Artificial Neural Network and Radial Basis Function Approaches for Computational Assessment of Fractal-Fractional Electroosmotic Flow Model

Coupled heat and mass transfer in electroosmotic microfluidic systems is difficulut to investigate since the phenomenon is nonlinear and exhibits memory effects that cannot be accurately captured by classical integer-order models. The existing literature is mostly based on deterministic numerical methods and is not very keen on the predictive performance of data-driven models, namely artificial neural networks (ANNs), of parameter-sensitive transport processes. This research gap leads to the current research that examines a fractal-fractional electroosmotic fluid flow model in a microchannel under sinusoidal wall oscillation and time-varying thermal and concentration fields, to improve the physical realism and predictive performance. The Momentum, energy and concentration equations are constructed with proper physical assumptions and generalized them with fractal-fractional derivative of singular kernel to include memory effects and geometric heterogeneity. The resulting non-dimensional equations are solved numerically using local radial basis function (LRBF) collocation method that offers a stable, mesh-free and very accurate computational framework to complex transport problems. Furthermore, an ANN-based surrogate model using Levenberg-Marquardt backpropagation algorithm is developed on the data generated by LRBF. The hybrid LRBF-ANN model provides an efficient solution and detailed parametric sensitivity analysis of each parameter along with effective prediction of the heat and mass transfer characteristics. The ANN model performance is strictly checked through regression analysis, curve fitting, and error histogram analysis revealing strong agreement with the numerical solution and excellent predictive accuracy. The parametric analysis shows that the fractal-fractional orders have a strong influence on the velocity, temperature distribution and mass diffusion profiles and provide a more expressive and vivid picture of the electroosmotic transport than classical formulations. These findings highlight the usefulness of ANN-assisted modelling of complex heat and mass transfer pehenomena and provide a powerful computational tool to optimize electroosmotic transport in microfluidic systems, biomedical engineering systems, lab-on-a-chip systems and thermal management systems.