Find effective thermal resistance between $A$ & $B$ of cube made up of $12$ rods of same dimensions and shown given thermal conductivity. [ $l =$ length of rod, $a =$ cross section area of rod]

A rod of length $L$ and uniform cross-sectional area has varying thermal conductivity which changes linearly from $2K$ at endAto $K$ at the other end $B$. The endsA and $B$ of the rod are maintained at constant temperature $100^o C$ and $0^o C$, respectively. At steady state, the graph of temperature : $T = T(x)$ where $x =$ distance from end $A$ will be

In the following figure, two insulating sheets with thermal resistances $R$ and $3R$ as shown in figure. The temperature $\theta$ is ...... $^oC$

The two ends of a rod of length $L$ and a uniform cross-sectional area $A$ are kept at two temperatures $T_1$ and $T_2 (T_1 > T_2)$. The rate of heat transfer,$\frac{ dQ }{dt}$, through the rod in a steady state is given by

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]

The dimensional formula for thermal resistance is