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This communication predominately discusses the rheological attributes of the Darcy–Forchheimer flow of a nanoliquid over a stretchy sheet with a magnetic impact. The present model considers the two diverse nanoparticles, such as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>C</mi><mi>u</mi></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mi>g</mi></mrow></semantics></math></inline-formula>, and water as a base liquid. The heat equation accounts for the consequences of thermal radiation and a nonlinear heat sink/source when evaluating heat transmission phenomena. The current mechanical system is represented by higher-order PDEs, which are then remodeled into nonlinear higher-order ODEs that employ appropriate symmetry variables. The current mathematical systems are numerically computed by implementing the bvp4c technique. The characteristic attitudes of the related pertinent factors on the non-dimensional profiles are sketched via the figures, tables, and charts. The analysis predicts that the speed of the nanoliquid particles becomes slower when there is more presence of a magnetic field and injection/suction parameters. The growing amount of radiation is also pointed out, and the Eckert number corresponds to enriching the thermal profile.