In this study, a new and optimized algorithm for designing a plate and frame heat exchanger has been investigated. The main goal of this algorithm is selecting the best heat exchanger in order to achieve the highest heat load with the lowest heat transfer area and consequently the lowest economic cost for specific conditions. Also, this algorithm covers the optimized design for a multi-pass plate and frame heat exchanger with set of different corrugated thermal plates. Variables include the type and size of plates, the number of directories in each stream, the amount of pressure drop, the number of plates with different corrugation in each direction and the cost. According our knowledge, this is the first classical method for designing an optimal plate and frame heat exchanger using mathematical modeling

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