In the current study, we have simultaneously addressed a problem related to the unsteady heat and mass transmission processes in Casson and Williamson nanofluid (i.e., nano sized particles are suspended in considered non-Newtonian fluids). Here both the fluids are considered with electrically conducting property and it is guessed that fluid flow is due to the slippery inclined stretching flat sheet with the appearance of a non-uniform internal heat generation/absorbtion effect. This study also explores the response of viscous dissipation, magnetic strength and Joule heating. Thermophoresis impact along with Brownian motion effect is incorporated and Buongiorno’s model is employed to examine these two aspects. Non-linear equations are made more simpler with the assistance of similarity variables. The numerical solutions are calculated by two different methods, viz., the Runga-Kutta Fehlberg method and bvp5c (along with shooting method) in MATLAB. Graphs are used to express the numerically examined results of concentration, velocity, temperature, Sherwood number, skin friction coefficient and Nusselt number. There is a very good correlation between the current findings and prior published studies in a few specific, constrained situations. The unsteadiness parameter is observed to have a diminishing relationship with the Casson and Williamson fluid momentum boundary layer thickness, thermal profile, and nanoparticle concentration profile. It’s important to remember that a magnetic field raises both the temperature and the nanoparticle concentration within boundary layer.
