Rotating Brinkman Type Fluid Flow with Heat Transfer and Bioconvection Effects

Traditional water filtration systems face fouling due to stagnant zones, increasing maintenance. A rotating system prevents this by eliminating stagnant zones, reducing fouling and clogging. This approach improves efficiency, reduces maintenance, and extends the filtration system's lifespan. This problem is mathematically simulated using the Brinkman fluid model in channel, ideal for describing fluid flow through a porous membrane considering viscosity. This study investigates unsteady Brinkman-type fluid flow with motile microorganisms and heat transfer through a vertical channel, incorporating rotation to enhance fluid mixing, improve heat transfer, and influence microorganism behavior. Using partial differential governing equations and boundary conditions, the study simulates the problem, transforming equations into dimensionless form through dimensionless variables and applying Laplace transformation for exact solutions of velocity, temperature, and bioconvection. Results show that increasing rotation factor decreases primary fluid velocity while increasing secondary fluid velocity. The increased secondary velocity disrupts these stagnant zones, preventing buildup and ensuring continuous flow. Additionally, a higher bioconvection Rayleigh number reduces overall fluid velocity, as microorganism clustering restricts flow movement. Conversely, an increase in the bioconvection Lewis number weakens bioconvection effects, stabilizing filtration performance by minimizing flow disturbances. These insights provide a theoretical foundation for optimizing rotating filtration systems to improve efficiency and longevity.