ANN‐Assisted Linear‐Stability Analysis of Buoyancy‐Induced Convection in Single‐Relaxation Viscoelastic Fluids Within a Tilted Slot

The linear stability of buoyancy‐driven convection in Rivlin–Ericksen and Maxwell liquids occupying a tilted slot is investigated analytically for stress‐free isothermal boundaries. The eigenvalue problem is solved using the regular perturbation method for small slot inclinations. For the Rivlin–Ericksen liquid, the critical Rayleigh and wave numbers match those of a Newtonian liquid, indicating stationary convection. In contrast, the Maxwell liquid permits oscillatory convection, and the corresponding critical oscillatory Rayleigh number and frequency are evaluated for a fixed Prandtl number by varying both the stress relaxation parameter and the inclination angle. Results show that the Rayleigh number decreases with increasing stress relaxation parameter values in the range (0, 30) and that oscillatory convection disappears beyond a certain threshold, while for intermediate relaxation parameters, oscillatory convection is preferred over stationary. In addition to the analytical investigation, an artificial neural network (ANN) model is developed to predict the onset parameters and convection type across varying relaxation and inclination conditions. The ANN results exhibit high predictive accuracy compared with the analytical solutions, demonstrating its effectiveness as a complementary tool for stability analysis in viscoelastic fluid systems.