Radiation effect on gravity-driven nanofluid flow over a convective heated wall: RSM and ANN prediction analysis

Gravity-driven flows occur in both reservoir engineering and biological systems such as nutrient transport in blood and macromolecular migration in plants. In each case, the incorporation of engineered nanoparticles systematically enhances heat and mass transfer, overcoming the limitations of conventional refrigerants. In light of these applications, present investigation contribute to the existing body of knowledge through the development of a computational tool and predictive paradigms to help optimize and predict the desire output of heat and mass transfer flow of Casson nanofluid over a heated plate. To analyze these complex, nanoparticle influenced phenomena, a mathematical model is presented under the Bernoulli principle with conservation equations. Similarity transformation is employed to reduce the governing partial differential equations into a systems of ordinary differential equations, which are then solved using the spectral local linearization method for rapid convergence and high accuracy. The obtained responses from the numerical computations are used as prediction data for both the Artificial Neural Network (ANN) and Response Surface Methodology (RSM) under the randomized Box-Behnken (BB) design. The ANN adopt the MATLAB inbuilt Bayesian regularization algorithm. Our findings highlight that, co-contribution of buoyancy induced number $Gr$ and soret phenomenon $Sr$ diminished the heat transfer rate. For both assisting and opposing flow, an enhance phenomenon of energy and momentum field is experienced. The interplay of opposing flow with higher thermal radiation experienced an enhanced heat transfer rate while significant involvement of the internally generated heat ($Ec$) optimizes the heat transfer mechanism identify as effective heat transfer management. Moreover, through the prediction algorithm by RSM/ANN, we acquired a useful knowledge on effective energy optimization and cooling techniques for numerous biomedical and industrial applications.