The temperatures of the two outer surfaces of a composite slab,consisting of two materials having coefficients of thermal conductivity $K$ and $2K$ and thicknesses $x$ and $4x$ respectively,are $T_2$ and $T_1$ $(T_2 > T_1)$. The rate of heat transfer through the slab in a steady state is $\left( \frac{A(T_2 - T_1)K}{x} \right)f$,where $f$ is equal to:

Two plates of the same thickness with coefficients of thermal conductivities $K_1$ and $K_2$ and cross-sectional areas $A_1$ and $A_2$ are connected as shown. Find the effective coefficient of thermal conductivity $K_{eq}$.

Two diagonally opposite corners of a square made of four thin rods of the same material and same dimensions are at temperatures $40^{\circ} C$ and $10^{\circ} C$. If only heat conduction takes place,then the temperature difference between the other two corners will be .......... $^{\circ} C$.

Consider a compound slab consisting of two different materials having equal thickness and thermal conductivities $K$ and $2K$ respectively. The equivalent thermal conductivity of the slab is

$A$ composite block is made of slabs $A, B, C, D$ and $E$ of different thermal conductivities (given in terms of a constant $K$) and sizes (given in terms of length,$L$) as shown in the figure. All slabs are of same width. Heat $Q$ flows only from left to right through the blocks. Then in steady state:
$(A)$ Heat flow through $A$ and $E$ slabs are same.
$(B)$ Heat flow through slab $E$ is maximum.
$(C)$ Temperature difference across slab $E$ is smallest.
$(D)$ Heat flow through $C =$ Heat flow through $B +$ Heat flow through $D$.

$A$ cylinder of radius $R$ is made of a material with thermal conductivity $K_1$. It is surrounded by a cylindrical shell of a material with thermal conductivity $K_2$,having an inner radius $R$ and an outer radius $2R$. The two ends of this composite system are maintained at two different temperatures. There is no heat loss from the surface of the cylinder in the steady state. Find the equivalent thermal conductivity of the system.