Two rods of the same length and material transfer a given amount of heat in $12 \, s$ when they are joined in parallel. But when they are joined in series,then they will transfer the same amount of heat under the same conditions in ........ $s$.

Three conducting rods of the same material and cross-section are shown in the figure. The temperatures at $A$, $D$, and $C$ are maintained at $20 ^oC$, $90 ^oC$, and $0 ^oC$ respectively. If there is no heat flow in $AB$, find the ratio of the lengths of $BD$ and $BC$.

$A$ wall consists of two layers $A$ and $B$ of equal thickness. Their thermal resistances are $R_1$ and $R_2$. Find the temperature of the interface.

Three rods of the same material,same length,and same cross-sectional area are connected as shown in the figure. Find the temperature of their junction in $^oC$.

Three identical rods $A, B$ and $C$ are placed end to end. $A$ temperature difference is maintained between the free ends of $A$ and $C$. The thermal conductivity of $B$ is thrice that of $C$ and half of that of $A$. The effective thermal conductivity of the system will be ($K_{A}$ is the thermal conductivity of rod $A$).

$A$,$B$ and $C$ are three identical conductors but made from different materials. They are kept in contact as shown. Their thermal conductivities are $K$,$2K$ and $K/2$. The free end of $A$ is at $100^{\circ} C$ and the free end of $C$ is at $0^{\circ} C$. During steady state,the temperature of the junction of $A$ and $B$ is nearly (in $^{\circ} C$)