Influence of enhanced mass transfer induced by Brownian motion on supported nanoliquids membrane: Experimental correlation and numerical modelling

•Establishment of mass transfer/momentum modelling of nanoliquid considering the Brownian motion role.•Development of a novel correlation to predict mass transfer coefficient in supported nanoliquid membrane.•Investigating experimental data with the predicting correlation of effective mass diffusion coefficient which was developed based on the heat and mass transfer.•Interpreting the influence of nanoparticle mass fraction and Rayleigh number via results of the nanoparticles Brownian motion and nanoliquid mass transfer modelling.•Evaluating nanoparticle mass fraction on convection mass transfer via Brownian motion. The Brownian motion of nanoparticles in a liquid system can be considered as the predominant mechanism governing the mass transfer improving behavior of nanofluids. A predicting correlation of effective mass diffusivity in supported nanoliquid membrane was developed base on the heat and mass transfer analogy. According to the comparing the correlation results with experimental data, the validity of predicting correlation was investigated and the AARE value was 21.28%. For the first time a theoretical two-dimensional model was established to clarify the role of nanoparticles and their Brownian motion on convection mass transfer, considering the fundamental influence of the Brownian motion, and model outputs including streamline, iso-concentration, nanoparticle distribution, and Sherwood number graphs in the different defined conditions were interpreted. Comparing the case that taking of Brownian motion effect into account and neglecting its influence, it was observed that by the Brownian motion, the mass transfer improvement in any defined condition achieves, although the highest enhancement was gained by the lowest nanoparticle mass fraction. [Display omitted]