This study aims to investigate the behavior of the micropolar hybrid nanofluid (Cu-TiO2) in a stretching and shrinking channel while maintaining a continuous laminar flow. External effects from magnetic field, thermal and solar radiation are also considered in the model. The governing differential (momentum, micro-rotation, and energy) equations are transformed into dimensionless forms via similarity transformations based on the boundary layer theory. The resulting ordinary differential equations are solved numerically using the fourth-order Runge-Kutta-Gill technique with the shooting method. The effects of nanoparticles transport on fluid flow and heat transfer are discussed and compared to the pure water case. The results are presented in tables or graphs such as velocity, temperature, angular-velocity profiles, and concentration.