Two rods $A$ and $B$ of same cross-sectional are $A$ and length $l$ connected in series between a source $(T_1 = 100^o C)$ and a sink $(T_2 = 0^o C)$ as shown in figure. The rod is laterally insulated The ratio of the thermal resistance of the rod is 

The two ends of a rod of length $L$ and a uniform cross-sectional area $A$ are kept at two temperatures $T _{1}$ and $T _{2}\left( T _{1} > T _{2}\right) .$ The rate of heat transfer, $\frac{ dQ }{ dt }$ through the rod in a steady state is given by

A cylindrical metallic rod in thermal contact with two reservoirs of heat at its two ends conducts an amount of heat $Q$ in time $t$. The metallic rod is melted and the material is formed into a rod of half the radius of the original rod. What is the amount of heat conducted by the new rod, when placed in thermal contact with same two reservoirs in time $t$

Two rods of same length and material transfer a given amount of heat in $12\,s,$ when they are joined end to end. But when they are joined lengthwise, then they will transfer same heat in same conditions in ………. $\sec$

Three rods $A, B,$ and $C$ of thermal conductivities $K, 2K$ and $4K$, cross-sectional areas $A, 2A$ and $2A$ and lengths $2l, l$ and $l$ respectively are connected as shown in the figure. If the ends of the rods are maintained at temperatures $100\,^oC$, $50\,^oC$, and $0\,^oC$ respectively, then the temperature $\theta$ of the junction is