Box–Behnken design-based multi-parametric optimization of species transportation rate in magnetized Casson nanofluid flow on a stretching sheet with gyrotactic microbes and pollutant dispersion
摘要
This article investigates the characterization of heat and species transfer in Casson nanofluid flow with gyrotactic microbes driven by a stretching surface, with the particular relevance to environmental engineering applications such as pollutant dispersion, wastewater treatment, and contaminant control processes. The formulated mathematical model incorporates magnetism, non-Newtonian rheology, pollutant external term, and bioconvective terms due to microorganism dynamics. Further, the thermal characteristics are enhanced for the combined effects of thermal radiation, heat source, thermophoresis, and Brownian motion. The standard equations proposed here are converted into their corresponding non-dimensional model by using similarity transformation and numerical solution is adopted to find the solution of these transformed equations. Particularly, the shooting-based technique with the bvp4c routine in MATLAB is employed for the computations, and the physical responses of the variables are demonstrated via graphical plots and validated against existing studies to ensure the accuracy and reliability of the result. A statistical analysis utilizing response surface methodology (RSM) is carried out using Box–Behnken design (BBD) for the optimized rate of species transmission on in the bioconvective magnetic nanofluid transport. The quadratic RSM model demonstrates high predictive accuracy with an adjusted R2 of 0.9954 and a predicted R2 of 0.9868, while ANOVA indicates strong statistical significance (F = 433.94, p < 0.0001), revealing that Lewis number, Brownian motion parameter, and pollutant external parameter are the most influential parameters affecting the Sherwood number.