A numerical and statistical analysis of the unsteady ternary hybrid nanofluid flow and heat transfer over a generalized stretching/shrinking wall

This study analyzes unsteady ternary hybrid nanofluid flow and heat transfer over a generalized stretching/shrinking wall using both analytical and numerical methods. By applying similarity transformations, the governing nonlinear partial differential equations are reduced to a system of ordinary differential equations, which are numerically solved using the MATLAB bvp4c function. We find that the system exhibits two solution branches—an upper and a lower—within certain parameter ranges. A detailed stability analysis is conducted to determine the stability of these solutions. Additionally, the study presents analytical solutions for specific cases, which are relevant to heat exchangers in low-velocity environments. Next, MINITAB software is used to statistically model the interactions of the parameters and assess their impact on the heat transfer performance (measured through the local Nusselt number), identifying low, medium, or strong effects through regression analysis. Finally, a sensitivity analysis is performed on the regression function obtained in MINITAB, focusing on key input parameters. To the best of our knowledge, this study is novel, as no previous work has explored this problem, making both the analytical and numerical results original.