Biological waste to energy conversion and hydrogen production utilizing statistical analysis of motile number for radiation absorption on bio-convective MHD flow of Williamson nanofluid

The non-Newtonian behavior distinguished by the Williamson nanofluid is enriched with the Brownian motion of the nanoparticles that enhance thermal conductivity and radiation absorption. Moreover, bio-convection is useful in enhanced nutrient transport due to the motility of microorganisms, which is vital for microbial energy conversion processes. The current study aims to investigate the magneto-driven bio-convective transport of non-Newtonian Williamson nanofluid that is useful in converting organic waste to energy and hydrogen production processes. The inclusion of inertial drag, magnetic field, and higher-order chemical reaction provides a broad model for the thermal and solutal transport phenomena. The role of drag, representing resistance to flow through a permeable medium, magnetization that induces Lorentz forces, is presented to optimize the fluid motion and heat transfer. The utilization of chemical reactions within the system is to simulate hydrogen production through thermochemical processes. The modelled problem is in dimensional form and appropriate similarity transformations are adopted for the reformulation of the model into dimensionless. Further, a traditional numerical scheme i.e. shooting-based Runge-Kutta fourth-order is proposed for the solution of the transformed phenomena. More appropriately, a statistical method likely “response surface methodology” (RSM) is utilized to assess the influence of motile numbers with the variation of numerous factors. Finally, the result demonstrates that the bio-convection, MHD flow, and nanofluid properties significantly enhance waste-to-energy conversion and hydrogen production.