$A$ slab consists of two parallel layers of two different materials of same thickness having thermal conductivities $K_1$ and $K_2$. The equivalent conductivity of the combination is

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 $, W$)

Two rods of the same length and material transfer a given amount of heat in $12 \, s$ when they are joined in parallel. But when they are joined in series,then they will transfer the same amount of heat under the same conditions in ........ $s$.

Five metal rods of the same cross-sectional area $A$ and same length $l$ are connected as shown in the figure. If the thermal conductivities of copper and steel are $K_1$ and $K_2$ respectively,then the resultant thermal resistance between $A$ and $C$ is:

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

$A$ cylinder of radius $R$ made of a material of thermal conductivity $k_1$ is surrounded by a cylindrical shell of inner radius $R$ and outer radius $2R$ made of a material of thermal conductivity $k_2$. The two ends of the combined system are maintained at different temperatures. There is no loss of heat from the cylindrical surface and the system is in steady state. The effective thermal conductivity of the system is