In this work, numerical investigation of the natural convection and entropy generation characteristics of biological Ag-water nanofluid in a horizontal annulus having fins attached to the inner cylinder is aimed. The impacts of nanoparticle volume concentration (φ = 0, 0.1, 0.5 and 1%), Rayleigh number (Ra = 103, 104 and 105), and number of fins (n = 0, 2, 4 and 8) on the flow structure, temperature distribution, average Nusselt number (Nu) as well as on the thermal, frictional and total entropy generation rates are examined comprehensively. The computational outcomes indicate that the fin attachment and the increment of its number significantly improve Nu up to 35.50%, while the entropy generation rate sourced by heat transfer significantly increases up to 39.07% accordingly, compared to the finless annulus. The frictional entropy generation is remarkably decreased at low Ra by the increment of the number of fins, nevertheless, it is notably increased at high Ra. Besides, the inclusion of nanoparticles significantly contributes to the augmentation of Nu, being attained up to around 30% with a volume fraction of φ = 1%, whereas it significantly increases both thermal and frictional entropy generation rates, which can respectively reach up to 30.25 and 77.60% at the same volume fraction in the finless annulus.