Which of the following factors affect the thermal conductivity of a rod?

For the figure shown, when arc $ACD$ and $ADB$ are made of same material, the heat carried between $A$ and $B$ is $H$ . If $ADB$ is replaced with another material, the heat carried becomes $2H$ . If the temperatures at $A$ and $B$ are fixed at $T_1$ and $T_2$ , what is the ratio of the new conductivity to the old one of $ADB$

Two metallic blocks $M_{1}$ and $M_{2}$ of same area of cross-section are connected to each other (as shown in figure). If the thermal conductivity of $M _{2}$ is $K$ then the thermal conductivity of $M _{1}$ will be ]...............$K$ [Assume steady state heat conduction]

Aring consisting of two parts $ADB$ and $ACB$ of same conductivity $k$ carries an amount of heat $H$. The $ADB$ part is now replaced with another metal keeping the temperatures $T_1$ and $T_2$ constant. The heat carried increases to $2H$. What $ACB$ should be the conductivity of the new$ADB$ part? Given $\frac{{ACB}}{{ADB}}= 3$

A copper pipe of length $10 \,m$ carries steam at temperature $110^{\circ} C$. The outer surface of the pipe is maintained at a temperature $10^{\circ} C$. The inner and outer radii of the pipe are $2 \,cm$ and $4 \,cm$, respectively. The thermal conductivity of copper is $0.38 kW / m /{ }^{\circ} C$. In the steady state, the rate at which heat flows radially outward through the pipe is closest to ............. $\,kW$

Three rods made of the same material and having same cross-sectional area but different lengths $10\, cm, 20\, cm$ and $30\, cm$ are joined as shown. The temperature of the junction is......... $^oC$