With explanationQuestion $1(20$ marks$)$

A double$-$pipe heat exchanger is designed to condense saturated steam as Figure $1.$ Water flows at an average temperature of $37\mathrm{.}8C$ and an average velocity of $2\mathrm{.}6\frac{m}{s}.$ If the inner surface temperature of the inner pipe is $65\mathrm{.}6C$ and the heat exchanger is $3\mathrm{.}5m$ long, determine:

$($i$)$ the heat transfer rate from the steam to water.

$($ii$)$ the inlet and outlet temperature difference of water.