Spectral and Taguchi approaches to entropy generation minimization of a particulate Casson-micropolar nanofluid suspension in an unsteady flow regime

This study models the unsteady flow, heat transfer, and entropy generation of a Casson-micropolar Al2O3 water nanofluid in a convectively heated, permeable vertical microchannel that account for the combined effects of viscous, Darcy and Joule dissipation. Motivated by efficient thermal management of high-heat-flux systems (microelectronics cooling, lab-on-chip devices) that increasingly relies on yield-stress, and microstructural nanofluids, yet the transient startup behaviour and thermodynamic irreversibility of such fluids in convectively bounded microchannels remain largely unexplored. Subject to the given conditions, governing equations are formulated and solved via bivariate spectral collocation method (BSCM) that discretizes the temporal and spatial directions simultaneously on Chebyshev-Gauss-Lobatto grids, with convergence confirmed by grid-independence and benchmarked against existing steady-state solutions. A Taguchi L27/ANOVA analysis with the smaller-the-better criterion then identifies the parameter combination minimizing the total entropy generation. Findings identified that volumetric flow rate exhibits a bounded, and non-monotonic transient response before settling to a quasi-steady value. Velocity and temperature fields increased with thermal radiation, the Eckert number and the convective heating (Biot) parameter. The microrotation profile undergoes a sign reversal near the channel mid-plane. The fluid-friction irreversibility dominates over heat-transfer irreversibility (Bejan number remains below approximately 0.35 throughout), and the Taguchi-ANOVA analysis identifies the Brinkman number as the dominant factor controlling entropy generation (77.9% contribution), followed by the pressure gradient and nanoparticle volume fraction, with the optimum entropy obtained at a higher Darcy number and nanoparticle volume fraction combined with lower Brinkman number, radiation parameter, pressure gradient and magnetic field.