12.2.1 Co-Current Flow
The heat transfer fluid will be a coolant for exothermic reactions and a heating medium for endothermic reactions. If the flow rate of the heat transfer fluid is sufficiently high with respect to the heat released (or adsorbed) by the reacting mixture, then the heat transfer fluid temperature will be virtually constant along the reactor. In the material that follows we develop the basic equations for a coolant to remove heat from exothermic reactions, however these same equations apply to endothermic reactions where a heating medium is used to supply heat.
We now carry out an energy balance on the coolant in the annulus between R1 and R2 and between V and V + ΔV, as shown in Figure 12-2. The mass flow rate of the heat exchange fluid (e.g., coolant) is 
. We will consider the case when the reactor is cooled and the outer radius of the coolant channel R2 is insulated. Recall that by convention 
is the heat added to the system.
Figure 12-2. Co-current double pipe heat exchanger.
The reactant and the coolant flow in the same direction
The energy balance on the coolant in the volume between V and (V + ΔV) is
where Ta is the coolant temperature, and T is the temperature of the reacting mixture in the inner tube.
Dividing by ΔV and taking limit as ΔV → 0
Analogous to Equation (12-4), the change in enthalpy of the coolant can be written as
The variation of coolant temperature Ta down the length of reactor is
The equation is valid whether the heat transfer fluid is a coolant or a heating medium.
Typical heat transfer fluid temperature profiles are shown here for both exothermic and endothermic reactions when the heat transfer fluid enters at Ta0.
Figure 12-3. Heat transfer fluid temperature profiles for co-current heat exchanger. (a) Coolant. (b) Heating medium.
