Optimizing the thermal aspects of working liquid is a realistic procedure to boost heat transference effectiveness. Nanoliquids (including nano-particles adjourned in a base liquid) appear as a favorable aspirant. These cutting-edge liquids could function as both emergency and primary coolants in nuclear reactors contributing improved performance under critical conditions. This research accounts magnetically driven Sutterby nanomaterial squeezed flow configured by parallel convective walls. Convective squeezed flow subject to thermo-solutal buoyancy forces is formulated. Heat-mass transportation features are addressed through Cattaneo-Christov (CC) dual diffusive models. The expressions governing the nonlinear flow together with heat-mass transportation are derived by deploying lower magnetized Reynolds number and negligible dissipation assumptions, and then converted to dimensionless expressions by delineating the apposite similarity variables. Numerical solutions through shooting scheme are acquired. Results are outlined and physical elaboration is comprehensively addressed for sundry flow factors. Variations in dimensionless profiles is analyzed graphically and arithmetically. To ensure the accuracy of deployed solution scheme, the results obtained are compared with available limiting cases and found that our deployed scheme has good agreement with existing outcomes. It is inspected that Brownian diffusive factor intensifies the nano-particles concentration while thermophoresis variable exhibits reduction in concentration. Larger thermal-solutal relaxation factors yield lower temperature and nano-particles concentration.