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Hybrid nanofluids (HNFs) are a new breed of nanofluids that possess numerous tempting applications encompassing microfluidics, transportation, defense, medical, etc. The objective of this novel exploration is to inspect the behavior of Hamilton–Crosser (H-C) and Yamada–Ota (Y-O) HNF flow models past a stretching cylinder. The H-C model is also used to gauge which particle shape (blade, platelet, cylinder, brick) is more effective in the improvement of the heat transfer rate. The envisioned flow is influenced by the Hall current, Cattaneo–Christov (C-C) heat flux and variable thermal conductivity (TC). The uniqueness of the projected model is the notion of a heterogeneous reaction sprouting on the surface of the cylinder in the presence of an absorbent medium. Owing to this supposition, the chemical reaction occurs in the least possible time. The proposed model's novelty lies in the consideration of the surface catalyzed reaction in the HNF flow models past a stretching cylinder amalgamated with the unique impacts of the Hall current, C-C heat flux and variable TC. The thermal performance of the two renowned models H-C and Y-O is also evaluated. The MATLAB software bvp4c technique is used for numerical outcomes of this coupled system. The analysis depicts that the performance of the Y-O HNF flow model is far above the H-C HNF flow model. It is also inferred from the results that blade-shaped nanoparticles possess higher TC than the other nanoparticles. The heat transfer rate for blade-shaped nanoparticles is stronger than the other nanoparticles. The fluid concentration reduces for higher surface-catalyzed reaction parameter. The corroboration of the proposed model is also given in this study. The comparative results disclosed that in the case of the magnetic parameter M , the minimum error percentage is 0.015% for M = 0. 5 , and permeability parameter λ , the least error percentage is 0.037% for λ = 1. 0. [ABSTRACT FROM AUTHOR]