Plate

class pychemengg.heattransfer.externalflow.Plate

Bases: object

Models external flow over flat plat.

Parameters

`None_required`‘None’

This class takes no parameters for instance creation.

Examples

First import the module externalflow.

>>> from pychemengg.heattransfer import externalflow as extflow 
>>> plateobject = extflow.Plate()
# This will create an instance of the class 'Plate'.
# Methods of the class 'Plate' can then be called like so :-
# plateobject.method(kwarg1=x, ...)

Attributes

`None_required`‘None’

This class does not expose any instance attributes.

__init__(*args, **kwargs)

Methods

Nu_laminar_average([Re, Pr])	Average Nusselt number for isothermal laminar flow on flat plate.
Nu_laminar_local([Re, Pr])	Local Nusselt number for isothermal laminar flow on flat plate.
Nu_mixed_average([Re, Pr, Re_critical])	Average Nusselt number for isothermal ‘laminar + turbulent’ flow on flat plate.
Nu_turbulent_average([Re, Pr])	Average Nusselt number for isothermal turbulent flow on flat plate.
Nu_turbulent_local([Re, Pr])	Local Nusselt number for isothermal turbulent flow on flat plate.
Nu_unheated_laminar_average([Re, Pr, …])	Average Nusselt number for isothermal laminar flow on flat plate with unheated starting length.
Nu_unheated_laminar_local([Re, Pr, …])	Local Nusselt number for isothermal laminar flow on flat plate with unheated starting length.
Nu_unheated_turbulent_average([Re, Pr, …])	Average Nusselt number for isothermal turbulent flow on flat plate with unheated starting length.
Nu_unheated_turbulent_local([Re, Pr, …])	Local Nusselt number for isothermal turbulent flow on flat plate with unheated starting length.
Nu_uniformflux_laminar_average([Re, Pr])	Average Nusselt number for laminar flow on flat plate with uniform heat flux.
Nu_uniformflux_laminar_local([Re, Pr])	Local Nusselt number for laminar flow on flat plate with uniform heat flux.
Nu_uniformflux_turbulent_average([Re, Pr])	Average Nusselt number for turbulent flow on flat plate with uniform heat flux.
Nu_uniformflux_turbulent_local([Re, Pr])	Local Nusselt number for turbulent flow on flat plate with uniform heat flux.
__init__(*args, **kwargs)

Nu_laminar_average(Re=None, Pr=None)

Average Nusselt number for isothermal laminar flow on flat plate.

Parameters

Reint or float

Reynolds number for full length ‘L’ of plate.

Print or float

Prandtl number for the fluid.

Returns

Nuint or float

Average Nusselt number for laminar flow on flat plate.

Warning

A Nusselt number is returned based on the equation even if parameters (such as Re, Pr) do not fall in their respective allowable range limits (see above under ‘Notes’). However, if this happens, a warning is issued.

Notes

The following formula is used:

\[Nu = 0.664 Re^{0.5} Pr^{1/3}\]

where:

\(Pr > 0.6\)

\(Re < 5 * 10^5\)

Fluid properties are at film temp (\(T_{film}\)):

\(T_{film} = (T_{infinity} + T_{surface})/2\)

\(T_{infinity}\) = temperature of fluid away from surface

\(T_{surface}\) = 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 externalflow.

>>> from pychemengg.heattransfer import externalflow as extflow 
>>> plateobject = extflow.Plate()
# This will create an instance of the class 'Plate'.
# Then call the method like so :-
>>> plateobject.Nu_laminar_average(Re=4.024e4, Pr=2962)
1912.899190840437

Nu_laminar_local(Re=None, Pr=None)

Local Nusselt number for isothermal laminar flow on flat plate.

Parameters

Reint or float

Reynolds number at location/length ‘x’ on plate.

Print or float

Prandtl number for the fluid.

Returns

Nuint or float

Local Nusselt number at location/length ‘x’ on plate.

Warning

A Nusselt number is returned based on the equation even if parameters (such as Re, Pr) do not fall in their respective allowable range limits (see above under ‘Notes’). However, if this happens, a warning is issued.

Notes

The following formula is used:

\[Nu = 0.332 Re^{0.5} Pr^{1/3}\]

where:

\(Pr > 0.6\)

\(Re < 5 * 10^5\)

Fluid properties are at film temp (\(T_{film}\)):

\(T_{film} = (T_{infinity} + T_{surface})/2\)

\(T_{infinity}\) = temperature of fluid away from surface

\(T_{surface}\) = 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 externalflow.

