Slab¶

class pychemengg.heattransfer.steadystate.Slab(thickness=None, area=None, thermalconductivity=None)[source]¶

Bases: object

Models a rectangular object

Parameters

thicknessint or float: Thickness of rectangular slab
areaint or float: Area of rectangular slab (if area is not known put area = 1.0)
thermalconductivityint or float: Thermal conductivity of rectangular slab

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 
>>> innerWall = ss.Slab(thickness=0.13, thermalconductivity=0.7, area=1.0)
# This will create an instance of 'Slab' with a name 'innerwall' 

Attributes

thicknessint or float: Thickness of rectangular slab
areaint or float: Area of rectangular slab
thermalconductivityint or float: Thermal conductivity of rectangular slab

__init__(thickness=None, area=None, thermalconductivity=None)[source]¶

Methods

`__init__`([thickness, area, thermalconductivity])
`heatrateof_cond`([dT])	Computes heat rate of conduction for a rectangular object
`heatrateof_conv`([heattransfercoefficient, dT])	Computes heat rate of convection for a rectangular object
`heatrateof_rad`([T_infinity, T_surface, …])	Computes heat rate of radiation for a rectangular object
`resistanceof_cond`()	Computes resistance of conduction for a rectangular object
`resistanceof_conv`([heattransfercoefficient])	Computes resistance of convection for a rectangular object
`resistanceof_fouling`([foulingfactor])	Computes resistance of fouling for a rectangular object

heatrateof_cond(dT=None)[source]¶

Computes heat rate of conduction for a rectangular object

Parameters

dTint or float: Temperature difference between two faces of a slab

Returns

heatrateint or float: rate of heat transfer by conduction

Notes

Heat rate of conduction is calculated using the Fourier’s Law

\[Q (heatrate) = k A \frac{\Delta T}{\Delta x} \]

where:

k = thermal conductivity

A = area of heat transfer

\(\Delta T\) = temperature difference

\(\Delta x\) = slab thickness

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
>>> wall = ss.Slab(thickness=0.13, thermalconductivity=0.7, area=1.0)
>>> wall.heatrateof_cond(dT=100)
538.4615384615385

heatrateof_conv(heattransfercoefficient=None, dT=None)[source]¶

Computes heat rate of convection for a rectangular object

Parameters

heattransfercoefficientint or float: Heat transfer coefficient `h` for the slab surface
dTint or float: Temperature difference between slab 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
>>> wall = ss.Slab(thickness=0.13, thermalconductivity=0.7, area=1.0)
>>> wall.heatrateof_conv(heattransfercoefficient=134.0, dT=60)
8040.0

heatrateof_rad(T_infinity=None, T_surface=None, emissivity=None)[source]¶

Computes heat rate of radiation for a rectangular object

Parameters

T_infinityint or float: Temperature of surroundings in absolute temperature units
T_surfaceint or float: Temperature of slab surface in absolute temperature units
emissivityint or float: Emissivity of the slab

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

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

\(T_{surface}\) = 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
>>> wall = ss.Slab(area=1.4)
>>> wall.heatrateof_rad(T_infinity=10+273, T_surface=30+273, emissivity=0.95)
151.93639338614008

resistanceof_cond()[source]¶

Computes resistance of conduction for a rectangular object

Parameters

`None_required`‘None’: Uses attributes defined during instance creation

Returns

resistanceint or float: Conduction resistance

Notes

The following formula is used:

\[R_{conduction} = \frac{L}{kA} \]

where:

L = thickness

k = thermal conductivity

A = surface area of heat transfer

\(R_{conduction}\) = 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
>>> wall = ss.Slab(thickness=0.3, thermalconductivity=0.9, area=15)
>>> wall.resistanceof_cond()
0.022222222222222223

resistanceof_conv(heattransfercoefficient=None)[source]¶

Computes resistance of convection for a rectangular object

Parameters

heattransfercoefficientint or float: Heat transfer coefficient `h` for the slab surface

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
>>> wall = ss.Slab(thickness=0.3, thermalconductivity=0.9, area=0.25*1)
>>> wall.resistanceof_conv(heattransfercoefficient=10)
0.4

resistanceof_fouling(foulingfactor=None)[source]¶

Computes resistance of fouling for a rectangular object

Parameters

foulingfactorint or float

Fouling factor \(R_f\) for the slab 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
>>> wall = ss.Slab(thickness=0.3, thermalconductivity=0.9, area=0.25*1)
>>> wall.resistanceof_fouling(foulingfactor=0.0007)
0.0028