Mathematical study on Brinkman type carbon nanofluid flow in channel with bioconvection effect for water treatment applications.

Water pollution caused by the proliferation of microorganisms necessitates efficient treatment strategies to improve water quality. In this study, the bioconvective flow of a Brinkman carbon nanotubes (CNTs)-based nanofluid within a channel is analytically investigated to model water filtration processes in porous media. The Brinkman fluid model is employed to represent flow through permeable media, while the effects of motile microorganisms are incorporated through bioconvection. The governing linear partial differential equations, subject to appropriate initial and boundary conditions, are solved using the Laplace transform method to obtain exact solutions for velocity, temperature, and microorganism concentration profiles. The results reveal that increasing the CNTs volume fraction enhances the temperature and velocity profiles due to improved thermal conductivity, while significantly reducing microorganism concentration as a result of increased viscosity and enhanced mixing. Additionally, key parameters such as the bioconvection Lewis number, Rayleigh number, and Brinkman parameter are found to strongly influence the flow behavior. These findings provide valuable analytical insight into the interaction between nanoparticles, microorganisms, and porous media, with potential applications in optimizing water filtration and wastewater treatment systems.