Question $2(35$ points$)$

For the tubular reactor with heat exchange $(Q)$ as shown in Fig, Q$2,$ derive the three equations

required to calculate the temperature and conversion against the reactor volume if the heat

exchange fluid surrounding the reactor is changing. Clearly show the details of your derivation

and state all assumptions made.

Fig, Q$2.$ Tubular reactor with heat exchanger

where:

$Q^{}$ is the rate of heat flow to the system

$V$ is the volume

$T_0$ is the inlet temperature of the reactants.

$T_{AO}$ is the inlet temperature of the heat exchange fluid.

$F_{AO}$ is the inlet molar flow of the limiting reactant.