature difference (-).

buoyancy

Whether convection is buoyancy assisted (hot plate) (-).

NU_RA_PROBERT

This function calculates the Nusselt number for free convection between idealized horizontal plates using the Probert correlation. The model uses the Rayleigh number \mathrm{Ra} = \mathrm{Pr}\,\mathrm{Gr} and applies different power-law expressions by regime.

In the laminar range, heat transfer follows a quarter-power scaling, while higher Rayleigh values use a one-third-power turbulent-style relation. If buoyancy is not assisting or the Rayleigh number is below onset, the correlation returns the conduction limit.

\mathrm{Nu} = \begin{cases} 0.208\,\mathrm{Ra}^{0.25}, & 1708 < \mathrm{Ra} \le 2.2\times 10^4 \\ 0.092\,\mathrm{Ra}^{1/3}, & \mathrm{Ra} > 2.2\times 10^4 \end{cases}

Excel Usage

=NU_RA_PROBERT(Pr, Gr, buoyancy)

Pr (float, required): Prandtl number with respect to fluid properties (-).
Gr (float, required): Grashof number with respect to fluid properties and plate temperature difference (-).
buoyancy (bool, optional, default: true): Whether convection is buoyancy assisted (hot plate) (-).

Returns (float): Nusselt number between plates, or error message if invalid.

Example 1: Probert correlation at high Rayleigh

Inputs:

Pr	Gr	buoyancy
5.54	321000000	true

Excel formula:

=NU_RA_PROBERT(5.54, 321000000, TRUE)

Expected output:

111.462

Example 2: Probert correlation in laminar regime

Inputs:

Pr	Gr	buoyancy
0.7	20000	true

Excel formula:

=NU_RA_PROBERT(0.7, 20000, TRUE)

Expected output:

2.26254

Example 3: Probert correlation in turbulent regime

Inputs:

Pr	Gr	buoyancy
0.7	10000000	true

Excel formula:

=NU_RA_PROBERT(0.7, 10000000, TRUE)

Expected output:

17.599

Example 4: Probert correlation with buoyancy opposed

Inputs:

Pr	Gr	buoyancy
0.9	1000000	false

Excel formula:

=NU_RA_PROBERT(0.9, 1000000, FALSE)

Expected output:

1

Python Code

Show Code

from ht.conv_free_enclosed import Nu_Nusselt_Rayleigh_Probert as ht_Nu_Nusselt_Rayleigh_Probert

def Nu_Ra_Probert(Pr, Gr, buoyancy=True):
    """
    Calculate the Nusselt number between infinite horizontal plates using the Probert correlation.

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

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

    Args:
        Pr (float): Prandtl number with respect to fluid properties (-).
        Gr (float): Grashof number with respect to fluid properties and plate temperature difference (-).
        buoyancy (bool, optional): Whether convection is buoyancy assisted (hot plate) (-). Default is True.

    Returns:
        float: Nusselt number between plates, or error message if invalid.
    """
    try:
        return ht_Nu_Nusselt_Rayleigh_Probert(Pr=Pr, Gr=Gr, buoyancy=buoyancy)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Pr *

Prandtl number with respect to fluid properties (-).

Gr *

Grashof number with respect to fluid properties and plate temperature difference (-).

buoyancy

Whether convection is buoyancy assisted (hot plate) (-).

NU_VERT_THESS

This function computes the natural-convection Nusselt number between vertical plates using the Thess correlation. It supports both a general Rayleigh-based form and a geometry-adjusted form when plate height and length are provided.

Using \mathrm{Ra} = \mathrm{Pr}\,\mathrm{Gr}, the correlation applies a regime-dependent scaling and optionally adjusts by aspect ratio H/L. This allows a simple estimate when geometry is unknown and a more specific estimate when dimensions are available.

\mathrm{Nu} = 0.42\,\mathrm{Pr}^{0.012}\,\mathrm{Ra}^{0.25}\left(\frac{H}{L}\right)^{-0.25}

Excel Usage

=NU_VERT_THESS(Pr, Gr, H, L)

Pr (float, required): Prandtl number with respect to fluid properties (-).
Gr (float, required): Grashof number with respect to fluid properties and plate temperature difference (-).
H (float, optional, default: null): Height of vertical plate (m).
L (float, optional, default: null): Length of vertical plate (m).

