Gradient descent and response surface optimisation for nonlinear dynamics over an unstable heated wedge: lie group and sensitivity analysis

Abstract

Thermal conductivity and thermodynamic propertiesmake nanofluids highly effective in thermal analysis and engineering applications. Ternary hybrid nanofluids flow over wedge surfaces can significantly enhance hydraulics and geothermal applications. This study explores a novel approach to optimising manufacturing processes in industries like plastic film production, heat exchangers, glass fibres, petroleum, polymer sheets, and electronic cooling systems. A key innovation of this work is the application of H(OCH2CH2)nOH–H2O as a base fluid with AA7072 (nanofluid), ZrO2 + AA7072 (hybrid nanofluid), and MgO + AA7072 + ZrO2 (ternary hybrid nanofluid). The study investigates the heat transfer characteristics of these fluids as they flow over a wedge under the influence of various boundary conditions. Response surface methodology (RSM) and prediction through gradient descent-based machine learning is employed to optimise the thermal performance. The BVP4C solver in MATLAB is used to solve the governing equations numerically, and the gradient descent technique provides accurate predictions of the thermal behaviour through Python programming. From Table 3, the optimisation results indicate that the minimum value of 0.062983 is observed in case 2. In contrast, the maximum value of 13.5527 is recorded in case 3, demonstrating the significant impact of ternary hybrid nanofluids on heat transfer enhancement