If ε is the emissivity of surfaces and shields and n is the number of shields, introduced between the two surfaces, then overall emissivity is given by

Explanation:

1 shield kept between the plates will bring in 3 additional resistances extra into the network out of which 2 are surface resistances and 1 is space resistance.

Hence if there are n number of radiation shields, then a total 2n + 2 number of surface resistance and n + 1 number of space resistances will be there in the radiation network drawn with n number of shields.

The formula for heat flux without shield when every surfaces has emissivity ϵ,

If there are n number of shields kept between plates then, 

From the above equation, equivalent emissivity,