Three-Dimensional Magnetohydrodynamic Mixed Convection Flow of Nanofluids over a Nonlinearly Permeable Stretching/Shrinking Sheet with Velocity and Thermal Slip  
[PERSON]  
1 Department of Mathematics, Universiti Perathanan National Malaysia, Kuala Lumpur 57000, Malaysia; [EMAIL_ADDRESS]  
[PERSON]  
2 School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, UKM Bangi, Selangor 43600, Malaysia 2  
flow region. In contrast to the studies conducted by [PERSON] et al. [1] and [PERSON] et al. [2], [PERSON] and [PERSON] [3] revealed that dual solutions exist in both opposing and assisting flow regions. Other than that, a broader perspective was investigated by [PERSON] [4] who discovered that the upper branch of solutions was stable, but unstable for the lower branch. On top of that, he also looked into the issue of mixed convection flow in a saturated porous medium. Later, [PERSON] and [PERSON] [5] analysed two-dimensional mixed convection flow with prescribed wall heat flux, hence describing a comprehensive report of how both lower and upper branch solutions behave over all possible ranges of the buoyancy parameter deduced. In addition, [PERSON] et al. [6] extended the work of [PERSON] and [PERSON] [5] by determining the effects of suction and injection. They also examined the existence of dual solutions in both opposing and assisting flows for two cases: permeable and impermeable. Moreover, several other published papers have reported the existence of dual solutions in mixed convection flow (see [7; 8; 9; 10] for more details). Furthermore, studies concerning momentum and heat transfer characteristics of the boundary layer flow subject to magnetic field have gained great interest due to their benefits in controlling the cooling rate. In fact, this cooling rate has a significant function in enhancing the desired attributes of the final product to be applied in industrial fields, such as polymer technology. In view of this, numerous researchers like [PERSON] et al. [11], [PERSON] and [PERSON] [12], as well as [PERSON] et al. [13], have examined the magnetohydrodynamic (MHD) effect on boundary layer flow and heat transfer issues in both Newtonian and non-Newtonian fluids with various aspects. Nevertheless, these studies dismissed the notion of mixed convection. In fact, researches about MHD mixed convection flow have been carried out by many authors. For example, [PERSON] et al. [14] extended the work of [PERSON] et al. [1] by investigating the steady MHD flow, where they discovered that magnetic parameter increased the range of solutions, which in turn, decelerated the separation between the boundary layers. Other than that, [PERSON] et al. [15] studied the effects of MHD on mixed convection stagnation point flow over a vertical surface. As a result, they discovered that the velocity, temperature, and induced magnetic field profiles were affected by the buoyancy and magnetic parameters for both opposing and assisting flows. Besides, studies on unsteady MHD mixed convection flow in the presence of suction/injection and radiation, which is applied to a vertical stretching/shrinking surface, had been studied by [PERSON] et al. [16]. Meanwhile, in an incompressible Casson fluid, [PERSON] and [PERSON] [17] looked into the steady three-dimensional mixed convection flow past an exponential stretching sheet, together with the effects of magnetic field and heat generation. Moreover, recently, [PERSON] et al. [18] included the combined effects of MHD, chemical reactions, radiation, and velocity slip on mixed convection flow near a stagnation point over a vertical plate in a porous medium, along with convective boundary condition.