Q$.5$ In a counter$-$flow double pipe heat exchanger water flows through a copper tube $(19$ mm O$.$D$.$ and $16$ mm I.D$.),$ at a flow rate of $1\mathrm{.}48\frac{m}{s}.$ The oil flows through the annulus formed by inner copper tube and outer steel tube $(30$ mm O$.$D$.$ and $26$ mm I.D$.).$ The steel tube is insulated from outside. The oil enters at $0\mathrm{.}4k\frac{g}{s}$ and is cooled from $65C$ to $50C$ whereas water enters at $32C.$ Consider fouling factor for the water and oil sides as $0\mathrm{.}0005$ and $0\mathrm{.}0008m^2\frac{K}{W}$

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respectively. Also, the heat transfer coefficient at the inner surface of the annulus is $68\mathrm{.}2\frac{W}{m^2}K$ Neglecting the copper tube wall thermal resistance, calculate followings:

a$)$ The heat transfer coefficient at the inner side of copper tube

$[2$ Marks$]$

b$)$ The overall heat transfer coefficient

$[2$ Marks$]$

c$)$ LMTD

$[1$ Marks$]$

d$)$ The net heat transfer rate

$[1$ Marks$]$

e$)$ Length of tube

$[1$ Marks$]$

f$)$ The effectiveness of the heat exchanger

$[2$ Marks$]$

g$)$ NTU

$[1$ Marks$]$

Water and oil properties:

$\backslash$table$[[$Property$,$Oil,Water$],[(k\frac{g}{m^3}),850,995],[cp(k\frac{J}{k}gK),1\mathrm{.}89,4\mathrm{.}187],[k(\frac{W}{m}K),0\mathrm{.}138,0\mathrm{.}615],[$

$u(\frac{m^2}{s}),7\mathrm{.}44{10}^{-6},4\mathrm{.}18{10}^{-7}$