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Hybrid nanofluid has an extensive range of real-world applications. Hybrid nanofluid is a new and advanced nanofluid modification extensively used to increase thermal efficiency in fluid flow systems. The main objective of this research is to study magnetohydrodynamics hybrid nanofluid flow numerically in two dimensional over a vertical exponentially shrinking sheet, considering the effects of Joule heating and thermal slip condition. Furthermore, using the Tiwari-Das model, the influence of the suction parameter on variations of reduced skin friction and reduced heat transfer is also explored. The hybrid nanofluid in this research is an Al2O3+Cu/water hybrid nanofluid, in which water is the base fluid, and two types of solid nanoparticles, namely Alumina (Al2O3) and copper (Cu), are combined together. The governing partial differential (PDEs) equations are transformed into the ordinary differential equations (ODEs) using exponential similarity variables. The resulting ordinary differential equations (ODEs) are numerically solved using the three-stage Labatto III-A technique in the "MATLAB software's" bvp4c solver. Hybrid nanofluids have greater thermal efficiency than nanofluids and base fluid. Dual solutions are obtained in specified ranges of suitable parameters. The temperature profile rises in both solutions as the Eckert value enhances. Besides, In the first and second solutions, the thermal boundary layer thickness decreased gradually as the thermal slip parameter increased. Finally, the conclusions presented that solution duality exists when the suction parameter , while no flow of fluid is possible when .

The numerical investigation of unsteady magnetohydrodynamic (MHD) stagnation point flow of Al2O3-Cu/H2O hybrid nanofluid past a convectively heated permeable stretching/shrinking sheet with suction/injection effect is underlined. The characteristic of MHD and boundary condition with suction/injection has received a lot of consideration due to its across-the-board application in mechanical and chemical engineering. The governing continuity, momentum and energy equations are transformed into a system of nonlinear ordinary differential equations using similarity transformation, which is then solved using the bvp4c routine. Numerical results are obtained for the skin friction coefficient, local Nusselt number as well as the velocity and temperature profiles for certain values of the governing parameters, namely suction/injection parameter, copper nanoparticle volume fraction parameter and MHD parameter. Results showed that both velocity profile and temperature increase as the suction/injection parameter increases for the first solution and decreases for the second solution. Similarly, when increase the value of MHD parameter M, the velocity and temperature profiles are decreases for both solutions. The magnitude of the reduced skin friction coefficient and the local Nusselt number are notably increased for the first solution with increasing values of the suction/injection and MHD parameters. Finding also revealed that the skin friction coefficient is intensified in conjunction with the local Nussel number by adding up the copper nanoparticle volume fraction. In general, dual solutions are found to exist to a particular extent of the stretching/shrinking sheet.

Hybrid nanofluid is considered a modern and improvised form of nanofluid which usually used to enhance the performance of heat transfer in fluid flow systems. Previous studies found hybrid nanofluid offered a wide range of applications and this opened up numerous new opportunities to further explore the unknown behaviour of hybrid nanofluid under different body geometries and physical parameters. This paper numerically studied a two-dimensional mixed convection and radiative Al2O3-Cu/H2O hybrid nanofluid flow over a vertical exponentially shrinking sheet with partial slip conditions. The main objective is to investigate the effect of mixed convection and radiation on the velocity and temperature profiles, as well as the effect of suction on reduced skin friction and reduced heat transfer with respect to solid volume fraction of copper, velocity, and thermal slips. Exponential similarity variables transformed the governing system of partial differential equations into a system of ordinary differential equations which is solved via MATLAB’s bvp4c solver. Outcomes showed that the value of the reduced heat transfer upsurges in the first solution but declines in the second solution when the velocity slip rises. The reduced heat transfer decreases in both dual solutions when thermal slip is enhanced. As the intensity of thermal slip increases, the reduced skin friction rises in the first solution and decreases in the second. As the mixed convection parameter increases, no obvious variation is noticed in the temperature distribution within the first solution, but increasing trend is observed within the second solution. An increment in the temperature distribution also observed within the dual solutions as the thermal radiation parameter increases. In summary, findings from this study are particularly useful to understand various behaviour of Al2O3-Cu/H2O hybrid nanofluid under the influence of mixed convection, radiation, and partial slip conditions when it flows over a vertical exponential shrinking sheet.