Consider the radiation heat exchange inside an annulus between

Consider the radiation heat exchange inside an annulus between two very long concentric cylinders. The radius of the outer cylinder is R₀ and that of the inner cylinder is R_i. The radiation view factor of the outer cylinder onto itself is

F_{1– 1} = 0
F_{1– 2} = 1
Reciprocacy theorem
A₂ F_{2– 1} = A₁ F_{1– 2}

⇒ F_{2– 1} =	A₁	F_{1– 2}
	A₂

=	2πR_iL	=	R_i
	2πR_oL		R_o

F_{2– 1} + F_{2– 2} = 1

∴ F_{2– 2} = 1 - F_{2– 1} = 1 -	R_i
	R_o

1 -		R_i		^{1/ 3}
		R₀

1 -	R_i
	R₀