Temporal stability and non-unique solution of reacting Eyring Powell flows over shrinking wedges using neural networks - Khan, M.I.; Zeeshan, A.; Arain, M.B.; Alqahtani, A.S.; Malik, M.Y. (Engineering applications of artificial intelligence, 2025)
In this paper, author presents an innovative artificial intelligence techniques based on deep learning simulation algorithms due to wide range of applications in science, robotics and engineering. The deep learning simulation algorithm using the Levenberg-Marquardt Scheme with Back Propagation Neural Networks (LMS-BPNN) is evaluated in the flow investigation of the chemically reacting non-Newtonian fluid. An efficient similarity variable is applied to change Partial Differential Equations (PDEs) of a considered flow problem into dimensionless Ordinary Differential Equations (ODEs). An error is found to be 10−4 with function fit for scenarios 1–5, while performance in terms of mean squared error is found to be 10−10. It is seen that flow response output i.e. f′(η), θ(η) and ϕ(η) meet boundary requirements for different scenarios 1–5 with the deep learning-based technique LMS-BPNN. The dual solution is evaluated for flow response output parameter i.e. Cfx, Nux and Shx for different parameters with the proposed LMS-BPNN. The dual nature of Cfx is calculated for three cases of scenario 1, and the critical value is found to be −0.96195, −1.0581, and −1.11. The dual solution of Shx is calculated for various values of Kc=0.2,0.4,0.6, and it is found that λc=−1.1175 remains the same. The perturbation scheme is applied to the boundary layer problem to obtain the eigenvalues problem. The unsteady solution f(η,τ) converges to steady solution fo(η) for τ→∞ when γ≥0. However, an unsteady solution f(η,τ) diverges to a steady solution fo(η) for τ→∞ when γ<0. It is found that the boundary layer thickness for the second (lower branch) solution is higher than the first (upper branch) solution. This investigation is the evidence that the first (upper branch) solution is stable and reliable.