In this paper, both first and second laws of thermodynamics are employed to examine the combined effects of nonlinear thermal radiation, buoyancy forces, thermophoresis and Brownian motion on entropy generation rate in hydromagnetic couple stress nanofluid flow through a vertical channel with permeable walls. The model equations of momentum, energy balance and nanoparticle concentration are obtained and tackled numerically using a shooting technique coupled with Runge-Kutta-Fehlberg integration scheme. The numerical results for velocity, temperature and nanoparticles concentration profiles are utilised to determine the skin friction, Nusselt number, Sherwood number, entropy generation rate and Bejan number. It is found that the entropy production in the flow system can be effectively minimized by regulating the values of the thermophysical parameters for efficient operation. Some other interesting results are displayed graphically and discussed quantitatively.