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The aim of heat exchanger network synthesis is to design a cost-effective network configuration with the maximum energy recovery. Therefore, a nodes-based non-structural model considering a series structure (NNM) is proposed. The proposed model utilizes a simple principle based on setting the nodes on streams such that to achieve optimization of a heat exchanger network synthesis (HENS) problem. The proposed model uses several nodes to quantify the possible positions of heat exchangers so that the matching between hot and cold streams is random and free. Besides the stream splits, heat exchangers with series structures are introduced in the proposed model. The heuristic algorithm used to solve NNM model is a random walk algorithm with compulsive evolution. The proposed model is used to solve four scale cases of a HENS problem, the results show that the costs obtained by NNM model can be respectively lower 3226 $/a(Case 1), 11,056 $/a(Case 2), 2463 $/a(Case 3), 527 $/a(Case 4) than the best costs listed in literature.