The Borexino detector at Gran Sasso National Laboratories (INFN) has obtained extraordinary achievements for solar neutrino and geoneutrino physics during its lifetime. More recently, Borexino has provided the first experimental evidence of the subdominant CNO solar neutrino flux, thanks to an outstanding low background level obtained by means of intense purification campaigns and a continuous improvement of the detector thermal stabilization over the years. In particular, this impressive thermal steadiness has led to a progressive mitigation of the internal convective currents which are responsible for the continuous background contamination of the detector sensitive inner volume. To this purpose, numerical analyses are essential to better comprehend the detector fluid dynamics, the background behavior, and are also important to propose effective countermeasures to further reduce natural convection inside the detector. In this framework, the present work investigates the flow characteristics of the liquid scintillator by means of computational fluid dynamics analyses. In particular, a full 3D model of the Borexino inner vessel is considered in the simulations, addressing the complex nature of the natural convective currents under consideration both in transient and stationary conditions. The calculated flow pattern has been adopted to predict the transport behavior of 210Po, that is fundamental for the independent constraint of 210Bi, the main background constituent affecting CNO measurement. The convection-diffusion analysis demonstrates the applicability of the adopted methodology showing a good agreement between calculation and experimental data.