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Advection dominant fluid flows and transport processes in microfluidic mixing devices pose noteworthy challenges in design related simulations as regards numerical errors. In the present work, an unsteady flow model with decay constant was utilized for testing passive micro-mixer simulations for numerical error. The simulations were performed using OpenFOAM (Open-source Field Operation And Manipulation), a finite volume based open source software. Three types of hydrodynamic boundary conditions representing surface engineered device walls (hydro-active patches) were investigated as design test cases. Our study focuses upon simulated effect of these conditions on concentration profiles from the point of view of numerical error. We show that the model can be analytically treated in part to establish a particular feature in the simulated concentration profiles is a numerical artefact. Further, it is shown that this error is rectified either by changing the method of solving discretized equation or by coarsening the mesh. This process is also sensitive to the type of hydrodynamic boundary conditions imposed. A generalized grid convergence test we carried out attests to the reliability of these micro-fluidics simulation results, despite the fact that they display numerical artefacts. The paper addresses this anomaly to a strong interplay between difference equation solving methods, mesh parameters and boundary conditions in the partial differential equation (PDE) model for micro-flows in passive micro-mixers. Our investigation thus suggests that grid independence tests, instead of being based only upon cell variables and mesh parameters, should also be informed by PDE boundary conditions and difference equation solving methods.