$A$ composite rod is made of three rods of equal length and cross-section as shown in the figure. The thermal conductivities of the materials of the rods are $K/2, 5K$ and $K$ respectively. The ends $A$ and $B$ are at constant temperatures. All heat entering the face $A$ goes out of the end $B$,with no loss of heat from the sides of the bar. The effective thermal conductivity of the bar is:

$A$ window used to thermally insulate a room from outside consists of two parallel glass sheets each of area $2.6 \,m^2$ and thickness $1 \,cm$ separated by $5 \,cm$ thick stagnant air. In the steady state, the room-glass interface is at $18^{\circ} C$ and the glass-outdoor interface is at $-2^{\circ} C$. If the thermal conductivities of glass and air are respectively $0.8 \,Wm^{-1} K^{-1}$ and $0.08 \,Wm^{-1} K^{-1}$, the rate of flow of heat through the window is (in $\,W$)

$A$ copper rod $2 \ m$ long has a circular cross-section of radius $1 \ cm$. One end is kept at $100^{\circ}C$ and the other at $0^{\circ}C$,and the surface is covered by non-conducting material to prevent heat losses through the surface. The thermal resistance of the bar in Kelvin per Watt is (Take thermal conductivity $K = 401 \ W/m-K$ of copper):- (in $.9$)

Why do people prefer to give a layer of sand or foam insulation on ceilings made of concrete?

The temperature $\theta$ at the junction of two insulating sheets,having thermal resistances $R_{1}$ and $R_{2}$ as well as top and bottom temperatures $\theta_{1}$ and $\theta_{2}$ (as shown in figure) is given by

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