Advanced Computational Framework to Analyze the Stability of Non-Newtonian Fluid Flow through a Wedge with Non-Linear Thermal Radiation and Chemical Reactions

Muhammad Imran Khan, Ahmad Zeeshan, Rahmat Ellahi and Muhammad Mubashir Bhatti ()
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Muhammad Imran Khan: Department of Mathematics and Statistics, International Islamic University, Islamabad 44000, Pakistan
Ahmad Zeeshan: Department of Mathematics and Statistics, International Islamic University, Islamabad 44000, Pakistan
Rahmat Ellahi: Department of Mathematics and Statistics, International Islamic University, Islamabad 44000, Pakistan
Muhammad Mubashir Bhatti: College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China

Mathematics, 2024, vol. 12, issue 10, 1-24

Abstract: The main idea of this investigation is to introduce an integrated intelligence approach that investigates the chemically reacting flow of non-Newtonian fluid with a backpropagation neural network (LMS-BPNN). The AI-based LMS-BPNN approach is utilized to obtain the optimal solution of an MHD flow of Eyring–Powell over a porous shrinking wedge with a heat source and nonlinear thermal radiation ( R d ). The partial differential equations (PDEs) that define flow problems are transformed into a system of ordinary differential equations (ODEs) through efficient similarity variables. The reference solution is obtained with the bvp4c function by changing parameters as displayed in Scenarios 1–7. The label data are divided into three portions, i.e., 80% for training, 10% for testing, and 10% for validation. The label data are used to obtain the approximate solution using the activation function in LMS-BPNN within the MATLAB built-in command ‘nftool’. The consistency and uniformity of LMS-BPNN are supported by fitness curves based on the MSE, correlation index ( R ), regression analysis, and function fit. The best validation performance of LMS-BPNN is obtained at 462, 369, 642, 542, 215, 209, and 286 epochs with MSE values of 8.67 × 10 −10 , 1.64 × 10 −9 , 1.03 × 10 −9 , 302 9.35 × 10 −10 , 8.56 × 10 −10 , 1.08 × 10 −9 , and 6.97 × 10 −10 , respectively. It is noted that f ′ ( η ) , θ ( η ) , and ϕ ( η ) satisfy the boundary conditions asymptotically for Scenarios 1–7 with LMS-BPNN. The dual solutions for flow performance outcomes ( C f x , N u x , and S h x ) are investigated with LMS-BPNN. It is concluded that when the magnetohydrodynamics increase ( M = 0.01 , 0.05 , 0.1 ), then the solution bifurcates at different critical values, i.e., λ c = − 1.06329 , − 1.097 , − 1.17694 . The stability analysis is conducted using an LMS-BPNN approximation, involving the computation of eigenvalues for the flow problem. The deduction drawn is that the upper (first) branch solution remains stable, while the lower branch solution causes a disturbance in the flow and leads to instability. It is observed that the boundary layer thickness for the lower branch (second) solution is greater than the first solution. A comparison of numerical results and predicted solutions with LMS-BPNN is provided and they are found to be in good agreement.

Keywords: artificial neural network (ANN); non-Newtonian fluid; wedge flow; stability analysis; non-linear thermal radiation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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