Numerical investigation of heat transfer phenomena in Casson nanofluid with gyrotactic microorganisms on a nonlinear stretching surface

Efficient thermal and mass transport in fluid systems is highly demanded for advanced engineering and industrial applications. However, the sedimentation of nanoparticles considerably reduces the effectiveness of nanofluids, emerging as a critical challenge in stability and efficiency maintenance. Most existing literature still lacks a detailed analysis of MHD flow with nonlinear stretching, bioconvection, and heat generation in porous media. Such a limited approach has restricted the applications of nanofluids in complicated scenarios where thermal and magnetic effects co-occur. The present research work represents the study of MHD flow in Casson nanofluids over a nonlinear stretching sheet embedded in a porous medium with gyrotactic microorganisms and heat generation. A novelty in this work is to investigate the bioconvection induced by living microorganisms, which can prevent the sedimentation of nanoparticles and thus enhance the thermal and mass transfer characteristics. Unlike the earlier attempts, the present study investigates the effects of combined bioconvection, nonlinear stretching, and thermal gradient under MHD conditions in a sponge medium, which is not found elsewhere. Similarity transformations reduce the system of governing partial differential equations to a set of ordinary differential equations, solved numerically using the fourth-order Runge-Kutta method, for which validation against well-established results has been performed. The results indicate that the magnetic field intensity and nonlinear stretching decrease the velocity profiles, while Brownian motion and thermophoresis increase the temperature and decrease the concentration. Furthermore, the Lewis and Peclet numbers increase significantly influences the motile density profiles. These results are of prime importance in optimizing heat transfer and stability of fluids in advanced engineering applications. The physical consequences of this can be viewed in a wide array of areas: Casson fluids can serve to enhance the performance of coolants and reduce drag in engine systems in automotive engineering. In energy systems, these nanofluids are of vital importance in efficient thermal management, such as in nuclear power plants, air conditioners, and heat exchangers. Moreover, this study gives insight into biomedical applications, including nutrient transport in porous media and microfluidic devices. With the introduction of these gyrotactic microorganisms, newer ways of enhancing the stability of nanofluids are considered an unprecedented development in fluid dynamics.