Heat takes time

For heat transfer through conduction, the equation (simplified to one dimension) is $q = -k\frac{dT}{dx}$ , where $q$ is the heat flux rate (units of $Wm^{-2}$ ), $k$ is the thermal conductivity, and $\frac{dT}{dx}$ is the temperature gradient. For a series arrangement of same dimension components, the equivalent system has a conductivity which combines the way parallel resistances do in electric circuits, and vice-versa (for parallel - series). Evaluate this to get $q_1 = -\frac{2}{3}\kappa \frac{dT}{dx}$ and $q_2 = -3\kappa \frac{dT}{dx}$ . Same quantity of heat, say $Q$ is transported in times $t_1 = 9$ seconds and an unknown time $t_2$ across the same temperature gradient (net). Divide the equations and simplify to get $t_2 = 2$ seconds.

1>>>9/3=3 k=3 2k=6 2>>> 1/t=1/3 +1/6 t=2

IN SECOND CASE RESISTANCE IS 2/9 TIMES IN FIRST SO TIME TAKEN IS 2/9 TIMES THE INITIAL

As 2 blocks are identical in shape ,the 2 nd block takes 1/2 of time compared to block 1 .thus in con 1 ,to cross block 1 time required 6 s , & for block2 required time 3 s. .In con 2 ,as conductivity of block2 is double ,1/3 of heat energy passes through block 1.2/3 of energy passes through block2 .For this obviously the time required is 2 s