Dual Solutions of Magnetohydrodynamics Al2 O3 +Cu Hybrid Nanofluid Over a Vertical Exponentially Shrinking Sheet by Presences of Joule Heating and Thermal Slip Condition

Abstract

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 (Al2 O3) 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 Ɵ (ƞ) 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 S≥ Sci, while no flow of fluid is possible when S < Sci.