Numerical solutions in a laminar motion of magnetohydrodynamic Maxwell liquid past a permeable shrinking plate

In recent years, there has been a notable rise in interest in the boundary layer theory of non-Newtonian fluids, driven by both academic curiosity and engineering applications. The nonlinearity of the equations can manifest itself in various ways across a broad spectrum of industries, encompassing biotechnology, drilling operations, and the food sector. The term Maxwell fluid describes the characteristics related to relaxation time and falls within the category of rate-type fluids. Researchers are intrigued by the challenges associated with solving nonlinear and higher-order differential equations. In the present problem, the magnetohydrodynamics (MHD) Maxwell liquid over a porous contracting surface is discussed numerically. In the analysis, a consistent transfer of divider concentration is examined. The governing/controlling equations of the fluid flow are changed using similarity transformations. The numerical results were found by using the R-K-4th order-based shooting technique with the assistance of MATLAB software. The graphical representation is displayed through stability analysis. The results indicate that the first solution exhibits greater stability. The magnetic parameter and suction effect enhance the velocity profile, whereas the Deborah number yields opposite results.