Prediction of saddle-node bifurcation points and flow separation in thermal dispersion induced flow of nanofluid: stability analysis and parametric optimization

Purpose Despite considerable progress in fluid dynamics, the intricate interplay between buoyancy-induced forces and thermal dispersion in nanofluid flows over exponentially stretching/shrinking surfaces remains limited, particularly when multiple solutions emerge due to the nonlinearity of governing equations. This study aims to bridge that gap by examining the heat and momentum transport in AA7075-water nanofluid. Design/methodology/approach Using similarity transformations, the complex partial differential system is reduced to coupled nonlinear ordinary differential equations, which are solved numerically using MATLAB. The analysis reveals dual solutions within certain parameter ranges, accompanied by a saddle-node bifurcation and flow separation, indicating critical transitions in flow structure. A comprehensive temporal stability analysis is conducted to identify the stable solution. To gain deeper insight into the thermal performance, response surface methodology is used to construct a predictive quadratic regression model for the Nusselt number. Findings Sensitivity analysis shows a strong positive correlation between the thermal dispersion parameter and Nusselt number, emphasizing the role of dispersion in enhancing convective transport. Physically, increasing the dispersion parameter significantly improves heat transfer in both stretching and shrinking cases. However, in the shrinking regime, higher Darcy numbers and nanoparticle volume fractions reduce thermal efficiency due to increased resistance. Conversely, stretching flows benefit from increased permeability, which enhances convective heat transfer. Originality/value The research offers valuable insights into optimizing nanofluid-based thermal systems, particularly in microchannel flows, heat exchangers and material processing applications requiring precise thermal regulation. By identifying multiple solutions and analyzing their stability, the study advances understanding and improves predictive capabilities for controlling flow transitions in practical nanofluid environments.