Thermal Conductivity

pygasflow.atd.thermal_conductivity.thermal_conductivity_chapman_enskog(T, gas='O')

Compute the thermal conductivity of pure monoatomic gases.

Parameters:

Tfloat or array_like

Temperature of the air in [K]

gasstr, optional

Possible values are: ['N', 'O', 'Ar', 'He']

Returns:

kfloat or array_like

Thermal conductivity of the gas [W / (m * K)]

References

• “Basic of aerothermodynamics” by Ernst Heinrich, Table 13.1

• “Transport Phenomena” by R. Byron Bird, Warren E. Stewart, Edwing N. Lightfoot, Table E2

Examples

>>> import numpy as np
>>> from pygasflow.atd import thermal_conductivity_chapman_enskog
>>> thermal_conductivity_chapman_enskog(300, gas="O")
np.float64(0.049434309555779335)

Pint quantities can be used as well:

>>> import pint
>>> import pygasflow
>>> ureg = pint.UnitRegistry()
>>> pygasflow.defaults.pint_ureg = ureg
>>> thermal_conductivity_chapman_enskog(300 * ureg.K)
<Quantity(0.0494343096, 'watt / meter / kelvin')>

Comparison of the thermal conductivity of different gases over a range of temperatures.

import numpy as np
import matplotlib.pyplot as plt
from pygasflow.atd import thermal_conductivity_chapman_enskog
T = np.linspace(200, 1000)
gases = ['N', 'O', 'Ar', 'He']
fig, ax = plt.subplots()
for gas in gases:
    ax.plot(T, thermal_conductivity_chapman_enskog(T, gas=gas), label=gas)
ax.legend()
ax.set_xlabel("Temperature [K]")
ax.set_ylabel("Thermal Conductivity [W / (m * K)]")
plt.show()

(Source code, png, hires.png, pdf)

pygasflow.atd.thermal_conductivity.thermal_conductivity_eucken(cp, R, mu)

Compute the thermal conductivity of gases with the semi-empirical Eucken formula.

Parameters:

cpfloat or array_like

Specific heat at constant pressure. [J / (kg * K)]

Rfloat or array_like

Specific gas constant, which is equal to R0 / M with M the molecular weight.

mufloat or array_like

Viscosity [kg / (m * s)].

Returns:

kfloat or array_like

Thermal conductivity of the gas [W / (m * K)]

References

“Basic of Aerothermodynamics”, by Ernst H. Hirschel

Examples

>>> import numpy as np
>>> from pygasflow.atd import thermal_conductivity_eucken
>>> cp, R, mu = 1010, 288, 1.863e-05
>>> thermal_conductivity_eucken(cp, R, mu)
np.float64(0.0255231)

Pint quantities can be used as well:

>>> import pint
>>> import pygasflow
>>> ureg = pint.UnitRegistry()
>>> pygasflow.defaults.pint_ureg = ureg
>>> cp = 1010 * ureg.J / (ureg.kg * ureg.K)
>>> R = 288 * ureg.J / (ureg.kg * ureg.K)
>>> mu = 1.863e-05 * ureg.kg / (ureg.m * ureg.s)
>>> thermal_conductivity_eucken(cp, R, mu)
<Quantity(0.0255231, 'watt / meter / kelvin')>

pygasflow.atd.thermal_conductivity.thermal_conductivity_hansen(T)

Compute air’s thermal conductivity.

Parameters:

Tfloat or array_like

Temperature of the air in [K]

Returns:

kfloat or array_like

Thermal conductivity of the gas [W / (m * K)]

References

“Basic of Aerothermodynamics”, by Ernst H. Hirschel

Examples

>>> import numpy as np
>>> from pygasflow.atd import thermal_conductivity_hansen
>>> thermal_conductivity_hansen(300)
np.float64(0.0251357567)

Pint quantities can be used as well:

>>> import pint
>>> import pygasflow
>>> ureg = pint.UnitRegistry()
>>> pygasflow.defaults.pint_ureg = ureg
>>> thermal_conductivity_hansen(300 * ureg.K)
<Quantity(0.0251357567, 'watt / meter / kelvin')>

pygasflow.atd.thermal_conductivity.thermal_conductivity_power_law(T)

Compute air’s thermal conductivity.

Parameters:

Tfloat or array_like

Temperature of the air in [K]

Returns:

kfloat or array_like

Thermal conductivity of the gas [W / (m * K)]

References

“Basic of Aerothermodynamics”, by Ernst H. Hirschel

Examples

>>> import numpy as np
>>> from pygasflow.atd import thermal_conductivity_power_law
>>> thermal_conductivity_power_law(300)
np.float64(0.0251985236)

Pint quantities can be used as well:

>>> import pint
>>> import pygasflow
>>> ureg = pint.UnitRegistry()
>>> pygasflow.defaults.pint_ureg = ureg
>>> thermal_conductivity_power_law(300 * ureg.K)
<Quantity(0.0251985236, 'watt / meter / kelvin')>