MHD flow past a permeable quadratically stretching/shrinking sheet: numerical and asymptotic approaches

This study aims to investigate the impact of quadratic velocity on MHD flow over a permeable stretching/shrinking sheet using numerical and asymptotic approaches. The velocity of the sheet is given by $Uwx=λax+bx2$⁠, with $a,b>0$ and $λ$ as the stretching/shrinking parameter. By incorporating a quadratic velocity term, the study enhances understanding of boundary-layer behavior under varying magnetic field strength and suction/injection rates.

Using appropriate similarity transformations, the governing partial differential equations are reduced to a system of ordinary differential equations. Numerical solutions are obtained using MATLAB’s bvp4c solver, while asymptotic approximations are derived for extreme values of the stretching, suction/injection and magnetic field parameters. Both numerical and asymptotic approaches are used for analysis.

The results reveal that flow characteristics are significantly influenced by the stretching/shrinking parameter, magnetic field strength and suction/injection rates. The quadratic velocity term affects boundary layer stability and may lead to singularities in the shrinking case, depending on the interaction of suction/injection rate and magnetic field. Asymptotic results match well with numerical results for large parameter values, confirming the method’s reliability.

The findings are relevant to engineering applications, such as petroleum and chemical engineering, electromagnetic control of fluid flow and polymer processing, including rubber sheet manufacturing and plastic film drawing, offering insights for optimizing flow conditions in industrial applications.

This study extends classical boundary-layer theory by incorporating a quadratic velocity profile in MHD flow analysis. The strong agreement with existing literature confirms the validity of the approach used. The combined numerical and asymptotic approaches provide a comprehensive understanding of the system behavior, offering new insights into complex fluid interactions under magnetic fields, with the asymptotic solutions being new and original.