Numerical and machine learning investigation of heat and mass transfer in casson hybrid nanofluid flow over a Riga plate with bio-convection effects

The thermal and solutal transport characteristics of non-Newtonian hybrid nanofluids are crucial in biomedical engineering, energy conversion, and electromagnetic flow control. This study investigates steady two-dimensional boundary-layer motion of a Casson hybrid nanofluid over a Riga plate incorporating motile microorganisms to induce bioconvection. A comprehensive understanding of these transport mechanisms is essential for advancing thermal management systems, biomedical microfluidic devices, and electromagnetic flow control technologies. The governing equations, which integrate Casson rheology, electromagnetic forcing, magnetic resistance, thermal radiation, viscous dissipation, chemical reaction, Brownian motion, and thermophoresis, are transformed through similarity variables into coupled nonlinear ordinary differential equations. These equations are solved numerically using MATLAB’s bvp4c scheme with adaptive tolerance. Parametric analyses reveal that stronger Lorentz forcing via the Riga plate enhances velocity and heat transfer, whereas magnetic intensity and viscous dissipation attenuate momentum and reduce Nusselt numbers. A hybrid optimization framework combining Central Composite Design–based Response Surface Methodology (RSM) and Deep Neural Networks (DNN) is developed to predict the Nusselt responses (Nus₁, Nus₂). The trained DNN achieves regression accuracy of R ≈ 0.999 with a mean absolute error below 1%, validating its predictive capability. The proposed RSM–DNN hybrid model offers an efficient surrogate for rapid performance estimation and design optimization of Casson hybrid nanofluid systems under coupled magneto-electro-thermal and bioconvective environments. The results show that the Riga plate parameter helps to increase the fluid velocity, whereas the Casson parameter slows down the flow due to the fluid’s yield stress. The Schmidt number reduces the concentration distribution, while the bio-convection parameters affect the distribution of microorganisms in the fluid. In addition, the machine learning results closely match the numerical findings, showing that the model can reliably predict the behavior of the system.