The present study characterizes the flow of three-dimensional viscoelastic magnetohydrodynamic (MHD) nanofluids flow with entropy generation analysis past an exponentially permeable stretched surface with simultaneous impacts of chemical reaction and heat generation/absorption. The analysis was conducted with additional effects nonlinear thermal radiation and convective heat and mass boundary conditions. Apposite transformations were considered to transform the presented mathematical model to a system of differential equations. Analytical solutions of the proposed model were developed via a well-known homotopy analysis scheme. The numerically calculated values of the dimensionless drag coefficient, local Nusselt number, and mass transfer Nusselt number are presented, with physical insights. The graphs depicting the consequences of numerous parameters on involved distributions with requisite deliberations were also a part of this model. It is seen that the Bejan number is an increasing function of the thermal radiation parameter.