Here the reacting mixture and coolant flow in opposite directions for counter current flow of coolant and reactants. At the reactor entrance, V = 0, the reactants enter at temperature T0, and the coolant exits at temperature Ta2. At the end of the reactor, the reactants and products exit at temperature T, while the coolant enters at Ta0.
Figure 12-4. Counter current, double pipe heat exchanger.
Again we write an energy balance over a differential reactor volume to arrive at.
At the entrance V = 0 ∴ X = 0 and