LumpedSystem

class pychemengg.heattransfer.transient.LumpedSystem(surfacearea=None, volume=None, density=None, specificheat=None, thermalconductivity=None, heattransfercoefficient=None, T_infinity=None, T_initial=None)

Bases: object

Model for lumped system analysis.

Parameters

surfaceareaint or float

Surface area of solid object.

volumeint or float

Volume of solid object.

densityint or float

Density of solid object.

specificheatint or float

Specific heat of solid object.

thermalconductivityint or float

Thermal conductivity of solid object.

heattransfercoefficientint or float

Heat transfer coefficient between solid object and surrounding.

T_infinityint or float

Temperature of surroundings.

T_initialint or float

Temperature of solid object at time = 0.

Examples

First import the module transient

Units used in this example: SI system

However, any consistent units can be used

>>> from pychemengg.heattransfer import transient
>>> plate = transient.LumpedSystem(thermalconductivity=180, density=2800, specificheat=880, T_initial=700, T_infinity=15, heattransfercoefficient=53, surfacearea=2*1, volume=1*2e-2)
# This will create an instance of 'LumpedSystem' with a name 'plate' 

Attributes

See “Parameters”. All parameters are attributes. Additional attributes are listed below.

massint or float

Mass of solid object computed as (volume * density) of solid object.

characteristiclengthint or float

Characteristic length of object computed as (volume/surface area) of object.

__init__(surfacearea=None, volume=None, density=None, specificheat=None, thermalconductivity=None, heattransfercoefficient=None, T_infinity=None, T_initial=None)

Methods

__init__([surfacearea, volume, density, …])
calc_Bi()	Computes Biot number.
calc_heatrateof_conv_at_time_t([time])	Heat rate of convection between object and surroundings at a given time = t.
calc_maxheattransferpossible()	Maximum possible heat transfer between solid object and surroundings.
calc_temperature_of_solid_at_time_t([time])	Temperature of solid object at a given time = t.
calc_totalheat_transferred_during_interval_t([time])	Heat transferred between solid object and surroundings during time interval = 0 to t.

calc_Bi()

Computes Biot number.

Parameters

None_requiredNone

Attributes that are already defined are used in calculation.

Returns

Biint or float

Biot number

Notes

Biot number is calculated using the following formula.

\[Bi = \frac {h L_{c}} {k} \]

where:

h = heat transfer coefficient

k = thermal conductivity of solid object

\(L_c\) = characteristic length of solid object

Bi = Biot number

References

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

Examples

First import the module transient

Units used in this example: SI system

However, any consistent units can be used

>>> from pychemengg.heattransfer import transient
>>> plate = transient.LumpedSystem(thermalconductivity=180, density=2800, specificheat=880, T_initial=700, T_infinity=15, heattransfercoefficient=53, surfacearea=2*1, volume=1*2e-2)
# This will create an instance of 'LumpedSystem' with a name 'plate'
# Next call calc_Bi
>>> plate.calc_Bi()
0.0029444444444444444

calc_heatrateof_conv_at_time_t(time=None)

Heat rate of convection between object and surroundings at a given time = t.

Parameters

timeint or float

Time instant from begining of process, at which heat rate is to be found.

Returns

heat rate of convectionint or float; Positive: Heat is gained by object, Negative: Heat is lost by object

Heat rate of convection between solid object and surroundings at time = t.

Notes

Heat rate is calculated using the following formula:

\[q_{t} = h A_s (T_{infinity} - T_{t}) \]

where:

t = time at which temperature is to be computed

h = heat transfer coefficient

\(T_{infinity}\) = temperature of surrounding fluid

\(T_{t}\) = temperature of solid object at time = t

\(A_s\) = surface area of solid object

\(q_{t}\) = heat rate at time = t

References

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

Examples

First import the module transient

Units used in this example: SI system

However, any consistent units can be used

>>> from pychemengg.heattransfer import transient
>>> plate = transient.LumpedSystem(thermalconductivity=180, density=2800, specificheat=880, T_initial=700, T_infinity=15, heattransfercoefficient=53, surfacearea=2*1, volume=1*2e-2)
# This will create an instance of 'LumpedSystem' with a name 'plate'
# Let temperature at time = 60 s after start of the process be needed.
# Next call the following
>>> plate.calc_heatrateof_conv_at_time_t(time=60)
-63818.56987259833
# negative value indicates heat is being lost by the solid object

calc_maxheattransferpossible()

Maximum possible heat transfer between solid object and surroundings.