>>> from pychemengg.heattransfer import externalflow as extflow 
>>> plateobject = extflow.Plate()
# This will create an instance of the class 'Plate'.
# Then call the method like so :-
>>> plateobject.Nu_laminar_local(Re=4.024e4, Pr=2962)
956.4495954202185

Nu_mixed_average(Re=None, Pr=None, Re_critical=500000.0)

Average Nusselt number for isothermal ‘laminar + turbulent’ flow on flat plate.

Parameters

Reint or float

Reynolds number for full length ‘L’ of plate

Print or float for the fluid.

Prandtl number

Re_criticalint or float

Critical Reynolds number indicating transition between laminar <–> turbulent. Default value = \(5x10^5\).

Returns

Nuint or float

Average Nusselt number for ‘laminar + turbulent’ flow on flat plate.

Warning

A Nusselt number is returned based on the equation even if parameters (such as Re, Pr) do not fall in their respective allowable range limits (see above under ‘Notes’). However, if this happens, a warning is issued.

Notes

The following formula is used:

\[Nu = (0.037 Re^{0.8} – (0.037 Re_{critical}^{4/5} – 0.664Re_{critical}^{1/2}))Pr^{1/3}\]

where:

\(0.6 \eqslantless Pr \eqslantless 60\)

\(5*10^5 \eqslantless Re_x \eqslantless 10^7\)

\(Re_{critical}\) : is the number where fluid transitions from laminar to turbulent. This number can change from case to case, although it is often = \(5*10^5\). For example, by adding roughness to plate surface, the transition to turbulent flow can occur at lower Reynolds numbers.

Fluid properties are at film temp (\(T_{film}\)):

\(T_{film} = (T_{infinity} + T_{surface})/2\)

\(T_{infinity}\) = temperature of fluid away from surface

\(T_{surface}\) = temperature of surface

References

[1] Theodore L. Bergman, Adrienne S. Lavine, Frank P. Incropera. David P. DeWitt, “Fundamentals of Heat and Mass Transfer”, 8th Edition, Wiley.

Examples

First import the module externalflow.

>>> from pychemengg.heattransfer import externalflow as extflow 
>>> plateobject = extflow.Plate()
# This will create an instance of the class 'Plate'.
# Then call the method like so :-
>>> plateobject.Nu_mixed_average(Re=610626, Pr=0.7073, Re_critical=5e5)
625.480561991628

Nu_turbulent_average(Re=None, Pr=None)

Average Nusselt number for isothermal turbulent flow on flat plate.

Parameters

Reint or float

Reynolds number for full length ‘L’ of plate.

Print or float

Prandtl number for the fluid.

Returns

Nuint or float

Average Nusselt number for turbulent flow on flat plate.

Warning

A Nusselt number is returned based on the equation even if parameters (such as Re, Pr) do not fall in their respective allowable range limits (see above under ‘Notes’). However, if this happens, a warning is issued.

Notes

The following formula is used:

\[Nu = 0.037 Re^{0.8} Pr^{1/3}\]

where:

\(0.6 \eqslantless Pr \eqslantless 60\)

\(5*10^5 \eqslantless Re_x \eqslantless 10^7\)

Fluid properties are at film temp (\(T_{film}\)):

\(T_{film} = (T_{infinity} + T_{surface})/2\)

\(T_{infinity}\) = temperature of fluid away from surface

\(T_{surface}\) = 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 externalflow.

>>> from pychemengg.heattransfer import externalflow as extflow 
>>> plateobject = extflow.Plate()
# This will create an instance of the class 'Plate'.
# Then call the method like so :-
>>> plateobject.Nu_turbulent_average(Re=8.875e5, Pr=0.7387)
1918.1936389098291

Nu_turbulent_local(Re=None, Pr=None)

Local Nusselt number for isothermal turbulent flow on flat plate.

Parameters

Reint or float

Reynolds number at location/length ‘x’ on plate.

Print or float

Prandtl number for the fluid.

Returns

Nuint or float

Local Nusselt number at location/length ‘x’ on plate.

Warning

A Nusselt number is returned based on the equation even if parameters (such as Re, Pr) do not fall in their respective allowable range limits (see above under ‘Notes’). However, if this happens, a warning is issued.

