A shell$-$and$-$tube heat exchanger is used to cool biodiesel from $60[$C$]$ to $30[$C$].$ The biodiesel flows into the shell side at $5\mathrm{.}0[$m$3/$h$].$ The cooling water flows into the tube side at $10[$C$]$ and out at $30[$C$].$ The inside diameter of the copper pipe used in the exchanger is $1\mathrm{.}5[$in$].$ The wall of the copper pipe is $0\mathrm{.}072[$in$].$ The heat$-$transfer coefficient for the biodiesel on the shell side was measured as $340[$W$/($m$2*$K$)].$ The thermal conductivity of copper is $400[$W$/($m K$)].$ The average density of biodiesel in this temperature range is $880[$kg$/$m$3].$ The heat capacity of biodiesel is $2400[$J$/($kg$*$K$)].$ The heat capacity of water is $4200$ J$/($kg K$).$ The thermal conductivity of water is $0\mathrm{.}6$ W$/($m$*$K$).$

Calculate the flow rate of the cooling water.

Calculate the heat load on the exchanger.

Calculate the convective heat transfer coefficient for the water$/$tube side.

Calculate the overall heat transfer coefficient.

Calculate the area required for the heat exchanger. $($What will you do about the temperature? Will you use a shape factor?$)$

Calculate the total length of tubing required.

How many passes will the tubing make if the length of the shell is limited to $2[$m$].$