Cylinder

class pychemengg.heattransfer.steadystate.Cylinder(length=None, inner_radius=None, outer_radius=None, thermalconductivity=None)

Bases: object

Models a cylindrical object

Parameters

lengthint or float

Length of cylindrical object (if length is not known put length = 1.0)

inner_radius: `int or float`

Inner radius of cylindrical object

outer_radius: `int or float`

Outer radius of cylindrical object

thermalconductivityint or float

Thermal conductivity of cylindrical object

Examples

First import the module steadystate

Units used in this example: SI system

However, any consistent units can be used

>>> from pychemengg.heattransfer import steadystate as ss
>>> insulation = Cylinder(length=5, inner_radius=1.5e-3, outer_radius=3.5e-3, thermalconductivity=0.15)
# This will create an instance of 'Cylinder' with a name 'insulation'  

Attributes

lengthint or float

Length of cylindrical object (if length is not known put length = 1.0)

inner_radius: `int or float`

Inner radius of cylindrical object

outer_radius: `int or float`

Outer radius of cylindrical object

thermalconductivityint or float

Thermal conductivity of cylindrical object

__init__(length=None, inner_radius=None, outer_radius=None, thermalconductivity=None)

Methods

__init__([length, inner_radius, …])
area([radius])	Computes surface area of a cylinder
heatrateof_cond([dT])	Computes heat rate of conduction for a cylindrical object
heatrateof_conv([heattransfercoefficient, …])	Computes heat rate of convection for a cylindrical object
heatrateof_rad([radius, T_infinity, …])	Computes heat rate of radiation for a cylindrical object
resistanceof_cond()	Computes resistance of conduction for a cylindrical object
resistanceof_conv([heattransfercoefficient, …])	Computes resistance of convection for a cylindrical object
resistanceof_fouling([foulingfactor, radius])	Computes resistance of fouling for a cylindrical object
volume([radius])	Computes volume of a cylinder

area(radius=None)

Computes surface area of a cylinder

Parameters

radiusint or float

Radius at which surface area is to be computed

Returns

areaint or float

Surface area of cylinder

Notes

Surface area of cylinder is computed using:

\[A = 2\pi rL \]

where:

r = radius

L = length

A = surface area

Examples

First import the module steadystate

Units used in this example: SI system

However, any consistent units can be used

>>> from pychemengg.heattransfer import steadystate as ss

>>> insulation = Cylinder(length=5, inner_radius=1.5e-3, outer_radius=3.5e-3, thermalconductivity=0.15)
# This will create an instance of 'Cylinder' with a name 'insulation'

>>> insulation.area(radius=insulation.outer_radius)
0.10995574287564275
# This computes surface area @ outer radius

>>> insulation.area(radius=insulation.inner_radius)
0.047123889803846894
# This computes surface area @ inner radius

>>> insulation.area(radius=1.5e-3)
0.047123889803846894
# This will also compute surface area @ inner radius, which is = 1.5e-3.
# Here the radius is entered as a number directly, rather than as an attribute.

heatrateof_cond(dT=None)

Computes heat rate of conduction for a cylindrical object

Parameters

dTint or float

Temperature difference between two surfaces of the cylinder

Returns

heatrateint or float

Rate of heat transfer by conduction

Notes

The following formula is used:

\[Q (heatrate) = \frac{\Delta T}{R_{conduction}} \]

where:

\(\Delta T\) = temperature difference

\(R_{conduction}\) = conduction resistance given by

\(R_{conduction} = \cfrac{ln(r_o/r_i)}{2\pi kL}\)

\(r_o\) = outer radius of cylinder

\(r_i\) = inner radius of cylinder

L = length

k = thermal conductivity

References

[1] Yunus A. Cengel and Afshin J. Ghajar, “Heat And Mass Transfer Fundamentals and Applications”, 6th Edition. New York, McGraw Hill Education, 2020

Examples

First import the module steadystate

Units used in this example: SI system

However, any consistent units can be used

>>> from pychemengg.heattransfer import steadystate as ss
>>> insulation = Cylinder(length=5, inner_radius=1.5e-3, outer_radius=3.5e-3, thermalconductivity=0.15)
>>> insulation.heatrateof_cond(dT=75)
417.12506315941755

heatrateof_conv(heattransfercoefficient=None, radius=None, dT=None)

Computes heat rate of convection for a cylindrical object

Parameters

heattransfercoefficientint or float

Heat transfer coefficient `h` for the cylinder surface

radiusint or float

Radius of cylinder where convective heat transfer rate is to be computed

dTint or float

Temperature difference between cylinder surface and surrounding fluid

Returns

heatrateint or float

Rate of heat transfer by convection

Notes

Heat rate of convection is calculated using the Newton’s Law

\[Q (heatrate) = h A \Delta T \]

where:

h = heat transfer coefficient

A = area of heat transfer

\(\Delta T\) = temperature difference

References

[1] Yunus A. Cengel and Afshin J. Ghajar, “Heat And Mass Transfer Fundamentals and Applications”, 6th Edition. New York, McGraw Hill Education, 2020

Examples

First import the module steadystate

Units used in this example: SI system

However, any consistent units can be used

>>> from pychemengg.heattransfer import steadystate as ss
>>> insulation = Cylinder(length=5, inner_radius=1.5e-3, outer_radius=3.5e-3, thermalconductivity=0.15)
>>> insulation.heatrateof_conv(heattransfercoefficient=12, radius=insulation.outer_radius, dT=90.6-30)
79.9598162191674
# NOTE: Mathematical expressions (such as: 90.6 - 30) can be used as an argument

heatrateof_rad(radius=None, T_infinity=None, T_surface=None, emissivity=None)

