In majority of industrial and engineering applications, enhanced heat transfer with minimum entropy production is the major concern. With several theoretical and experimental works, it has been found that replacing the traditional heat transfer liquids with nanoliquid is one of the reliable ways to enhance the thermal transport with minimum loss of system energy. In this regard, the current article deals with the convective nanoliquid flow and the associated thermal dissipation as well as entropy generation rates in a porous annular enclosure saturated nanoliquid. The vertical surface of interior and exterior cylinders is maintained with sinusoidal thermal conditions with different phase deviations, while the horizontal boundaries are thermally insulated. The governing physical equations are solved by implementing finite difference method (FDM). The variation in buoyant nanoliquid flow and the corresponding heat transport rates along with local and global entropy production rates are systematically examined. For the numerical simulations, a vast range of parameters such as the Rayleigh (103 ≤ Ra ≤ 105) and Darcy (10–6 ≤ Da ≤ 10–2) numbers, phase deviation (0 ≤ γ ≤ π), and nanoparticle volume fraction (0 ≤ ϕ ≤ 0.05) are considered in this analysis. The contributions of heat transfer entropy and fluid friction entropy to global entropy production in the geometry are determined through the Bejan number. The numerical results reveal the impact of various parameters on control of convective flow, heat transfer, and entropy generation rates. Further, the results are in excellent agreement with standard benchmark simulations. The predicted results could provide some vital information in choosing the proper choice of parameters to enhance the system efficiency.