Existence of dual solution for MHD boundary layer flow over a stretching/shrinking surface in the presence of thermal radiation and porous media: KKL nanofluid model

Present study is dedicated to analyze the closed form solution of nanofluid flow over a stretching/shrinking sheet with dual availability. Flow is developed through two-dimensional boundary layer theory. Appropriate tensor is used to generate the continuity, energy, and momentum equations. Converted governing partial differential equations (PDEs) into dimensionless non-linear ordinary differential equations (ODEs) by adoption of favorable similarity variables. The dimensionless ODEs of energy and momentum produced a dual nature solution in closed form under certain conditions. To deal with the nanofluid, the Koo-Kleinstreuer and Li (KKL) model is used, and the equations are solved using well-known software Maple. The effect of porosity Φ, suction/injection [Formula: see text] , stretching/shrinking λ, and magnetic effect M on skin friction, velocity, temperature, and streamlines are well explored and showcased. The results for the stable solutions have been showed that the upper branch's fluid velocity is increasing as the magnetic parameter M rises whereas the lower branch's fluid velocity is decreasing as M rises. Additionally, the CuO-nanofluid's velocity is impacted by the volume fraction of nanoparticles, with an increase in volume fraction causing a decrease in velocity. On both the lower and upper branches, the temperature profile is seen to improve as the Biot number increases. On the other hand, as the magnetic parameter varies and the magnetic field increases, the local Nusselt number against suction/injection decreases, as well as the rate of heat transfer in the upper branch decreases.