Which of the following circular rods, (given radius r and length l...

Heat conduction through a rod is given by $H=\frac{\Delta Q}{\Delta t}=K A\left(\frac{T_1-T_2}{l}\right) \Rightarrow \quad H \propto \frac{r^2}{l}$ ...(i) (a) When $r=2 r_0 ; l=2 l_0$$\begin{aligned} & H \propto \frac{\left(2 r_0\right)^2}{2 l_0} \\ \Rightarrow \quad & H \propto \frac{2 r_0{ }^2}{l_0}\end{aligned}$(b) When $r=2 r_0 ; l=l_0\begin{aligned} & H \propto \frac{\left(2 r_0\right)^2}{l_0} \\ \Rightarrow \quad & H \propto \frac{4 r_0^2}{l_0}\end{aligned}$$$(c) When$r=r_0 ; l=l_0 H \propto \frac{r_0^2}{l_0}$(d) When$r=r_0 ; l=2 l_0 H \propto \frac{r_0^2}{2 l_0}$ It is obvious that heat conduction will be more in case (b).