Artificial neural network-based stability analysis of magnetoconvective instability in thermally affected inclined porous channel

This study examines the onset of magnetoconvection in an inclined porous channel filled with a Casson fluid, where the walls are maintained at constant but unequal temperatures. Thermal anisotropy is considered to capture direction-dependent heat conduction. The fluid flow follows Darcy's law under the Oberbeck–Boussinesq approximation. Linear stability is analysed using normal modes and the obtained eigenvalue problem solved using the spectral method, while nonlinear thresholds are determined via the energy method. The governing boundary value problem is solved numerically using a shooting method with a sixth-order Runge–Kutta scheme. To complement the numerical results and improve predictive efficiency, a feedforward artificial neural network (ANN) trained with the Levenberg–Marquardt algorithm. The employed ANN predicts the critical Rayleigh number for both linear and nonlinear cases. The optimal ANN architecture is selected based on statistical metrics such as the coefficient of determination (R²), root mean square error (RMSE), and mean relative error (MRE), demonstrating excellent agreement with numerical outcomes. Parametric studies show that thermal anisotropy (ξ) enhances system stability, while higher Casson parameter values β promote instability due to increased yield stress effects. The Hartmann number (M) contributes to stabilization via magnetic damping. Transverse rolls are more stable than longitudinal rolls under the studied configuration. The incorporation of ANN significantly reduces computational effort and enables fast, accurate prediction across various parameter ranges. These findings have practical relevance in applications such as geothermal systems, biomedical cooling, enhanced oil recovery, and the thermal management of electrochemical and composite devices.