Plug Flow Reactor with Heat Transfer Jacket
The temperature in a plug flow reactor and the temperature of the heat transfer fluid in an annular region around the reactor (a jacket) are plotted as functions of the cumulative reactor volume. Select "conversion" to plot fractional conversion of A (the reaction is A → B) versus reactor volume. The reactor contents and the heat transfer fluid flow cocurrently. A crosssection representation of the reactor (green circle) and the annular region (blue circle, which has a 2m radius) is shown on each plot. Use sliders to vary the heat transfer fluid temperature, reactor radius, and heat of reaction. The reactant feed temperature is 305 K. The velocities of the heat transfer fluid and the reactant are fixed, so when the reactor radius increases, the inlet molar flow rate of A increases, and the volumetric flow rate of the heat transfer fluid decreases. Download the CDF file to view the simulation using the free Wolfram CDF player. 

Details
Mass balance:
where x is conversion, V is volume (m^{3}), r_{A} is the reaction rate, F_{A,0} is the molar flow rate of component A (kmol/h) that converts velocity of feed to molar flow rate of feed, V_{A} is the velocity of component A (m/s), r is the radius of the inner tube (cm), ρ_{A} is reactant density (kg/m^{3}), and MW_{A} is the molar mass of A (kg/kmol).
Rate law:
where k_{f} and k_{r} are the forward and reverse rate constants (1/h), A is a preexponential factor (1/h), E_{f} and E_{r} are the activation energies for the forward and reverse reactions (J/mol), R is the ideal gas constant (J/[mol K]), T is temperature (K), ΔH is the heat of reaction (kJ/mol), and C_{A,0} is the inlet concentration of A (kmol/m^{3}).
Energy balances:
where U is the heat transfer coefficient (kJ/m^{2} h K]), a = 2/r is the heat exchange area per unit volume of reactor (1/m), T_{a} is the temperature of the heat transfer fluid (K), c_{P,C} is the coolant heat capacity (kJ/[kg K]), m is the mass flow rate of coolant (kg/h) which converts velocity of heat transfer fluid to mass flow rate, V_{C} is the coolant velocity (m/h) and ρ_{C} is coolant density (kg/m^{3}).