Symmetry Reductions and Approximate Analytical Solutions for Boundary-Layer Flows
Keywords:
Lie symmetry analysis, Boundary-layer flows, Falkner–Skan equation, Homotopy analysis method (HAM), Semi-analytical solutions, Fluid mechanics.Abstract
Boundary-layer flows play a vital role in fluid mechanics, yet exact analytical solutions are scarce for many realistic configurations. This study develops a symmetry-based reduction strategy using Lie group analysis to simplify boundary-layer governing equations into tractable ordinary differential forms. The resulting nonlinear models are investigated through semi-analytical techniques, including homotopy-based methods, rational approximations, and asymptotic expansions. The approach is validated using classical flat-plate and wedge-flow problems and further applied to advanced cases involving magnetohydrodynamic nanofluids and porous media. Accuracy and convergence are evaluated against numerical benchmarks, demonstrating the method’s effectiveness in predicting shear stress and heat-transfer behavior for engineering applications.
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