<p>Maxwell fluid has attracted attention because of their impressive thermal characteristics and use in polymer processing, metal spinning and rolling, biomedical engineering, and cooling systems. This study emphasizes the graphical investigation of the flow behavior and heat transfer of a Maxwell ternary nanofluid (Al₂O₃-Cu-Fe₃O₄/water) over a shrinking surface with the impacts of a magnetic field, suction, shrinking parameter, and heat source or sink. Using a set of similarity transformations, ordinary differential equations (ODEs) are generated through alteration of the leading equations. The resulting equations are solved with the assistance of a well-established finite difference method (FDM). For the exactness and justification of the present outcomes, an assessment is conducted between the current solutions and the data that is accessible, which demonstrates a good consistency. Graphical results show that the velocity rises and the temperature declines for increasing magnetic field, suction, and shrinking parameter. In contrast, larger nanoparticle volume fractions, Biot number, and heat source feature cause an enlargement in the temperature outline. Larger suction parameter, shrinking parameter, and magnetic field parameter result in an increase in the heat flux about 6%, 3%, and 0.2%, respectively. The opposite is discovered with a higher volume fraction of nanoparticles and heat source parameter, which show a slight reduction in the heat flux of about (0.15&#xa0;to0.3)% and 2.6%, respectively.</p>