We will carry out an energy balance on the volume ΔV. There is no work done, i.e., , so Equation (11-10) becomes
The heat flow to the reactor, , is given in terms of the overall heat transfer coefficient, U, the heat exchange area, ΔA, and the difference between the ambient temperature Ta and the reactor temperature T.
where a is the heat exchange area per unit volume of reactor. For a tubular reactor ...