Exploration of numerical simulation for unsteady Casson nanofluid thin film flow over stretching surface with mixed convection effects using Buongiorno's nanofluid model

This study focuses on investigating the effects of viscous dissipation, magnetohydrodynmaics (MHD) and mixed convection on Casson nanofluid thin film flow over a vertical stretching surface, considering its unsteady, two-dimensional nature. The problem is formulated by assuming incompressible flow and employing boundary layer approximations, leading to a system of partial differential equations (PDEs). These PDEs are then transformed into nonlinear ordinary differential equations (ODEs) using similarity transformations. Numerical techniques, facilitated by computational software such as Mathematica, are employed to solve these nonlinear ODEs. The investigation probes into the mathematical analysis of various physical parameters, presenting their effects through graphical representations. The impact of parameters such as concentration Grashof number (Gc), thermal Grashof number (Gr), magnetic parameter (M), unsteadiness parameter (S), dimensionless film thickness (beta), and Casson fluid parameter (gamma) are examined. The velocity profile f '(eta)$f<^>{\prime}( \eta )$ exhibits an increase with rising values of Gc and Gr, while it decreases with increasing values of M, S, beta, and gamma. The results are further elucidated through tabular representations, providing insights into the variations of skin-friction coefficient, Sherwood number, and Nusselt number with respect to the aforementioned parameters.