Governing equations for describing the axial variation of temperature differences of fluids flowing in a three-channel single-pass heat exchanger are formulated by adopting similar assumptions as those used in the classical log-mean-temperature-difference (LMTD) method for two-channel heat exchangers. A special-case solution and a generalized solution of these governing differential equations are obtained for designing exchangers with split-flow channels in both parallel-flow and counterflow configurations. The special-case solution can be obtained under the condition of having identical axial-temperature distributions in the split-shell-how channels and is similar to the classical formulation for two-channel heat exchangers, but with some parameter modifications. Solutions of this general model confirm that the special-case model represents the optimum design of such heat exchangers. These results are also verified experimentally using a concentric-tube heat exchanger. Theoretically predicted heat-exchanger effectivenesses are found on the average to be within +/-5% of the experimental measurements.