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Question $3$:

$($a$)$ Heat is transferring from the internal surface $($at temperature $($T$1)$ and radius $(r1))$

to the external surface $($at temperature $($T$2)$ and radius $(r2))$ of a cylinder of length

$($ L $)$ and thermal conductivity $(k).$ Express the rate of one$-$dimensional conduction

through the cylinder wall in terms of the other parameters.

$(15$ marks$)$

$($b$)$ Heat is transferring from the internal surface $($at temperature $(T_1)$ and radius $($:$(r_1)\}$ to

the external surface $($at temperature $(T_2)$ and radius $($:$(r_2)\}$ of a sphere of thermal

conductivity $($ k $).$ Express the rate of one$-$dimensional conduction through the

sphere wall in terms of the other parameter