The dynamics of heating and cooling agitated and nonagitated batches with an external heat exchanger are well established. Fisher treated the heating of agitated batches by an external counterflow heat exchanger. Chaddock and Sanders extended the calculations to include the continuous addition of liquid to the tank and also took into account the heat of solution. Kern presented an analytical technique for non-agitated batches.

In all cases, the log mean temperature difference (LMTD) method is used in the derivations to express the heat delivered and received by the heat exchanger. The resulting equations are large, complex and unwieldy. This paper presents a simpler, less cumbersome approach, using the effectiveness-numbers of thermal units (E-NTU) method. An analytic comparison of agitated and nonagitated processes is also made.