The rate of heat flow through the cross-section of the rod shown in figure is ($T_2 > T_1$ and thermal conductivity of the material of the rod is $K$)
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${r_{eff}} = \sqrt {{r_1}{r_2}} $
$\frac{{dQ}}{{dt}} = \frac{{KA\left( {{T_2} - {T_1}} \right)}}{L} = \frac{{K\pi {r_1}{r_2}\left( {{T_2} - {T_1}} \right)}}{L}$
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