A hollow tube has a length l, inner radius R_(1) and outer radius R_(2) . The material has a thermal conductivity K. Find the heat flowing thr

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A hollow tube has a length l, inner radius R_(1) and outer radius R_(2) . The material has a thermal conductivity K. Find the heat flowing through the walls of the tube if
(a) the flat ends are maintained at temperature T_(1) and T_(2)(T_(2)gtT_(1))
(b) the inside of the tube is maintained at temperature T_(1) and the outside is maintained at T_(2) .

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Correct Answer - (2piKl(T_(2)-T_(1)))/(In(R_(2)//R_(1)))

Let an element which is hollow cyl. of Radius and width dr
dR = (dr)/(K2pirl) R = (1)/(2piKl) underset(R_(1))overset(R_(2))int (dr)/(r ) = (1)/(2piKl)
(In r)_(R_(1))^(R_(2)) = (1)/(2piKl)In ((R_(2))/(R_(1)))
i_(H) = (T_(2)-T_(1))/((1)/(2piKl)ln(R_(2)//R_(1))) =(2piKl(T_(2)-T_(1)))/(ln(R_(2)//R_(1)))