Sensitivity analysis of microbial characteristics of trihybrid carreau nanofluid using response surface methodology and ANOVA.

This study considers the sensitivity analysis of a trihybrid Carreau nanofluid by examining the transport and distribution of motile microorganisms within a suspension composed of titanium oxide, copper, and silver nanoparticles dispersed in sodium alginate as the base fluid. Sodium alginate is selected due to its shear-thinning rheological behavior, which is well represented by the Carreau fluid model. The nanofluid-microorganism mixture is assumed to flow over a nonlinearly stretched Riga surface under time-dependent stagnation-point conditions. The proposed model considers two-dimensional laminar flow in a porous medium, incorporating the effects of Newtonian heating, Stefan blowing, nonlinear thermal radiation, viscous dissipation, and chemical reactions. The governing partial differential equations (PDEs), derived from the fundamental conservation laws of mass, momentum, energy, nanoparticle concentration, and microorganism density, are transformed into a system of coupled nonlinear ordinary differential equations (ODEs) through appropriate similarity transformations. These equations are solved numerically using MATLAB's bvp4c algorithm. Furthermore, Response Surface Methodology (RSM) based on a Central Composite Design (CCD) is employed to optimize the velocity, thermal, solutal, and microbial transport characteristics. The combined effects of nanoparticle volume fractions (0.01-0.05) and unsteady parameters (0.1-0.6) on the Nusselt number, Sherwood number, and motile microorganism density factor are systematically examined. A sensitivity analysis is also conducted to assess the influence of nanoparticle loading on the microbial density response, highlighting the robustness and stability of the proposed microbial nanofluid system. The trihybrid nanofluid shows significantly improved thermal performance 24% and microbe's acclivity reduction 18% as compared to the conventional fluid. The statistical significance of the input factors is confirmed by an ANOVA (ANalysis Of Variance) with a model [Formula: see text] value of more than 99%. Findings indicate that silver nanoparticles improve velocity, temperature, concentration and microbial gradients with increased concentration of the silver nanoparticles because of the high thermal conductivity and bioactivity but titanium oxide has a high microbial impact. The trihybrid nanofluid displays much better thermal performance and microbial activity in comparison with conventional nanofluids and optimized configurations of nanofluids obtained with the help of RSM.