Numerical analysis is performed for magnetohydrodynamics (MHD) couple stress nanofluid flow over a stretching sheet with melting and nonlinear radiation. The second law of thermodynamics is also incorporated with first-order slip. Nanofluid characteristics for thermophoresis and Brownian moments are encountered. The system that comprises differential equations of partial derivatives is remodeled into the system of differential equations via similarity transformations and then solved numerically through the Runge-Kutta-Fehlberg fourth-fifth (RKF-45) order technique. The physical parameters, which emerges from the derived system are discussed in graphical format. The significant outcomes of the current investigation are that the velocity field decays for a higher magnetic parameter. Another, important outcome of the study is both temperature and concentration are increasing functions of the first-order slip. Nusselt and Sherwood numbers are decreasing with an increase in magnetic strength. Further, Bejan number augment due to enhancement in the first-order slip and couple stress fluid parameters whereas a differing tendency is shown for magnetic and radiation parameters.