Parameters

None_requiredNone

This class takes no parameters for instance creation.

Returns

maximum heat transfer possible: int or float; Positive: Heat is gained by object, Negative: Heat is lost by object

Maximum heat transfer posssible between object and surroundings

Notes

Maximum heat transfer possible between solid object and surroundings is calculated using the following formula. This is based on the assumption that final object temperature will eventually reach surrounding temperature of \(T_{infinity}\)

\[q_{max} = m C_p (T_{infinity} - T_{initial}) \]

where:

m = mass of solid object

\(C_{p}\) = specific heat of solid object

\(T_{infinity}\) = temperature of surrounding, which the solid object will eventually attain

\(T_{initial}\) = temperature of solid object at time = initial

\(q_{max}\) = max heat transfer possible

References

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

Examples

First import the module transient

Units used in this example: SI system

However, any consistent units can be used

>>> from pychemengg.heattransfer import transient
>>> plate = transient.LumpedSystem(thermalconductivity=180, density=2800, specificheat=880, T_initial=700, T_infinity=15, heattransfercoefficient=53, surfacearea=2*1, volume=1*2e-2)
# This will create an instance of 'LumpedSystem' with a name 'plate'
# Next call the following
>>> plate.calc_maxheattransferpossible()
-33756800.0
# negative value indicates heat is being lost by the solid object

calc_temperature_of_solid_at_time_t(time=None)

Temperature of solid object at a given time = t.

Parameters

timeint or float

Time instant from begining of process, at which temperature of solid object is to be found.

Returns

temperatureint or float

Temperature of solid object at time = t

Notes

Temperature of solid object at time = t is calculated using the following formula:

\[T(t) = T_{infinity} + (T_{initial} - T_{infinity}) e^{-bt} \]

where:

\(T_{infinity}\) = temperature of surrounding fluid

\(T_{initial}\) = intitial temperature of solid object

\(b = \frac{hA_s}{\rho V C_p}\)

t = time at which temperature is to be computed

where:

h = heat transfer coefficient

\(A_s\) = surface area of solid object

\(\rho\) = density of solid object

V = volume of solid object

\(C_p\) = specific heat of solid object

References

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

Examples

First import the module transient

Units used in this example: SI system

However, any consistent units can be used

>>> from pychemengg.heattransfer import transient
>>> plate = transient.LumpedSystem(thermalconductivity=180, density=2800, specificheat=880, T_initial=700, T_infinity=15, heattransfercoefficient=53, surfacearea=2*1, volume=1*2e-2)
# This will create an instance of 'LumpedSystem' with a name 'plate'
# Let temperature at time = 60 s after start of the process be needed.
# Next call the following
>>> plate.calc_temperature_of_solid_at_time_t(time=60s)
617.0619799301729

calc_totalheat_transferred_during_interval_t(time=None)

Heat transferred between solid object and surroundings during time interval = 0 to t.

Parameters

timeint or float

Time-limit after start of process for which heat transferred is to be computed.

Returns

total heat transferredint or float; Positive: Heat is gained by object, Negative: Heat is lost by object

Total heat transferred between object and surroundings during interval 0 to t

Notes

Total heat transferred in interval 0 to t is calculated using the following formula:

\[q_{0 \to t} = m C_p (T_{t} - T_{inintial}) \]

where:

t = time marking the interval [0, t] for which heat transferred is to be computed

m = mass of object

\(C_{p}\) = specific heat of object

\(T_{t}\) = temperature of object at time = t

\(T_{initial}\) = temperature of object at time = 0

\(q_{0 \to t}\) = heat transferred in interval [0, t]

References

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

Examples

First import the module transient

Units used in this example: SI system

However, any consistent units can be used

>>> from pychemengg.heattransfer import transient
>>> plate = transient.LumpedSystem(thermalconductivity=180, density=2800, specificheat=880, T_initial=700, T_infinity=15, heattransfercoefficient=53, surfacearea=2*1, volume=1*2e-2)
# This will create an instance of 'LumpedSystem' with a name 'plate'
# Let heat transferred in time = 60 s after start of the process be needed.
# Next call the following
>>> plate.calc_totalheat_transferred_during_interval_t(time=60)
-4087185.6290410785
# negative value indicates heat is being lost by the solid object