Returns (float): Nusselt number between plates, or error message if invalid.

Example 1: Thess correlation without geometry

Inputs:

Pr	Gr
0.7	3210000

Excel formula:

=NU_VERT_THESS(0.7, 3210000)

Expected output:

6.11259

Example 2: Thess correlation with plate geometry

Inputs:

Pr	Gr	L	H
0.7	3210000	10	1

Excel formula:

=NU_VERT_THESS(0.7, 3210000, 10, 1)

Expected output:

28.7933

Example 3: Thess correlation with small aspect ratio

Inputs:

Pr	Gr	L	H
1.2	500000	2	0.5

Excel formula:

=NU_VERT_THESS(1.2, 500000, 2, 0.5)

Expected output:

16.5673

Example 4: Thess correlation at higher Rayleigh

Inputs:

Pr	Gr
0.9	100000000

Excel formula:

=NU_VERT_THESS(0.9, 100000000)

Expected output:

20.6584

Python Code

Show Code

from ht.conv_free_enclosed import Nu_Nusselt_vertical_Thess as ht_Nu_Nusselt_vertical_Thess

def Nu_Vert_Thess(Pr, Gr, H=None, L=None):
    """
    Calculate the Nusselt number between vertical plates using the Thess correlation.

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

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

    Args:
        Pr (float): Prandtl number with respect to fluid properties (-).
        Gr (float): Grashof number with respect to fluid properties and plate temperature difference (-).
        H (float, optional): Height of vertical plate (m). Default is None.
        L (float, optional): Length of vertical plate (m). Default is None.

    Returns:
        float: Nusselt number between plates, or error message if invalid.
    """
    try:
        return ht_Nu_Nusselt_vertical_Thess(Pr=Pr, Gr=Gr, H=H, L=L)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Pr *

Prandtl number with respect to fluid properties (-).

Gr *

Grashof number with respect to fluid properties and plate temperature difference (-).

Height of vertical plate (m).

Length of vertical plate (m).

NU_VHELIX_ALI

This function returns the natural-convection Nusselt number for a vertical helical coil using the Ali correlation. It is intended for coil-in-tank applications where convection occurs in the surrounding fluid.

The model uses Prandtl and Grashof numbers to estimate heat-transfer enhancement relative to conduction based on an empirical power-law fit.

\mathrm{Nu}_L = 0.555\,\mathrm{Gr}_L^{0.301}\,\mathrm{Pr}^{0.314}

Excel Usage

=NU_VHELIX_ALI(Pr, Gr)

Pr (float, required): Prandtl number of the surrounding fluid (-).
Gr (float, required): Grashof number of the surrounding fluid (-).

Returns (float): Nusselt number for a vertical helical coil, or error message if invalid.

Example 1: Ali correlation example

Inputs:

Pr	Gr
4.4	100000000000

Excel formula:

=NU_VHELIX_ALI(4.4, 100000000000)

Expected output:

1808.58

Example 2: Ali correlation at mid range

Inputs:

Pr	Gr
10	10000000000

Excel formula:

=NU_VHELIX_ALI(10, 10000000000)

Expected output:

1170.29

Example 3: Ali correlation with higher Prandtl number

Inputs:

Pr	Gr
100	50000000000

Excel formula:

=NU_VHELIX_ALI(100, 50000000000)

Expected output:

3914.56

Example 4: Ali correlation with lower Prandtl number

Inputs:

Pr	Gr
5	1000000000

Excel formula:

=NU_VHELIX_ALI(5, 1000000000)

Expected output:

470.727

Python Code

Show Code

from ht.conv_free_enclosed import Nu_vertical_helical_coil_Ali as ht_Nu_vertical_helical_coil_Ali

def Nu_VHelix_Ali(Pr, Gr):
    """
    Calculate the Nusselt number for natural convection around a vertical helical coil using the Ali correlation.

