In co$-$current configuration $($Figure$-1),$ a hydrocarbon liquid flowing through a $r=1cm($internal$)$ radius heat exchanger tube with length $1m.$ The liquid enters at a temperature of $=0$ and is cooled by a boiling liquid on the outside of the tube, the latter liquid's boiling point is $Tc=373K.$ We can model the hydrocarbon liquid temperature as a function of the tube coordinate $z$ with the single differential equation:

$m_h{C}_{ph}\frac{d{T}_h}{dz}=2rh(T_c-T_h)$

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where the heat transfer coefficient is given as $h=550\frac{W}{m^2(K)},Cph=2100\frac{J}{kgK},$ and the mass flow rate of the hydrocarbon stream is $mh=0\mathrm{.}5k\frac{g}{s}.$

Compute the hydrocarbon stream outlet temperature $)=(1$ and $T_b$ vs $Z$

Figure I Heat exchanger co$-$current configuration