Revolutionizing Heat Transfer and Fluid Flow Models: Fractional Calculus and Non-Newtonian Dynamics Meet Advanced Numerical Methods

This research explores the recent advancements in mathematical modelling of heat transfer and fluid flows, emphasizing fractional calculus, non-Newtonian fluid dynamics, and nanofluid models. We discuss the use of fractional derivatives in modelling complex thermal and flow behaviours in various engineering contexts, including permeable surfaces and porous media. Applications range from industrial heat exchangers to biomedical devices. Numerical methods such as the Iterative Power Series (IPS) technique and Finite Element Methods (FEM) are employed to solve the nonlinear equations governing these phenomena. A comprehensive comparison of these methods highlights their strengths and limitations in terms of accuracy, convergence, and computational efficiency. The results reveal significant insights into the optimization of thermal systems, with fractional models demonstrating superior adaptability to anomalous flow and heat transfer conditions. The findings contribute to the development of more efficient and effective engineering designs, and the study suggests directions for future research in this field.