Question $1(40$ Marks$)$

In a counterflow double pipe heat exchanger water flows through a copper tube with outer diameter of $0\mathrm{.}019$ m and inner diameter $0\mathrm{.}016$ m at a flow velocity of $\backslash (1\mathrm{.}48\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash ).$ The oil flows through the annulus formed by inner copper tube and outer steel tube with outer diameter $0\mathrm{.}03$ m and inner diameter $0\mathrm{.}026$ m $.$ The steel tube is insulated from the outside. The oil enters at $\backslash (0\mathrm{.}4\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$s$\}\backslash )$ and is cooled from $\backslash (65^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ to $\backslash (50^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ whereas water enters at $\backslash (32^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ Neglect the copper tube wall thermal resistance.

The Fouling factor on water side is $\backslash (0\mathrm{.}0005\backslash$mathrm$\{$~m$\}^\{2\}\backslash$mathrm$\{$~K$\}/\backslash$mathrm$\{$W$\}\backslash ),$ and the Fouling factor, oil side $\backslash (=0\mathrm{.}0008\backslash$mathrm$\{$~m$\}^\{2\}\backslash )$ K$/$W

A$.$ Determine the final temperature of the water. $[3$ Marks$]$

B$.$ Determine whether the water flow is Turbulent or Laminar $[4$ Marks$]$

C$.$ Determine the Convective Heat Transfer coefficient from the water side $[4$ Marks$]$

D$.$ Determine whether the oil flow is Turbulent or Laminar $[4$ Marks$]$

E$.$ Determine the convective Heat Transfer coefficient for the oil side $[4$ Marks$]$

F$.$ Determine the overall Heat Transfer coefficient for this Heat Exchanger for the following:

i$)$ Considering Fouling $[5$ Marks$]$

ii$)$ Neglecting Fouling $[4$ Marks$]$

G$.$ Calculate the length of the tube required.

i$)$ Considering Fouling $[3$ Marks$]$

ii$)$ Neglecting Fouling $[3$ Marks$]$

H$.$ Describe Fouling and explain how it can influence the performance of a Coal Fired Thermal Power Plant. $[6$ Marks$]$