Heat transfer by radiation (ht.radiation)¶
- ht.radiation.blackbody_spectral_radiance(T, wavelength)[source]¶
Returns the spectral radiance, in units of W/m^2/sr/µm.
\[I_{\lambda,blackbody,e}(\lambda,T)=\frac{2hc_o^2} {\lambda^5[\exp(hc_o/\lambda k T)-1]} \]- Parameters
- Tfloat
Temperature of the surface, [K]
- wavelengthfloat
Length of the wave to be considered, [m]
- Returns
- Ifloat
Spectral radiance [W/(m^2*sr*m)]
Notes
Can be used to derive the Stefan-Boltzman law, or determine the maximum radiant frequency for a given temperature.
References
- 1
Bergman, Theodore L., Adrienne S. Lavine, Frank P. Incropera, and David P. DeWitt. Introduction to Heat Transfer. 6E. Hoboken, NJ: Wiley, 2011.
- 2
Spectral-calc.com. Blackbody Calculator, 2015. http://www.spectralcalc.com/blackbody_calculator/blackbody.php
Examples
Checked with Spectral-calc.com, at [2].
>>> blackbody_spectral_radiance(800., 4E-6) 1311694129.7430933
Calculation of power from the sun (earth occupies 6.8E-5 steradian of the sun):
>>> from scipy.integrate import quad >>> rad = lambda l: blackbody_spectral_radiance(5778., l)*6.8E-5 >>> quad(rad, 1E-10, 1E-4)[0] 1367.9827067638964
- ht.radiation.grey_transmittance(extinction_coefficient, molar_density, length, base=2.718281828459045)[source]¶
Calculates the transmittance of a grey body, given the extinction coefficient of the material, its molar density, and the path length of the radiation.
\[\tau = base^{(-\epsilon \cdot l\cdot \rho_m )} \]- Parameters
- extinction_coefficientfloat
The extinction coefficient of the material the radiation is passing at the modeled frequency, [m^2/mol]
- molar_densityfloat
The molar density of the material the radiation is passing through, [mol/m^3]
- lengthfloat
The length of the body the radiation is transmitted through, [m]
- basefloat, optional
The exponent used in calculations; e is more theoretically sound but 10 is often used as a base by chemists, [-]
- Returns
- transmittancefloat
The fraction of spectral radiance which is transmitted through a grey body (can be liquid, gas, or even solid ex. in the case of glasses) [-]
Notes
For extinction coefficients, see the HITRAN database. They are temperature and pressure dependent for each chemical and phase.
References
- 1
Modest, Michael F. Radiative Heat Transfer, Third Edition. 3rd edition. New York: Academic Press, 2013.
- 2
Eldridge, Ralph G. “Water Vapor Absorption of Visible and Near Infrared Radiation.” Applied Optics 6, no. 4 (April 1, 1967): 709-13. https://doi.org/10.1364/AO.6.000709.
Examples
Overall transmission loss through 1 cm of precipitable water equivalent atmospheric water vapor at a frequency of 1.3 um [2]:
>>> grey_transmittance(3.8e-4, molar_density=55300, length=1e-2) 0.8104707721191062
- ht.radiation.q_rad(emissivity, T, T2=0)[source]¶
Returns the radiant heat flux of a surface, optionally including assuming radiant heat transfer back to the surface.
\[q = \epsilon \sigma (T_1^4 - T_2^4) \]- Parameters
- emissivityfloat
Fraction of black-body radiation which is emitted, [-]
- Tfloat
Temperature of the surface, [K]
- T2float, optional
Temperature of the surrounding material of the surface [K]
- Returns
- qfloat
Heat exchange [W/m^2]
Notes
Emissivity must be less than 1. T2 may be larger than T.
References
- 1
Bergman, Theodore L., Adrienne S. Lavine, Frank P. Incropera, and David P. DeWitt. Introduction to Heat Transfer. 6E. Hoboken, NJ: Wiley, 2011.
Examples
>>> q_rad(emissivity=1, T=400) 1451.613952
>>> q_rad(.85, T=400, T2=305.) 816.7821722650002
- ht.radiation.solar_spectrum(model='SOLAR-ISS')[source]¶
Returns the solar spectrum of the sun according to the specified model. Only the ‘SOLAR-ISS’ model is supported.
- Parameters
- modelstr, optional
The model to use; ‘SOLAR-ISS’ is the only model available, [-]
- Returns
- wavelengthsndarray
The wavelengths of the solar spectra, [m]
- SSIndarray
The solar spectral irradiance of the sun, [W/(m^2*m)]
- uncertaintiesndarray
The estimated absolute uncertainty of the measured spectral irradiance of the sun, [W/(m^2*m)]
Notes
The power of the sun changes as the earth gets closer or further away.
In [1], the UV and VIS data come from observations in 2008; the IR comes from measurements made from 2010-2016. There is a further 28 W/m^2 for the 3 micrometer to 160 micrometer range, not included in this model. All data was corrected to a standard distance of one astronomical unit from the Sun, as is the resultant spectrum.
The variation of the spectrum as a function of distance from the sun should alter only the absolute magnitudes.
[2] contains another dataset.
99.9% of the time this function takes is to read in the solar data from disk. This could be reduced by using pandas.
References
- 1
Meftah, M., L. Damé, D. Bolsée, A. Hauchecorne, N. Pereira, D. Sluse, G. Cessateur, et al. “SOLAR-ISS: A New Reference Spectrum Based on SOLAR/SOLSPEC Observations.” Astronomy & Astrophysics 611 (March 1, 2018): A1. https://doi.org/10.1051/0004-6361/201731316.
- 2
Woods Thomas N., Chamberlin Phillip C., Harder Jerald W., Hock Rachel A., Snow Martin, Eparvier Francis G., Fontenla Juan, McClintock William E., and Richard Erik C. “Solar Irradiance Reference Spectra (SIRS) for the 2008 Whole Heliosphere Interval (WHI).” Geophysical Research Letters 36, no. 1 (January 1, 2009). https://doi.org/10.1029/2008GL036373.
Examples
>>> wavelengths, SSI, uncertainties = solar_spectrum()
Calculate the minimum and maximum values of the wavelengths (0.5 nm/3000nm) and SSI:
>>> min(wavelengths), max(wavelengths), min(SSI), max(SSI) (5e-10, 2.9999e-06, 1330.0, 2256817820.0)
Integration - calculate the solar constant, in untis of W/m^2 hitting earth’s atmosphere.
>>> import numpy as np >>> np.trapz(SSI, wavelengths) 1344.802978