Question

Consider two concentric spheres with diameter 12cm and 18cm forming an enclosure. The view factor, from the inner surface of the outer sphere to its own , is

• A. $\frac{4}{9}$
• B. 1
• C. $\frac{5}{9}$
• D. 0

Answer 1

The correct option is C $\frac{5}{9}$



$d_1=12cm,$
$d_2=18cm,$

$F_{1-2}=1$

Using reciprocity theorem

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

$4\pi r_1^2\times 1=4\pi r_2^2\times F_{2-1}$
$F_{2-1}={\left(\frac{r_1}{r_2}\right)}^2={\left(\frac{12}{18}\right)}^2={\left(\frac{2}{3}\right)}^2=\frac{4}{9}$

Using summation rule.

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

$\frac{4}{9}+F_{2-2}=1$

$F_{2-2}=1-\frac{4}{9}=\frac{5}{9}$