Impact of Multiple Linear Regression Strategies on Unsteady Thin Film Flow of Al₂O₃ Nanofluid Over a Stretching Sheet

Abstract

This study is motivated by the need for advanced thermal management in industries such as electronics, energy and biomedical engineering, where efficient heat transfer is essential for performance and reliability. By analyzing the thermophysical properties of a base fluid with differently shaped Al2O3 nanoparticles in unsteady thin-film flow over a stretching layer, the paper explores heat transfer enhancement. Internal heat generation and convective boundary effects are incorporated, transforming complex nonlinear partial differential equations (PDEs) into ordinary differential equations (ODEs) using similarity transformations, with MATLAB BVP4C solver providing insights. Key parameters like Biot number, Eckert number and slip parameter are manipulated, showing that higher Prandtl numbers and slip parameters reduce thermal diffusivity. The thermal state of the Al2O3 nanofluid, influenced by the conductivity parameter is significantly affected by the presence of nanoparticles and impacts results in applications requiring precise and accurate outcomes. The degradation (M = K = φ = 0) results are tabulated to evaluate the efficacy of the current approach. A multiple linear regression model for unsteady flow delivers strong predictive performance with errors 10−5, reinforcing previous findings and highlighting its utility in predicting physical quantities in thin-film nanotechnology which plays a vital role in applications like electronics cooling, heat exchangers, solar panels and biomedical devices.