This article explores an unsteady radiative two-dimentional stagnation point flow of a Casson
fluid along a stretching and shrinking sheet which is depending on the mixed convection,
convective condition, and the slip condition. Additionally, the effect of heat generation and Joule
heating is deemed. This study formulates the nonlinear Partial Differential Equations (PDEs), that
are initially transformed into the non-dimensional Ordinary Differential Equations (ODEs) based
on the dimensionless variables. The bvp4c function in MATLAB has been employed to find the
dual solutions for the dimensionless ODEs. These solutions have been determined with regards to
the fluid velocity, skin friction coefficient, temperature, and the local Nusselt number which have
been found under the influence of the related fluid parameters. It has been found that the friction
drags respectively enhances and declines in the stable and unstable flows caused by rising values
of Casson parameter, mixed convection, and slip parameter. The heat transfer rate respectively
improves with the improvement of radiation, Biot number and Prandtl number although it declines with the improvement of heat generation parameter. According to our deep knowledge, the
outcomes of the existing effort are innovative and had not been previously evaluated by someone.
Our work can produce a paradigm considering forthcoming analyses of non-Newtonian fluids.