Multiple solution of MHD Casson fluid flow in porous channel with chemical reactions and thermal radiation effects

This study focused on evaluating the synergistic effects of magnetohydrodynamics, Casson fluid properties, thermal radiation, chemical reactions, and heat transfer mechanisms within a porous channel. Through the application of similarity transformation, nonlinear governing equations are converted into nonlinear ordinary differential equations. These modified equations were then numerically solved in MATLAB using the Runge- Kutta method alongside the shooting technique to ensure precise results. The investigation yielded various numerical solutions for the dimensionless velocity, temperature, concentration, skin friction coefficient, heat transfer coefficient, and Sherwood number, all of which are presented in both tabular and graphical formats. Three distinct solutions emerged from the analysis, differentiated by variations in the Reynolds number, Casson number, expansion or contraction ratio, and magnetic parameters. These solutions demonstrate differences in the parameters under investigation. Solutions within the ranges of y [5 , infinity] and R [31 . 07 , infinity] are influenced by the specific values of the magnetic number M [0 , 2 . 0]. For each M value, there exists a unique set of solutions for y and R that satisfy the established parameters. As the magnetic number varies, so does the range of feasible solutions, highlighting the sensitivity of the system to magnetic influence. The values of y and R are adjusted according to the chosen M value.