Implementing the Vieta–Lucas Collocation Optimization Method for MHD Casson and Williamson Model under the Effects of Heat Generation and Viscous Dissipation

Theoretical investigation of magnetohydrodynamics (MHD) Casson and Williamson fluid flow and heat and mass transfer in laminar flow through a stretching sheet in the presence of heat generation is carried out in this study. The convective wall temperature and convective wall mass boundary condition are taken into account in this study. A study is also provided, which looks into the impact of viscous dissipation. Except for a temperature-dependent thermal conductivity, all properties of the proposed model are assumed to be constants in the study. The spectral collocation method based on the shifted Vieta–Lucas polynomials is used to give an approximate formula for the n-order derivative and solve numerically the coupled momentum, energy, and mass equations. This method is used to convert the problem’s system of ordinary differential equations (ODEs) into a nonlinear system of algebraic equations. This system is built as a restricted optimization problem and optimized to obtain the series solution’s unknown coefficients. Some theorems are provided to investigate the method’s convergence. The statistics, which are given visually, were compared to the results of other researchers’ theoretical analysis.