Magneto-bioconvective stagnation point flow of a three-dimensional Casson nanofluid over a rotating Riga surface with exponential heat source: Homotopy analysis method

The present study investigates a three-dimensional Casson nanofluid flow over a Riga sheet near a stagnation point under the influence of an applied magnetic field, an exponential heat source, and a rotating frame. This study, in particular, delves into how these combined physical mechanisms influence velocity, temperature, nanoparticle concentration, and microorganism distributions. Also, it assesses whether the Homotopy Analysis Method is capable of yielding precise analytical solutions for such a highly nonlinear transport model. The original nonlinear partial differential equations representing magneto-bioconvective Casson nanofluid flow are first converted to a dimensionless system of ordinary differential equations by using appropriate similarity transformations. The coupled system thus obtained is then solved analytically by the Homotopy Analysis Method. The solutions achieved through this method are checked against results from the literature to ensure their validity. The finding shows that enhancement in the Casson fluid parameter, magnetic parameter, and mass Grashof number leads to a notable decrease in velocity field as a result of increased flow resistance. In contrast, the higher Hartmann numbers produced by the Riga sheet aid fluid motion via electromagnetic forcing. A stronger heat source and larger Biot number cause temperature distribution to rise, whereas thermophoresis lowers nanoparticle concentration. Also, higher activation energy affects concentration transport, but an increase in Peclet number boosts microorganism distribution and bioconvection strength. The analytical results presented here not only deepen the understanding of coupled magneto-bioconvective transport phenomena but also highlight the possibility of various applications including microelectronic cooling, renewable energy systems, electromagnetic flow control, biomedical transport, microbial fuel cells, and advanced nanofluid-based thermal technologies.