The main goal of the current study is to evaluate the effects of a hybrid heat transfer enhancement method, i.e. simultaneous deployment of active and passive techniques, with employing an ecofriendly-produced graphene nanoplatelets nanofluid from the viewpoint of the second law of thermodynamics. The numerical simulations are performed for the tubes enhanced with the innovative rotary twisted tape. Employing the rotary twisted tape intensifies the flow mixing, disrupts the thermal boundary layer, and reduces the temperature gradients dramatically. The total entropy generation and total exergy destruction of nanofluid extremely diminish by the rotational speed elevation. The maximum decrement in the total entropy generation is 87.38%, which occurs by elevating the rotational speed from 0 to 900 rpm. The concentration increase considerably contributes to the exergy destruction decrement besides total entropy generation reduction. The lower twisted ratio exhibits the smaller thermal irreversibility, and the best second law efficiency equals to 0.932. (C) 2020 Elsevier B.V. All rights reserved.