Question

Two identical rods with different thermal conductivities $k _{1} \& k _{2}$ and different temperatures are first placed along length and then along area, then the ratio of rates of heat flow in both cases is

• A. $\frac{k_{1} k_{2}}{k_{1}+k_{2}}$
• B. $\frac{4 k_{1}^{2} k_{2}}{\left(k_{1}+k_{2}\right)^{2}}$
• C. $\frac{\left(k_{1}+k_{2}\right)^{2}}{4 k_{1}}$
• D. $\frac{4 k_{1} k_{2}}{\left(k_{1}+k_{2}\right)^{2}}$

Answer 1

Answer: (D)

According to the relations.
In series combination
$K _{ s }=\frac{2 K _{1} K _{2}}{ K _{1}+ K _{2}}$
In parallel combination
$K _{ P }=\frac{ K _{1}+ K _{2}}{2}$
$\frac{ K _{ S }}{ K _{ P }}=\frac{\frac{2 K _{1} K _{2}}{ K _{1}+ K _{2}}}{\frac{ K _{1}+ K _{2}}{2}}=\frac{4 K _{1} K _{2}}{\left( K _{1}+ K _{2}\right)^{2}}$