Heat transfer by radiation (ht.radiation)

ht.radiation.blackbody_spectral_radiance(T, wavelength)[source]

Returns the spectral radiance, in units of W/m^3/sr.

\[I_{\lambda,blackbody,e}(\lambda,T)=\frac{2hc_o^2} {\lambda^5[\exp(hc_o/\lambda k T)-1]}\]
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^3/sr]

Notes

Can be used to derive the Stefan-Boltzman law, or determine the maximum radiant frequency for a given temperature.

References

[R829831]Bergman, Theodore L., Adrienne S. Lavine, Frank P. Incropera, and David P. DeWitt. Introduction to Heat Transfer. 6E. Hoboken, NJ: Wiley, 2011.
[R830831](1, 2) Spectral-calc.com. Blackbody Calculator, 2015. http://www.spectralcalc.com/blackbody_calculator/blackbody.php

Examples

Checked with Spectral-calc.com, at [R830831].

>>> blackbody_spectral_radiance(800., 4E-6)
1311692056.2430143
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:

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.

References

[R831833]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