Effect of water-based Alumina-copper MHD hybrid nanofluid on a power-law form stretching/shrinking sheet with joule heating and slip condition: dual solutions study

The application of hybrid nanofluid is now being employed to augment the efficiency of heat transfer rates. A numerical study was conducted to investigate the flow characteristics of water-based-alumina copper hybrid nanofluids towards a power-law form stretching/shrinking sheet. This study also considered the influence of magnetic, Joule heating, and thermal slip parameters. This study is significant because it advances our understanding of hybrid nanofluids in the presence of magnetic fields, power-law form stretching/shrinking sheet, and heat transfer mechanisms, providing valuable insights for optimizing and innovating thermal management systems in various industrial applications such as polymers, biological fluids, and manufacturing processes like extrusion, plastic and metal forming, and coating processes. The main objective of this study is to examine the impact of specific attributes, including suction and thermal slip parameters on temperature and velocity profiles. In addition, this exploration examined the reduced skin friction and reduced heat transfer in relation to the solid volume fraction copper and magnetic effects on shrinkage sheet and thermal slip parameter on suction effect. To facilitate the conversion of a nonlinear partial differential equation into a collection of ordinary differential equations, it is necessary to incorporate suitable similarity variables into the transformation procedure. The MATLAB bvp4c solver application is utilized in the conclusion process to solve ordinary differential equations. No solution was found in the sort of when , and . As the intensity of the Eckert number increases, the temperature profile and boundary layer thickness also increase. The reduced heat transfer rate upsurged in both solutions for solid volume fraction copper for shrinking sheet, while the opposite actions can be noticed in both solutions for thermal slip parameter for suction effect. Finally, the study conducted an analysis to identify two distinct solutions for shrinking sheet and suction zone, while considering different parameter values for the copper volume fractions, magnetic and thermal slip condition effect.