Total emissivity calculation

 

The total emissivity for the spectral surface illustrated is determined from the banded values of emissivity by:

            ,

where

 

The banded fractional function F_b(λ1-λ2) describes the fraction of spectral power from a blackbody distribution that falls between the wavelengths λ₁ and λ₂. Typically, the banded fractional function would be evaluated with tabulated data for F_b(0-λ), whose value depends only on the product λT.

 

The first calculation of total emissivity used a function FlT( ) that evaluates F_b(0-λ):

 

bands=[0 2 4 Inf]; % location steps between bands (um)

el=[0 0.8 0.4]; % band values of spectral emissivity

T=800;

etot = el(2)*(FlT(4*T)-FlT(2*T))+el(3)*(1-FlT(4*T)) % total emissivity

etot = 0.51146

 

The same calculation can be done more concisely with the FlTb( ) function that evaluates F_b(λ1-λ2):

 

Fb=FlTb(bands,T)

Fb = 0.019727 0.298376 0.681897

etot=sum(el.*Fb) % total emissivity

etot = 0.51146

 

The same calculation can be done even more concisely with the function Total( ) that evaluates etot directly:

 

etot=Total(el,bands,T)

etot = 0.51146