# Source code for ht.radiation

```
# -*- coding: utf-8 -*-
'''Chemical Engineering Design Library (ChEDL). Utilities for process modeling.
Copyright (C) 2016, Caleb Bell <Caleb.Andrew.Bell@gmail.com>
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.'''
from __future__ import division
from math import exp, e
import os
from fluids.constants import c, h, k, sigma
from fluids.numerics import numpy as np
__all__ = ['blackbody_spectral_radiance', 'q_rad', 'grey_transmittance',
'solar_spectrum']
[docs]def blackbody_spectral_radiance(T, wavelength):
r'''Returns the spectral radiance, in units of W/m^2/sr/µm.
.. math::
I_{\lambda,blackbody,e}(\lambda,T)=\frac{2hc_o^2}
{\lambda^5[\exp(hc_o/\lambda k T)-1]}
Parameters
----------
T : float
Temperature of the surface, [K]
wavelength : float
Length of the wave to be considered, [m]
Returns
-------
I : float
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.
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
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
'''
to_exp = h*c/(wavelength*T*k)
if to_exp > 709.7:
return 0.0
else:
exp_term = exp(to_exp)
return 2.*h*c*c*wavelength**-5/(exp_term - 1.0)
[docs]def q_rad(emissivity, T, T2=0):
r'''Returns the radiant heat flux of a surface, optionally including
assuming radiant heat transfer back to the surface.
.. math::
q = \epsilon \sigma (T_1^4 - T_2^4)
Parameters
----------
emissivity : float
Fraction of black-body radiation which is emitted, [-]
T : float
Temperature of the surface, [K]
T2 : float, optional
Temperature of the surrounding material of the surface [K]
Returns
-------
q : float
Heat exchange [W/m^2]
Notes
-----
Emissivity must be less than 1. T2 may be larger than T.
Examples
--------
>>> q_rad(emissivity=1, T=400)
1451.613952
>>> q_rad(.85, T=400, T2=305.)
816.7821722650002
References
----------
.. [1] Bergman, Theodore L., Adrienne S. Lavine, Frank P. Incropera, and
David P. DeWitt. Introduction to Heat Transfer. 6E. Hoboken, NJ:
Wiley, 2011.
'''
T_T = T*T
T2_T2 = T2*T2
return sigma*emissivity*(T_T*T_T - T2_T2*T2_T2)
[docs]def grey_transmittance(extinction_coefficient, molar_density, length, base=e):
r'''Calculates the transmittance of a grey body, given the extinction
coefficient of the material, its molar density, and the path length of the
radiation.
.. math::
\tau = base^{(-\epsilon \cdot l\cdot \rho_m )}
Parameters
----------
extinction_coefficient : float
The extinction coefficient of the material the radiation is passing at
the modeled frequency, [m^2/mol]
molar_density : float
The molar density of the material the radiation is passing through,
[mol/m^3]
length : float
The length of the body the radiation is transmitted through, [m]
base : float, optional
The exponent used in calculations; `e` is more theoretically sound but
10 is often used as a base by chemists, [-]
Returns
-------
transmittance : float
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.
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
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.
'''
transmittance = molar_density*extinction_coefficient*length
return base**(-transmittance)
[docs]def solar_spectrum(model='SOLAR-ISS'):
r'''Returns the solar spectrum of the sun according to the specified model.
Only the 'SOLAR-ISS' model is supported.
Parameters
----------
model : str, optional
The model to use; 'SOLAR-ISS' is the only model available, [-]
Returns
-------
wavelengths : ndarray
The wavelengths of the solar spectra, [m]
SSI : ndarray
The solar spectral irradiance of the sun, [W/(m^2*m)]
uncertainties : ndarray
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.
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
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.
'''
if model == 'SOLAR-ISS':
folder = os.path.join(os.path.dirname(__file__), 'data')
pth = os.path.join(folder, 'solar_iss_2018_spectrum.dat')
data = np.genfromtxt(pth, dtype=np.float64, delimiter=' ')
wavelengths, SSI, uncertainties = data[:, 0], data[:, 1], data[:, 2]
wavelengths *= 1E-9
SSI *= 1E9
# Convert -1 uncertainties to nans
uncertainties[uncertainties == -1] = np.nan
uncertainties *= 1E9
return wavelengths, SSI, uncertainties
```