In this study, the effect of multiple convective conditions on a viscous unsteady incompressible electrically conductive nanofluid is analyzed. In addition, the fluid is squeezed between two parallel plates in the presence of an applied magnetic field. Nonlinear partial differential equations are remodelled into ordinary ones by introducing similarity transformations, which are solved numerically using the shooting iteration technique together with the Runge–Kutta sixth-order integration scheme; after that, the impact of affined parameters on the temperature and velocity distribution is shown by means of tables and graphs. Our studies suggest that the fluid temperature and the heat transfer rate decrease with the squeeze parameter.