This paper investigates entropy generation rate in a temperature-dependent variable viscosity unsteady nanofluid flow past a convectively heated impulsively moving permeable cylindrical surface. The governing equations based on the modified Stokes first problem assumption are obtained and transformed using appropriate similarity variables into nonlinear ordinary differential equations. The numerical shooting method together with the Runge-Kutta Fehlberg integration scheme are employed to effectively solve the problem. The effects of related parameters on the nanofluid velocity, temperature, skin friction, Nusselt number, entropy generation rate and Bejan number are displayed graphically and quantitatively explained. It is found that an upsurge in nanoparticles volume fraction enhances the skin friction, Nusselt number, entropy production rate and the Bejan number.