Notes

The following formula is used:

\[Nu = 0.0296 Re^{0.8} Pr^{1/3}\]

where:

\(0.6 \eqslantless Pr \eqslantless 60\)

\(5*10^5 \eqslantless Re_x \eqslantless 10^7\)

Fluid properties are at film temp (\(T_{film}\)):

\(T_{film} = (T_{infinity} + T_{surface})/2\)

\(T_{infinity}\) = temperature of fluid away from surface

\(T_{surface}\) = 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 externalflow.

>>> from pychemengg.heattransfer import externalflow as extflow 
>>> plateobject = extflow.Plate()
# This will create an instance of the class 'Plate'.
# Then call the method like so :-
>>> plateobject.Nu_laminar_average(Re=4.024e4, Pr=2962)
1912.899190840437

Nu_unheated_laminar_average(Re=None, Pr=None, unheatedlength=None, length=None)

Average Nusselt number for isothermal laminar flow on flat plate with unheated starting length.

Parameters

Reint or float

Reynolds number on plate (plate length to be used to compute Re).

Print or float

Prandtl number for the fluid.

unheatedlengthint or float

Initial length of plate that is not participating in heat transfer.

lengthint or float

Overall length of plate.

Returns

Nuint or float

Average Nusselt number over the plate.

Warning

A Nusselt number is returned based on the equation even if parameters (such as Re, Pr) do not fall in their respective allowable range limits (see above under ‘Notes’). However, if this happens, a warning is issued.

Notes

The following formula is used:

\[Nu = \left( Nu_{for \zeta=0} \right) \left( \frac{L}{L-\zeta} \right) \left[1- \left(\frac{\zeta}{L} \right)^{3/4} \right]^{2/3}\]

where:

\(Pr > 0.6\)

\(Re < 5 * 10^5\)

\(\zeta\) = Length of plate that is not heated

L = Overall length of plate over which average Nusselt number is to be computed

Fluid properties are at film temp (\(T_{film}\)):

\(T_{film} = (T_{infinity} + T_{surface})/2\)

\(T_{infinity}\) = temperature of fluid away from surface

\(T_{surface}\) = 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 externalflow.

>>> from pychemengg.heattransfer import externalflow as extflow 
>>> plateobject = extflow.Plate()
# This will create an instance of the class 'Plate'.
# Then call the method like so :-
>>> plateobject.Nu_unheated_laminar_average(Re=61062, Pr=0.7073, unheatedlength=0.1, length=0.5)
144.1942769849126

Nu_unheated_laminar_local(Re=None, Pr=None, unheatedlength=None, xlocation_tofindNu=None)

Local Nusselt number for isothermal laminar flow on flat plate with unheated starting length.

Parameters

Reint or float

Reynolds number at location/length ‘x’ on plate.

Print or float

Prandtl number for the fluid.

unheatedlengthint or float

Initial length of plate that is not participating in heat transfer.

xlocation_tofindNuint or float

x position to find local Nusselt number

Returns

Nuint or float

Local Nusselt number at location/length ‘x’ on plate.

Warning

A Nusselt number is returned based on the equation even if parameters (such as Re, Pr) do not fall in their respective allowable range limits (see above under ‘Notes’). However, if this happens, a warning is issued.

Notes

The following formula is used:

\[Nu = \cfrac {Nu_{for\zeta=0}} {[1-(\zeta/x)^{3/4}]^{1/3}}\]

where:

\(Pr > 0.6\)

\(Re < 5 * 10^5\)

\(\zeta\) = length of plate that is not heated

x = position along length of plate where local Nusselt number is to be computed

Fluid properties are at film temp (\(T_{film}\)):

\(T_{film} = (T_{infinity} + T_{surface})/2\)

\(T_{infinity}\) = temperature of fluid away from surface

\(T_{surface}\) = 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 externalflow.

>>> from pychemengg.heattransfer import externalflow as extflow 
>>> plateobject = extflow.Plate()
# This will create an instance of the class 'Plate'.
# Then call the method like so :-
>>> plateobject.Nu_unheated_laminar_local(Re=61062, Pr=0.7073, unheatedlength=0.1, xlocation_tofindNu=0.5)
82.28737639413838

Nu_unheated_turbulent_average(Re=None, Pr=None, unheatedlength=None, length=None)

Average Nusselt number for isothermal turbulent flow on flat plate with unheated starting length.

