Studies related to enhancing heat transfer has attained much attention of researchers to avail optimized heat-transfer devices. High viscous fluids are of great importance as they are widely used in petroleum products, organic chemistry, coating, printing, and so forth. In this study, heat transfer mechanism driven by Eyring-Powell nanoliquid flow in a vertical microchannel is examined. Impact of considering buoyancy force, magnetic field, and convective boundary on the thermal system is demonstrated. The modeled nondimensional equations are computed by using the Runge-Kutta-Fehlberg method. The vital roles of thermophoresis and Brownian motion are discussed in detail. The significance of second law analysis for thermal systems is presented. The causes of irreversibilities in a microchannel due to Eyring-Powell nanoliquid flow is also demonstrated in the current research study. The upshots of the current investigations are visualized through graphical elucidation. It is established that minimization of entropy generation can be achieved by enhancing the mechanism of thermophoresis. The convective boundary helps in transmitting heat from the thermal system to the ambience hence the lower thermal field is attained.