The three rods shown in the figure have identical dimensions. Heat flows from the hot end at a rate of $40 \, W$ in the arrangement $(a)$. Find the rate of heat flow when the rods are joined as in arrangement $(b)$ (Assume $K_{Al} = 200 \, W/m^{\circ}C$ and $K_{Cu} = 400 \, W/m^{\circ}C$). (in $, W$)

Three identical rods have been joined at a junction to make a $Y$-shaped structure. If two free ends are maintained at $90\,^{\circ}C$ and the third end is at $30\,^{\circ}C$,what is the junction temperature $\theta$ in $^{\circ}C$?

The temperatures of the two outer surfaces of a composite slab,consisting of two materials having coefficients of thermal conductivity $K$ and $2K$ and thickness $x$ 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:

$A$ composite slab consists of two materials having coefficients of thermal conductivity $K$ and $2K$,thickness $x$ and $4x$ respectively. The temperatures of two outer surfaces of the composite slab are $T_2$ and $T_1$ respectively $(T_2 > T_1)$. 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:

The rate of flow of heat through a copper rod with a temperature difference of $28^{\circ} C$ is $1400 \ cal s^{-1}$. The thermal resistance of the copper rod will be:

Four rods of the same material and having the same cross-section and length have been joined as shown in the figure. The temperature of the junction of the four rods will be ............... $^{\circ}C$.