The rheology of Burgers nanofluid flow over a stretching cylinder with convective transport of thermal and solutal energy is studied in the present article. The relaxation and retardation properties of viscoelastic fluid are examined for flow field and energy distribution. Moreover, the thermophoretic and Brownian forces are also incorporated in the phenomena of thermal and solutal energy distribution. The thermal conductivity of the fluid is taken as temperature dependent. The homotopy analysis method (HAM) is adopted to solve the governing ordinary differential equations (ODEs). The impact of physical parameters on the flow field and energy transport is depicted using graphs. The outcomes proved that both thermophoretic and Brownian forces significantly boosted the temperature field but in the case of concentration field these show conflicting behaviour. The Burgers parameter of viscoelastic fluid enhances the thermal and solutal conduction in the fluid and decreases the fluid velocity. Moreover, due to the increase in temperature-dependent thermal conductivity, the transport of energy increases. The outcomes of this study are validated by comparing numerical data with some previous studies.