Mathematical analysis of nonlinear models and their role in dynamics

Micropolar fluids provide a more accurate description of fluid behavior at small scales, where classical continuum models may fail to capture complicated microscale interactions. These interactions become significant in situations involving non-Newtonian fluids, complex geometries, and materials with internal structures. Unlike traditional fluids, micropolar fluids consider the effects of micro-rotations and micro-deformations. The objective of this exploration is to investigate the characteristics of flow in a micropolar-Casson fluid that is doubly stratified, and is induced by a stretching sheet. Additionally, the study investigates the transfer of both thermal energy and mass species over a two-dimensional porous medium. By utilizing suitable similarity transformations, a system of nonlinear ordinary differential equations (ODEs) is derived by transforming the governing partial differential equations (PDEs) that describe the physics of the problem. The combination of a fourth-order Runge-Kutta integration scheme and the Shooting method is utilized to solve these equations. Various graphs and tables are utilized to illustrate the impact of physical parameters on the dimensionless quantities. Our findings exhibit strong conformity with the existing results in literature for specific scenarios. Furthermore, the outcomes highlight that the velocity and micro-rotation are enhanced by the material parameter.