The matrix formalism introduced by Domingos for the calculation of the effectiveness of assemblies of heat exchangers is extended to the case of complex exchangers, for which the restriction of complete mixing for each fluid in the inlet and outlet streams is relaxed. Rectangular matrices are used to relate the inlet and outlet temperatures, and their properties are discussed. The method can be used to find explicit solutions for configurations of practical interest, which are analyzed as assemblies of simpler units, coupled together in various ways. The formalism is illustrated by a model calculation of a 1–2 shell-and-tube exchanger with a finite number of baffles, for TEMA E (normal flow) and TEMA J (divided flow) types of shells.

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