## 1 Introduction
[13] acquired numerical results for hydro-magnetic Falkner Skan flow of the Casson fluid past a moving wedge, along with heat transfer. [PERSON] et al. [14] deliberated thermal diffusion effects and radiation on Casson-fluid flow with convective boundary conditions. [PERSON] et al. [15] deliberated the thermos-diffusion consequences on the Casson fluid over an unsteady stretching surface in the existence of thermal radiations and the magnetic field. They found that the Casson parameters and unsteadiness parameter have the propensity to denigrate the velocity dissemination. [PERSON] et al. [16] studied the free convective boundary layer flow of nano-fluid over a penetrable upward horizontal plate in a porous medium with thermal convective boundary conditions. Recently, [PERSON] et al. [17] explored the hydro-magnetic slip flow of water-based nano-fluid over a wedge with a convective surface in the existence of heat generation or absorption. [PERSON] and [PERSON] [18] analyzed magneto-hydrodynamic boundary layer flow and heat transfer of nano-fluid past over penetrable stretching sheet using velocity, thermal, and solute slip boundary conditions. [PERSON] [19] presented an imperative numerical inquiry on the convective heat transfer performance of nanofluids over a penetrable stretching surface in the presence of partial slip, thermal buoyancy, and internal heat generation/absorption. The transfer of heat, investigated through the thermal radiation, has enormous applications in different technical processes, satellites, nuclear power-plants, astronomical vehicles, gas turbines, comprising missiles, and in several propulsion devices for jets. Linear radiations are not systematically in effect for the enormous temperature alteration. [PERSON] et al. [20] deliberated the consequences of radiation in the existence of a uniform magnetic field of nano-fluid on the curved stretching surface by integrating the slip effect. In recent times, [PERSON] et al. [21] deliberated a numerical study of the effects of radiation on chemically reacting MHD nano-fluid prejudiced by the heat source/sink, and the collective heat and mass transfer analysis aimed at mixed convection flow over the vertical surface, with radiation and chemical reaction explained by [PERSON] et al. [22]. [PERSON] et al. [23] deliberated the velocity slip effects, temperature jump, solutal slip, and thermal radiation, on steady flow, and the transfer of heat and mass of incompressible Jeffrey nano-fluid over the horizontal stretching surface. [PERSON] et al. [24] scrutinized the unsteady MHD flow of the curved stretching surface. The literature remains silent whether we have to investigate the impact of multiple slips on MHD unsteady Casson nano-fluid flow, heat, and mass transfer in the presence of heat source with thermo-diffusion effect over a stretching/shrinking sheet. The objective of this article was to prolong the recent work of [PERSON] and [PERSON] [25]. Appropriate similarities have been used for transformation, and the governing non-linear partial differential equations are rendered in the non-dimensional and non-linear system of ODEs. The resulting system of non-linear ODEs has been solved numerically with an efficient and validated variational finite element method (FEM) with the boundary conditions. We also use a special case for the existing model to compare our outcomes along with previous studies. A parametric study has been performed to inquire into the mass and heat transfer characteristics and also the impact of different parameters of the flow. After that, we have provided a numerical comparison of our results and discussed them with graphs. In future studies, transient flow with slip effects in the presence of mixed convection and chemical reaction at the sheet can be examined.