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

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

    Args:
        Pr (float): Prandtl number of the surrounding fluid (-).
        Gr (float): Grashof number of the surrounding fluid (-).

    Returns:
        float: Nusselt number for a vertical helical coil, or error message if invalid.
    """
    try:
        return ht_Nu_vertical_helical_coil_Ali(Pr=Pr, Gr=Gr)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Pr *

Prandtl number of the surrounding fluid (-).

Gr *

Grashof number of the surrounding fluid (-).

NU_VHELIX_PRR

This function computes the Nusselt number for natural convection around a vertical helical coil using the Prabhanjan-Rennie-Raghavan correlation. It models external convection from the coil to surrounding fluid in a vessel.

The formulation is expressed in Rayleigh number form, where \mathrm{Ra} = \mathrm{Pr}\,\mathrm{Gr} for the selected characteristic length and temperature definition.

\mathrm{Nu}_H = 0.0749\,\mathrm{Ra}_H^{0.3421}

Excel Usage

=NU_VHELIX_PRR(Pr, Gr)

Pr (float, required): Prandtl number at film temperature (-).
Gr (float, required): Grashof number at film temperature (-).

Returns (float): Nusselt number for a vertical helical coil, or error message if invalid.

Example 1: Prabhanjan-Rennie-Raghavan correlation example

Inputs:

Pr	Gr
4.4	100000000000

Excel formula:

=NU_VHELIX_PRR(4.4, 100000000000)

Expected output:

720.621

Example 2: Prabhanjan-Rennie-Raghavan correlation at mid range

Inputs:

Pr	Gr
6	50000000000

Excel formula:

=NU_VHELIX_PRR(6, 50000000000)

Expected output:

632.128

Example 3: Prabhanjan-Rennie-Raghavan correlation at higher Rayleigh

Inputs:

Pr	Gr
8	200000000000

Excel formula:

=NU_VHELIX_PRR(8, 200000000000)

Expected output:

1120.76

Example 4: Prabhanjan-Rennie-Raghavan correlation at lower Rayleigh

Inputs:

Pr	Gr
5	20000000000

Excel formula:

=NU_VHELIX_PRR(5, 20000000000)

Expected output:

434.092

Python Code

Show Code

from ht.conv_free_enclosed import Nu_vertical_helical_coil_Prabhanjan_Rennie_Raghavan as ht_Nu_vertical_helical_coil_Prabhanjan_Rennie_Raghavan

def Nu_VHelix_PRR(Pr, Gr):
    """
    Calculate the Nusselt number for natural convection around a vertical helical coil using the Prabhanjan-Rennie-Raghavan correlation.

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

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

    Args:
        Pr (float): Prandtl number at film temperature (-).
        Gr (float): Grashof number at film temperature (-).

    Returns:
        float: Nusselt number for a vertical helical coil, or error message if invalid.
    """
    try:
        return ht_Nu_vertical_helical_coil_Prabhanjan_Rennie_Raghavan(Pr=Pr, Gr=Gr)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Pr *

Prandtl number at film temperature (-).

Gr *

Grashof number at film temperature (-).

RAC_RAYLEIGH

This function estimates the critical Rayleigh number for the onset of natural convection between enclosed parallel horizontal plates. It distinguishes insulated and uninsulated top-boundary conditions, which shift the instability threshold.

The result is a geometry-dependent stability limit based on plate spacing and in-plane dimensions. This value is typically used as an input to enclosed-convection Nusselt correlations.

\mathrm{Ra}_c = f\!\left(\frac{L}{H},\frac{W}{H},\text{boundary condition}\right)

Excel Usage

=RAC_RAYLEIGH(H, L, W, insulated)

H (float, required): Distance between the two plates (m).
L (float, required): Length of the plates (m).
W (float, required): Width of the plates (m).
insulated (bool, optional, default: true): Whether the top plate is insulated (-).

Returns (float): Critical Rayleigh number, or error message if invalid.

