Flow stability simulation over a stretching/shrinking surface with thermal radiation and viscous dissipation of hybrid nanofluids

The main objective of this work is to investigate viscous dissipation with thermal radiation impact on hybrid nanofluid flow past an exponentially stretching/shrinking surface along with magnetic field, and heat source/sink, slip boundary conditions. Water ( H_2O ) is taken into account as a host fluid with copper (Cu) and alumina ( Al_2O_3 ) as nanoparticles to form a hybrid nano liquid (Cu- H_2O - Al_2O_3 ). The coupled nonlinear partial differential equations are transmuted into ordinary differential equations using similarity transformations with boundary conditions and these ODEs are simplified using numerical solver, bvp4c in MATLAB. The behavior of momentum profiles, thermal profiles, coefficient of heat transfer ( Nux_1 ) and skin friction ( C_f ) are explored using the pertinent parameters such as Eckert Number ( Ec_1 ), Suction Parameter ( S_1 ), Magnetic Parameter ( M_1 ), Radiation Parameter ( Nr_1 ), Stretching/Shrinking Parameter ( λ ), Velocity and thermal slip Parameters ( A_1 and B_1 ), Heat source/sink Parameter ( β _1 ), variable thermal Parameter ( ϵ ), thermal conductivity (K) are depicted through tables and graphs. The present simulation is more stable and convergence when compared with the existing literature, which is portrayed in the tables. The presence of dual solution is noticed for Ec_1 = 0.1, 0.11,0.12 when the critical value of λ (= λ _c ) are λ _c_1 = - 1.60355799, λ _c_2 = - 1.60322884 and λ _c_3 = - 1.6031348, respectively. The existence of the dual solution is reported due to the presence of shrinking surface and suction, further, the first solution is found to be more stable. The novelty of the current simulation includes MHD hybrid nano liquid flow stability with the impact of viscous dissipation and thermal radiation past stretching/shrinking permeable plane to fill the research gap in the existing literature. The applications of transmission of heat by stretching/shrinking surface in boundary layers is used in various fields such as polymer and material processing, biomedical engineering, heat exchangers, etc.