In constrained optimization, valuable analytical insight can be gained by focusing attention on the terms of a problem before obtaining any solution particular to the numerical values of the given parameters. The necessary optimality conditions derived from the first semi-log derivatives may give a general result useful as a design rule for all similar problems. This approach is illustrated in the determination of optimal area allocation among the stages of two different multistage heat exchanger systems. This area allocation minimizes the total heat transfer area of the system with respect to: (1) interstage temperature for a given overall temperature change of the process stream; (2) “base area,” newly defined here as the ratio of capacity rate to the overall heat transfer coefficient.

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