(untitled) (European Journal of Pure and Applied Mathematics, 2025)
The current work examines the transfer of heat/mass in a thin liquid film (TLF) with high viscosity on a surface that is continuously stretching. Through thorough mathematical modeling, a system of PDEs is established. The application of appropriate similarity transformations results in the formulation of a set of nonlinear ODEs from the original system of PDEs. Here, we introduce a reliable numerical technique to analyze the solution characteristics of the proposed problem. This technique depends on applying shifted Chebyshev polynomials of the sixth-order (SCP6s). Initially, we obtain an approximate expression for the derivatives by using SCP6s. In this study, we employ a spectral collocation procedure, leveraging the unique characteristics of SCP6s. This approach enables the transformation of the presented problem into a set of nonlinear algebraic equations. Notably, we emphasize the presentation of specific theorems that pertain to examining the convergence of the proposed approximation technique. Our present findings exhibit a remarkable concurrence with the investigations that have been previously reported.