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

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) (k1 k2/k1+k2) (B) (4 k12 k2/(k1+k2)2) (C) ((k1+k2)2/4 k1) (D) (4 k1 k2/(k1+k2)2)

Tardigrade Admin · Accepted Answer

According to the relations. In series combination K s =(2 K 1 K 2/ K 1+ K 2) In parallel combination K P =( K 1+ K 2/2) ( K S / K P )=((2 K 1 K 2/ K 1+ K 2)/( K 1+ K 2)2)=(4 K 1 K 2/( K 1+ K 2)2)

Q. 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

$\frac{k _{1} k _{2}}{k _{1} + k _{2}}$

$\frac{4 k _{1}^{2} k _{2}}{( k _{1} + k _{2} ) ^{2}}$

$\frac{( k _{1} + k _{2} ) ^{2}}{4 k _{1}}$

$\frac{4 k _{1} k _{2}}{( k _{1} + k _{2} ) ^{2}}$

Q. Two identical rods with different thermal conductivities k1​&k2​ and different temperatures are first placed along length and then along area, then the ratio of rates of heat flow in both cases is

k1​+k2​k1​k2​​

(k1​+k2​)24k12​k2​​

4k1​(k1​+k2​)2​

(k1​+k2​)24k1​k2​​

According to the relations. In series combination Ks​=K1​+K2​2K1​K2​​ In parallel combination KP​=2K1​+K2​​ KP​KS​​=2K1​+K2​​K1​+K2​2K1​K2​​​=(K1​+K2​)24K1​K2​​

Q. 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

$\frac{k _{1} k _{2}}{k _{1} + k _{2}}$

$\frac{4 k _{1}^{2} k _{2}}{( k _{1} + k _{2} ) ^{2}}$

$\frac{( k _{1} + k _{2} ) ^{2}}{4 k _{1}}$

$\frac{4 k _{1} k _{2}}{( k _{1} + k _{2} ) ^{2}}$