Proper Orthogonal Decomposition (POD) is a well-examined order reduction method. In this paper, it is implemented as a non-intrusive method for the cost-effective simulation of a multi-stream heat exchanger. Three-dimensional fluid-solid domains are analyzed conjugately, and the numerical results provide snapshots. The dimensionless vector-valued approach is suggested for the extraction of the base vectors. The Kriging (KRG) method is employed to approximate the coefficients of the bases. Reynolds numbers of the flow streams are variable parameters in the snapshots, and the field is reconstructed at two Reynolds number combinations. The field is reconstructed for two situations: one with full interpolation of the POD weighting coefficients and another with partial extrapolation for them. The deviation of the results is calculated regarding the corresponding CFD solution as the reference. In 96% of the comparative test cases, the estimated total heat exchanges and exit temperatures via POD have deviations less than 20%, and a substantial reduction in computational cost is attained. A deviation accumulation is observed due to the integration in post-processing. The partial extrapolation increases the deviation of heat exchange and temperature all over the domain because of the unified analysis.
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