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Total hemispherical emissivity

Total hemispherical emissivity

Total hemispherical emissivity

Hi all,
I want to calculate the total hemispherical emissivity of a surface when the emissivity curve changes with wavelength (assume spectral emissivity does not change with temperature)

I have seen examples in text books that show how to calculate emittance by integration on simple square wave profiles but how is this calculated if you have a wavy profile as the below image? The equation attached is used to calculate total hemispherical emissivity at different temperatures, i'm not sure how?

How can you calculate the change in total hemispherical emissivity with temperature changes? This would be related to changes in emissivity at different wavelengths due to temperature.

RE: Total hemispherical emissivity

It would seem that it would be numerically integrated , breaking the curve into 100 smaller sections, and the energy released at each change in wavelength is calculated using wiens displacement law.

"...when logic, and proportion, have fallen, sloppy dead..." Grace Slick

RE: Total hemispherical emissivity

A hemispherical emissivity integral would naturally require a 2D integral of some sort, which you are not showing. Nevertheless, it's typically assumed that emissive surfaces are Lambertian, and if so, then the radiant intensity is just the radiant flux divided by π steradians

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