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Abstract
Boundary layer flow and heat transfer problems play a fundamental role in fluid mechanics, thermal engineering, energy systems, materials processing, and transport phenomena. Owing to the nonlinear nature of the governing equations, numerical methods have become indispensable tools for obtaining accurate solutions. Among the available computational techniques, the Finite Difference Method (FDM) and the Finite Element Method (FEM) are the two most widely employed approaches for boundary layer simulations. This review presents a comparative computational analysis of FDM and FEM with particular emphasis on their formulation, accuracy, convergence behavior, computational efficiency, flexibility, and engineering applicability. The historical development of boundary layer theory and numerical methods is first examined, followed by a classification of the reviewed literature according to major research themes and application areas. The strengths and limitations of both methods are critically evaluated using evidence from classical boundary layer studies, heat transfer investigations, magnetohydrodynamic flows, nanofluid transport, porous media systems, slip-flow problems, and recent computational developments. The analysis indicates that FDM remains highly effective for similarity-transformed boundary layer equations and structured computational domains because of its simplicity and low computational cost, whereas FEM offers superior flexibility and adaptability for complex geometries, coupled transport phenomena, and multiphysics applications. Emerging trends involving hybrid numerical frameworks, adaptive computational strategies, Physics-Informed Neural Networks, and AI-assisted solvers are also discussed. The findings provide practical guidance for selecting appropriate numerical techniques and identify promising directions for future research in computational fluid dynamics and heat transfer modeling.
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