Question

For two concentric spheres with inner diameter $d_1$ and outer diameter $d_2$, the view factor of inner surface of outer sphere, to itself is given by

• A. $1-\frac{d_1}{d_2}$
• B. $1-{\left(\frac{d_1}{d_2}\right)}^2$
• C. 0
• D. 1

Answer 1

The correct option is B $1-{\left(\frac{d_1}{d_2}\right)}^2$

$F_{1-2}=1\left(fromthegeometry\right)$
Using Reciprocity theorem

$A_1{F}_{1-2}=A_2{F}_{1-2}$

$A_1\times 1=A_2{F}_{2-1}$

$F_{2-1}=\frac{A_1}{A_2}$

$F_{2-1}=\frac{4\pi r_1^2}{4\pi r_2^2}$

$F_{2-1}=\frac{d_1^2}{d_2^2}$

Using Summation rule,

$F_{2-1}+F_{2-2}=1$

$F_{2-2}=1-F_{2-1}$

$F_{2-2}=1-\frac{d_1^2}{d_2^2}$

$F_{2-2}=1-{\left(\frac{d_1}{d_2}\right)}^2$