Coupled heat, mass, and bioconvective transport in a triply stratified MHD Casson nanofluid over an exponentially stretching surface

Abstract

In many fluid systems, stratification has a significant impact on heat and mass transmission, making it challenging to maintain uniform and stable mixtures in engineering, biomedical and industrial processes. This study aims to investigate the magnetohydrodynamic Casson nanofluid flow over an exponentially stretching sheet with velocity slip and gyrotactic microorganisms, inspired by food processing, temperature control, pharmaceutical manufacturing and biomedical technologies. The mathematical model includes convective boundary conditions, viscous dissipation, Joule heating and nonlinear Forchheimer drag. The controlling nonlinear PDEs are transformed into a coupled system of ODEs using appropriate similarity transformations. The resulting boundary-value problem is solved numerically by combining the Runge–Kutta method with the shooting technique. A detailed analysis is conducted of how the governing parameters affect the temperature, velocity, concentration of nanoparticles, density of microorganisms and other engineering quantities. Magnetic forcing, porous resistance and velocity slip suppress momentum transport, whereas Joule heating, radiation and viscous dissipation enhance the thermal field. Thermal, solutal and microorganism stratification reduce the corresponding boundary-layer distributions. Brownian motion and thermophoresis modify coupled heat and nanoparticle transport, while activation energy and reaction kinetics control species retention and depletion. Streamline, heat-flux and mass-flux trajectories further reveal spatial transport features not captured by one-dimensional profiles. The present study is a comprehensive analysis of Casson nanofluid flow in a triply stratified medium under the impact of inclined MHD forcing, nonlinear porous resistance, reactive nanoparticle transport and gyrotactic bioconvection. The combination of similarity profiles, engineering quantities, spatial flux trajectories, sensitivity analysis and numerical uncertainty assessment provides a more comprehensive physical interpretation applicable to porous reactors, polymer processing, pharmaceutical transport, bioreactors and thermal-management systems.