Application of Fibonacci wavelets using operational matrix and differential transform method to study rectangular porous fin for nonlinear temperature in moving condition

In this study, a novel numerical technique, the Fibonacci Wavelet Collocation Method (FWCM), is developed to analyze the nonlinear temperature distribution in a permeable moving fin within a rectangular domain. The governing highly nonlinear ordinary differential equation is formulated using Darcy's model and solved using FWCM and the Differential Transformation Method (DTM). The accuracy and efficiency of FWCM are validated by comparing its results with exact solutions and DTM. The proposed method demonstrates superior accuracy, achieving deviations of less than 0.001% from exact solutions, while DTM exhibits relatively higher errors. Additionally, FWCM requires 40% fewer computational resources compared to conventional numerical techniques, making it a more efficient alternative for solving complex heat transfer problems. The impact of key physical parameters on temperature distribution is analyzed through graphical and tabular representations. The findings confirm the robustness of FWCM in handling highly nonlinear ordinary differential equations, making it a promising approach for engineering applications involving heat transfer in porous media.