Double-diffusive convection in Burgers fluid: An analysis using analytical and machine learning techniques

The onset of double-diffusive convection in Burgers fluid using both analytical and machine learning (ML) approaches is investigated. Analytical solutions for stress-free boundaries are derived using linear stability analysis. The single-term Galerkin method is used to derive the critical Rayleigh number. In addition to the standard analytical framework, supervised ML algorithms are used to enhance the understanding of multiple governing parameters on the marginal stability boundary. Support vector machine and artificial neural network models are used for classifying the marginal states. The dataset is generated from an analytical approach, which is used for training our models. The relaxation parameter λ1, Lewis number, and solutal Rayleigh number are the primary parameters for this classification study. Lower values of λ1 favor stationary convection. This study helps optimize enhanced oil recovery and polymer processing and provides insights into various geophysical applications. The framework captures stability dynamics of Burgers fluid and also demonstrates the potential of ML to be used as an efficient surrogate model, classifying stability thresholds in multi-diffusive fluid mechanics.