Parameters

Reint or float

Reynolds number on plate (plate length to be used to compute Re).

Print or float

Prandtl number for the fluid.

unheatedlengthint or float

Initial length of plate that is not participating in heat transfer.

lengthint or float

Overall length of plate.

Returns

Nuint or float

Average Nusselt number over the plate.

Warning

A Nusselt number is returned based on the equation even if parameters (such as Re, Pr) do not fall in their respective allowable range limits (see above under ‘Notes’). However, if this happens, a warning is issued.

Notes

The following formula is used:

\[Nu = \left( Nu_{for \zeta=0} \right) \left( \frac{L}{L-\zeta} \right) \left[1- \left(\frac{\zeta}{L} \right)^{9/10} \right]^{8/9}\]

where:

\(0.6 \eqslantless Pr \eqslantless 60\)

\(5*10^5 \eqslantless Re_x \eqslantless 10^7\)

\(\zeta\) = Length of plate that is not heated

L = Overall length of plate over which average Nusselt number is to be computed

Fluid properties are at film temp (\(T_{film}\)):

\(T_{film} = (T_{infinity} + T_{surface})/2\)

\(T_{infinity}\) = temperature of fluid away from surface

\(T_{surface}\) = 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 externalflow.

>>> from pychemengg.heattransfer import externalflow as extflow 
>>> plateobject = extflow.Plate()
# This will create an instance of the class 'Plate'.
# Then call the method like so :-
>>> plateobject.Nu_unheated_turbulent_average(Re=610620, Pr=0.7073, unheatedlength=0.1, length=0.5)
1381.0927382916545

Nu_unheated_turbulent_local(Re=None, Pr=None, unheatedlength=None, xlocation_tofindNu=None)

Local Nusselt number for isothermal turbulent flow on flat plate with unheated starting length.

Parameters

Reint or float

Reynolds number at location/length ‘x’ on plate.

Print or float

Prandtl number for the fluid.

unheatedlengthint or float

Initial length of plate that is not participating in heat transfer.

xlocation_tofindNuint or float

x position to find local Nusselt number

Returns

Nuint or float

Local Nusselt number at location/length ‘x’ on plate.

Warning

A Nusselt number is returned based on the equation even if parameters (such as Re, Pr) do not fall in their respective allowable range limits (see above under ‘Notes’). However, if this happens, a warning is issued.

Notes

The following formula is used:

\[Nu = \cfrac {Nu_{for\zeta=0}} {[1-(\zeta/x)^{9/10}]^{1/9}}\]

where:

\(0.6 \eqslantless Pr \eqslantless 60\)

\(5*10^5 \eqslantless Re_x \eqslantless 10^7\)

\(\zeta\) = length of plate that is not heated

x = position along length of plate where local Nusselt number is to be computed

Fluid properties are at film temp (\(T_{film}\)):

\(T_{film} = (T_{infinity} + T_{surface})/2\)

\(T_{infinity}\) = temperature of fluid away from surface

\(T_{surface}\) = 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 externalflow.

>>> from pychemengg.heattransfer import externalflow as extflow 
>>> plateobject = extflow.Plate()
# This will create an instance of the class 'Plate'.
# Then call the method like so :-
>>> plateobject.Nu_unheated_turbulent_local(Re=610620, Pr=0.7073, unheatedlength=0.1, xlocation_tofindNu=0.5)
1155.3088951877935

Nu_uniformflux_laminar_average(Re=None, Pr=None)

Average Nusselt number for laminar flow on flat plate with uniform heat flux.

Parameters

Reint or float

Reynolds number for full length ‘L’ of plate.

Print or float

Prandtl number for the fluid.

Returns

Nuint or float

Average Nusselt number for laminar flow on flat plate.

Warning

A Nusselt number is returned based on the equation even if parameters (such as Re, Pr) do not fall in their respective allowable range limits (see above under ‘Notes’). However, if this happens, a warning is issued.

Notes

The following formula is used:

\[Nu = 0.664 Re^{0.5} Pr^{1/3}\]

where:

\(Pr > 0.6\)

\(Re < 5 * 10^5\)

Fluid properties are at film temp (\(T_{film}\)):

\(T_{film} = (T_{infinity} + T_{surface})/2\)

\(T_{infinity}\) = temperature of fluid away from surface

\(T_{surface}\) = 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 externalflow.