Computes heat rate of radiation for a cylindrical object

Parameters

radiusint or float

Radius of cylinder where radiation heat transfer rate is to be computed

T_infinityint or float

Temperature of surroundings in absolute temperature units

T_surfaceint or float

Temperature of cylinder surface in absolute temperature units

emissivityint or float

Emissivity of the cylinder

Returns

heatrateint or float (returns a positive value)

Rate of heat transfer by radiation

Notes

Heat rate of radiation is calculated using the Stefan-Boltzmann law

\[Q (heatrate) = \sigma \epsilon A (T_{infinity}^4 - T_{surface}^4) \]

where:

\(\sigma\) = Stefan-Boltzmann constant

\(\epsilon\) = emissivity of object

A = area of heat transfer

\(T_{infinity}^4\) = absolute temperature of surroundings

\(T_{surface}^4\) = absolute temperature of surface

References

[1] Yunus A. Cengel and Afshin J. Ghajar, “Heat And Mass Transfer Fundamentals and Applications”, 6th Edition. New York, McGraw Hill Education, 2020

Examples

First import the module steadystate

Units used in this example: SI system

However, any consistent units can be used

>>> from pychemengg.heattransfer import steadystate as ss
>>> insulation = Cylinder(length=5, inner_radius=1.5e-3, outer_radius=3.5e-3, thermalconductivity=0.15)
>>> insulation.heatrateof_rad(radius=insulation.outer_radius, T_infinity=30+273, T_surface=90.6+273, emissivity=0.95)
53.60018341250309

resistanceof_cond()

Computes resistance of conduction for a cylindrical object

Parameters

`None_required`‘None’

Uses attributes defined during instance creation

Returns

resistanceint or float

Conduction resistance

Notes

The following formula is used:

\[R_{conduction} = \cfrac{ln(r_o/r_i)}{2\pi kL}\]

where:

\(r_o\) = outer radius of cylinder

\(r_i\) = inner radius of cylinder

L = thickness

k = thermal conductivity

\(R_{conduction}\) = conduction resistance

References

[1] Yunus A. Cengel and Afshin J. Ghajar, “Heat And Mass Transfer Fundamentals and Applications”, 6th Edition. New York, McGraw Hill Education, 2020

Examples

First import the module steadystate

Units used in this example: SI system

However, any consistent units can be used

>>> from pychemengg.heattransfer import steadystate as ss
>>> insulation = Cylinder(length=5, inner_radius=1.5e-3, outer_radius=3.5e-3, thermalconductivity=0.15)
>>> insulation.resistanceof_cond()
0.1798021903357468

resistanceof_conv(heattransfercoefficient=None, radius=None)

Computes resistance of convection for a cylindrical object

Parameters

heattransfercoefficientint or float

Heat transfer coefficient `h` for the cylindrical surface

radiusint or float

Radius of cylinder where convective heat transfer is to be computed

Returns

resistanceint or float

Convection resistance

Notes

The following formula is used:

\[R_{convection} = \frac{1}{hA} \]

where:

h = heat transfer coefficient

A = area of heat transfer

\(R_{convection}\) = convection resistance

References

[1] Yunus A. Cengel and Afshin J. Ghajar, “Heat And Mass Transfer Fundamentals and Applications”, 6th Edition. New York, McGraw Hill Education, 2020

Examples

First import the module steadystate

Units used in this example: SI system

However, any consistent units can be used

>>> from pychemengg.heattransfer import steadystate as ss
>>> insulation = Cylinder(length=5, inner_radius=1.5e-3, outer_radius=3.5e-3, thermalconductivity=0.15)
>>> insulation.resistanceof_conv(heattransfercoefficient=12, radius=insulation.outer_radius)
0.7578806813899779

resistanceof_fouling(foulingfactor=None, radius=None)

Computes resistance of fouling for a cylindrical object

Parameters

foulingfactorint or float

Fouling factor \(R_f\) for the cylindrical surface

typical units are \(m^2\) K/W

Returns

resistanceint or float

Fouling resistance

Notes

The following formula is used:

\[R_{fouling} = \frac{R_f}{A} \]

where:

\(R_f\) = fouling factor

A = fouled area of heat transfer

\(R_{fouling}\) = fouling resistance

References

[1] Yunus A. Cengel and Afshin J. Ghajar, “Heat And Mass Transfer Fundamentals and Applications”, 6th Edition. New York, McGraw Hill Education, 2020

Examples

First import the module steadystate

Units used in this example: SI system

However, any consistent units can be used

>>> from pychemengg.heattransfer import steadystate as ss
>>> insulation = Cylinder(length=5, inner_radius=1.5e-3, outer_radius=3.5e-3, thermalconductivity=0.15)
>>> insulation.resistanceof_fouling(foulingfactor=0.0007, radius=insulation.outer_radius)
0.006366197723675814

volume(radius=None)

Computes volume of a cylinder

Parameters

radiusint or float

Radius at which volume is to be computed

Returns

volumeint or float

Volume of cylinder

Notes

Volume of cylinder is computed using:

\[V = \pi r^2 L \]

where:

r = radius

L = length

V = volume

Examples

First import the module steadystate

Units used in this example: SI system

However, any consistent units can be used

>>> insulation = Cylinder(length=5, inner_radius=1.5e-3, outer_radius=3.5e-3, thermalconductivity=0.15)
This will create an instance of 'Cylinder' with a name 'insulation'

>>> insulation.volume(radius=insulation.outer_radius)
0.00019242255003237485
# This computes volume @ outer radius

>>> insulation.volume(radius=insulation.inner_radius)
3.534291735288517e-05
# This computes volume @ inner radius

>>>  insulation.volume(radius=1.5e-3)
3.534291735288517e-05
# This will also compute volume @ inner radius, which is = 1.5e-3.
# Here the radius is entered as a number directly, rather than as an attribute.