Question

View factor of a large cylinder of 10cm in radius and 60cm in length from a co - axial smaller cylinder of 5cm radius and the same length is 0.34. View factor of the large cylinder of itself (concave inner surface) is 0.25. The view factor of the larger cylinder with respect to either annular end is _______

• A. 0.58
• B. 0.29
• C. 0.17
• D. 0.41

Answer 1

The correct option is B 0.29





Given :

$F_{1-2}=0.34$
$F_{2-2}=0.25$

Using summation rule :

$F_{2-1}+F_{22}+F_{2-3}+F_{2-4}=1......\left(1\right)$

Using reciprocity theorem:

$A_1{F}_{12}=A_2{F}_{21}$

$\pi d_{1}L\times F_{12}=\pi d_{2}L\times F_{21}$

$r_1{F}_{12}=r_2{F}_{21}$

$5\times 0.34=10\times F_{21}$

$F_{21}=0.17$

From equation (1)

$F_{2-1}+F_{2-2}+F_{2-3}+F_{2-4}=1$

$0.17+0.25+F_{2-3}+F_{2-4}=1$

$F_{2-3}+F_{2-4}=0.58$

$\text{Due to symmetry},F_{2-3}=F_{2-4}$

$\Rightarrow F_{2-3}=F_{2-4}=\frac{0.58}{2}=0.29$

Shape factor for either annular end means either $F_{2-3}or{F}_{2-4}$