Bioconvection in polar fluid with microstructure: A fractional heat and mass transfer model with non-singular and non-local kernel

Bioconvection flows occur in working fluids where the growth of microorganisms is subject to convective flows. Understanding the flow behavior of these fluids is essential for many biological and environmental processes, such as the purification of water, drug delivery, and microbial ecology. This article explores the bioconvection flow over a vertical flat plate, involving a micropolar fluid with mass and heat transfer. In the beginning, partial differential equations (PDEs) are used to formulate the problem, which use a non-singular and non-local kernel to take into consideration the memory impacts of the system. The problem is formulated and exact solutions are obtained by using the Laplace transform technique, finding solutions that satisfy both the governing equations and specific conditions, and then representing these solutions graphically. The statement highlights the importance of considering variable Prandtl number in thermal boundary layer modeling. When viscosity and thermal conductivity depend on temperature, treating Prandtl number as a variable is crucial for accurate results. Specifically, as thermal conductivity parameter increases, it leads to higher velocities and temperatures within the boundary layers being studied. Understanding the effect of mass Schmidt number is essential in various practical applications such as chemical engineering processes, where precise control of mass transfer is important for optimizing reactions and product quality in micropolar fluid systems. When Schmidt number increases, it means that momentum diffusion (viscosity) dominates over mass diffusion, causing species to diffuse more slowly in the fluid. One of the key advantages of fractional derivatives like the ABC operator is their ability to model memory effects in systems, where past states influence current behavior. This is particularly important in fields like control theory, neurodynamics, fluid dynamics, and finance, where historical data impacts future behavior. Engineering interest quantities are also calculated and shown in tabular form.