This research investigates two-dimensional MHD incompressible boundary layer Hyperbolic Tangent nanofluid flow across a non-linear stretching plate. Similarity transformations are employed to convert the governing non-linear partial differential equations (PDEs) into coupled non-linear ordinary differential equations (ODEs). The MATLAB built-in routine bvp4c has been used for finding the numerical solutions of the dimensionless velocity, temperature, and concentration profiles. The current findings are validated with already published results. The influence of some important parameters on the velocity, temperature, and concentration profiles are displayed through graphs and tables. It is observed that for increasing values of magnetic parameter $M$ and hyperbolic Tangent parameter $We\text{,}$ the boundary layer thickness of the velocity profile decreases while it increases for the temperature profile.

This research work describes and investigates Williamson nanofluid flow over an exponentially stretching permeable vertical plate with temperature-dependent thermal conductivity and viscosity. The governing non-linear partial differential equations (PDEs) are metamorphosed into coupled non-linear ordinary differential equations (ODEs) by using similarity transformation. The succeeding equations were numerically solved using MATLAB function bvp4c for various values of parameters. For velocity, temperature, concentration, the skin friction coefficient, and the local Nusselt number, data are presented in the form of graphs and tables. It is noted that for increasing values of magnetic parameter $M$, Williamson parameter $\lambda ,$ and viscosity parameter $\alpha$, the boundary layer thickness of the velocity profile decreases, while it increases for the temperature profile. The findings of the present work are validated through the published results.