>>> from pychemengg.heattransfer import externalflow as extflow 
>>> plateobject = extflow.Plate()
# This will create an instance of the class 'Plate'.
# Then call the method like so :-
>>> plateobject.Nu_uniformflux_laminar_average(Re=4.024e4, Pr=2962)
1912.899190840437

Nu_uniformflux_laminar_local(Re=None, Pr=None)

Local Nusselt number for laminar flow on flat plate with uniform heat flux.

Parameters

Reint or float

Reynolds number at location/length ‘x’ on plate.

Print or float for the fluid.

Prandtl number

Returns

Nuint or float

Local Nusselt number at location/length ‘x’ on plate.

Warning

A Nusselt number is returned based on the equation even if parameters (such as Re, Pr) do not fall in their respective allowable range limits (see above under ‘Notes’). However, if this happens, a warning is issued.

Notes

The following formula is used:

\[Nu = 0.453 Re^{0.5} Pr^{1/3}\]

where:

\(Pr > 0.6\)

\(Re < 5 * 10^5\)

Fluid properties are at film temp (\(T_{film}\)):

\(T_{film} = (T_{infinity} + T_{surface})/2\)

\(T_{infinity}\) = temperature of fluid away from surface

\(T_{surface}\) = 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 externalflow.

>>> from pychemengg.heattransfer import externalflow as extflow 
>>> plateobject = extflow.Plate()
# This will create an instance of the class 'Plate'.
# Then call the method like so :-
>>> plateobject.Nu_uniformflux_laminar_local(Re=61062, Pr=0.7073)
99.73592054582787

Nu_uniformflux_turbulent_average(Re=None, Pr=None)

Average Nusselt number for turbulent flow on flat plate with uniform heat flux.

Parameters

Reint or float

Reynolds number for full length ‘L’ of plate.

Print or float

Prandtl number for the fluid.

Returns

Nuint or float

Average Nusselt number for turbulent flow on flat plate.

Warning

A Nusselt number is returned based on the equation even if parameters (such as Re, Pr) do not fall in their respective allowable range limits (see above under ‘Notes’). However, if this happens, a warning is issued.

Notes

The following formula is used:

\[Nu = 0.037 Re^{0.8} Pr^{1/3}\]

where:

\(0.6 \eqslantless Pr \eqslantless 60\)

\(5*10^5 \eqslantless Re_x \eqslantless 10^7\)

Fluid properties are at film temp (\(T_{film}\)):

\(T_{film} = (T_{infinity} + T_{surface})/2\)

\(T_{infinity}\) = temperature of fluid away from surface

\(T_{surface}\) = 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 externalflow.

>>> from pychemengg.heattransfer import externalflow as extflow 
>>> plateobject = extflow.Plate()
# This will assign the class 'Plate' to the variable 'plateobject'.
# Then call the method like so :-
>>> plateobject.Nu_uniformflux_turbulent_average(Re=8.875e5, Pr=0.7387)
1918.1936389098291

Nu_uniformflux_turbulent_local(Re=None, Pr=None)

Local Nusselt number for turbulent flow on flat plate with uniform heat flux.

Parameters

Reint or float

Reynolds number at location/length ‘x’ on plate.

Print or float

Prandtl number for the fluid.

Returns

Nuint or float

Local Nusselt number at location/length ‘x’ on plate.

Warning

A Nusselt number is returned based on the equation even if parameters (such as Re, Pr) do not fall in their respective allowable range limits (see above under ‘Notes’). However, if this happens, a warning is issued.

Notes

The following formula is used:

\[Nu = 0.0308 Re^{0.8} Pr^{1/3}\]

where:

\(0.6 \eqslantless Pr \eqslantless 60\)

\(5*10^5 \eqslantless Re_x \eqslantless 10^7\)

Fluid properties are at film temp (\(T_{film}\)):

\(T_{film} = (T_{infinity} + T_{surface})/2\)

\(T_{infinity}\) = temperature of fluid away from surface

\(T_{surface}\) = 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 externalflow. >>> from pychemengg.heattransfer import externalflow as extflow >>> plateobject = extflow.Plate() # This will create an instance of the class ‘Plate’. # Then call the method like so :- >>> plateobject.Nu_uniformflux_turbulent_local(Re=610620, Pr=0.7073) 1166.9047896712561