This study examines the flow of an incompressible flow over a linear stretching surface with the inclusion of momentum and thermal slip conditions. A scaling set of alterations is applied to the governing system for both with and without magnetic field situations. The physical system being leftover invariant caused by some associations surrounded by the transformations. Later we find the absolute invariants 3^rd -order ODEs for the linear momentum equation and two 2^nd order ODEs consistent with the energy and concentration are obtained. The equations that coincide with the boundary circumstances are elucidated mathematically. The physical pertinent parameters as shown in graphs and the friction factor, Nusselt number and Salts 1 and 2 Sherwood numbers are shown in surface plots. We observed that the momentum slip parameter decelerates the skin friction coefficient in the presence of a magnetic field and enhances in the absence of the magnetic field parameter. The thermal slip parameter enhances the Nusselt number in both the presence and absence of magnetic field parameter. Finally, the thermal and concentration buoyancy ratio parameters are shown to upsurge the friction factor, Nusselt and Salts 1 and 2 Sherwood numbers in both cases of $M=0$ and $M=1$.

In this work, the adaptive neuro-fuzzy inference system (ANFIS) and particle swarm optimization (PSO) were used to anticipate the behavior of heat transfer in ternary hybrid nanofluid flow through thin films. For intricate heat transfer processes in nanofluid applications, the combined ANFIS-PSO model improved forecast accuracy. The simulated PDEs were converted into ODEs by varying similarity factors. A ternary hybrid nanofluid across the surface, radiation, heat source/sink, and non-uniform magnetic field were used to theoretically examine the unique properties of unstable thin film flow; nanoparticles, namely $MWCNT,SWCNT$, and $Ti{O}_2$, were used in both the Casson and non-Casson scenarios, using the base fluid, blood. The ANFIS-PSO models were trained using the numerical results from MATLAB's built-in BVP4C function to control the complexity and predict the results. Plotting and analysis were done to see how various flow parameters affect temperature, velocity, and heat transfer. A ternary hybrid nanofluid without a Casson scenario had a higher Nusselt number, per the study's conclusions, than a Casson ternary nanofluid with blood as the base fluid with nanoparticles $SWCNT+Ti{O}_2+MWCNT.$ It was discovered that the truth values are accurately predicted by ANFIS-PSO models, and in most of the runs in Table 3, in Case-2, the rate of heat transmission is 1% higher than in Case-1.