Example 1: Critical Rayleigh for uninsulated top plate

Inputs:

H	L	W	insulated
1	0.5	2	false

Excel formula:

=RAC_RAYLEIGH(1, 0.5, 2, FALSE)

Expected output:

2530.5

Example 2: Critical Rayleigh for insulated top plate

Inputs:

H	L	W	insulated
1	0.5	2	true

Excel formula:

=RAC_RAYLEIGH(1, 0.5, 2, TRUE)

Expected output:

2071.01

Example 3: Critical Rayleigh for square plates

Inputs:

H	L	W	insulated
1	1	1	false

Excel formula:

=RAC_RAYLEIGH(1, 1, 1, FALSE)

Expected output:

6974

Example 4: Critical Rayleigh for thin gap

Inputs:

H	L	W	insulated
0.2	1	2	true

Excel formula:

=RAC_RAYLEIGH(0.2, 1, 2, TRUE)

Expected output:

16998.4

Python Code

Show Code

from ht.conv_free_enclosed import Rac_Nusselt_Rayleigh as ht_Rac_Nusselt_Rayleigh

def Rac_Rayleigh(H, L, W, insulated=True):
    """
    Calculate the critical Rayleigh number for enclosed parallel plates.

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

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

    Args:
        H (float): Distance between the two plates (m).
        L (float): Length of the plates (m).
        W (float): Width of the plates (m).
        insulated (bool, optional): Whether the top plate is insulated (-). Default is True.

    Returns:
        float: Critical Rayleigh number, or error message if invalid.
    """
    try:
        return ht_Rac_Nusselt_Rayleigh(H=H, L=L, W=W, insulated=insulated)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

H *

Distance between the two plates (m).

L *

Length of the plates (m).

W *

Width of the plates (m).

insulated

Whether the top plate is insulated (-).

RAC_RAYLEIGH_DISK

This function computes the critical Rayleigh number for the onset of natural convection between enclosed parallel disks. It supports insulated and uninsulated top-boundary cases, each with different stability thresholds.

The critical value depends on the disk aspect ratio through spacing and diameter, and is commonly used to determine when convection begins in enclosed disk geometries.

\mathrm{Ra}_c = f\!\left(\frac{D}{H},\text{boundary condition}\right)

Excel Usage

=RAC_RAYLEIGH_DISK(H, D, insulated)

H (float, required): Distance between the two disks (m).
D (float, required): Diameter of the disks (m).
insulated (bool, optional, default: true): Whether the top disk is insulated (-).

Returns (float): Critical Rayleigh number for disks, or error message if invalid.

Example 1: Critical Rayleigh for small uninsulated disks

Inputs:

H	D	insulated
1	0.4	false

Excel formula:

=RAC_RAYLEIGH_DISK(1, 0.4, FALSE)

Expected output:

151200

Example 2: Critical Rayleigh for large uninsulated disks

Inputs:

H	D	insulated
1	4	false

Excel formula:

=RAC_RAYLEIGH_DISK(1, 4, FALSE)

Expected output:

1891.52

Example 3: Critical Rayleigh for insulated disks

Inputs:

H	D	insulated
2	1	true

Excel formula:

=RAC_RAYLEIGH_DISK(2, 1, TRUE)

Expected output:

24347.3

Example 4: Critical Rayleigh at mid aspect ratio

Inputs:

H	D	insulated
0.5	1	true

Excel formula:

=RAC_RAYLEIGH_DISK(0.5, 1, TRUE)

Expected output:

2266.9

Python Code

Show Code

from ht.conv_free_enclosed import Rac_Nusselt_Rayleigh_disk as ht_Rac_Nusselt_Rayleigh_disk

def Rac_Rayleigh_disk(H, D, insulated=True):
    """
    Calculate the critical Rayleigh number for enclosed parallel disks.

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

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

    Args:
        H (float): Distance between the two disks (m).
        D (float): Diameter of the disks (m).
        insulated (bool, optional): Whether the top disk is insulated (-). Default is True.

    Returns:
        float: Critical Rayleigh number for disks, or error message if invalid.
    """
    try:
        return ht_Rac_Nusselt_Rayleigh_disk(H=H, D=D, insulated=insulated)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

H *

Distance between the two disks (m).

D *

Diameter of the disks (m).

insulated

Whether the top disk is insulated (-).