Hall effects and Cattaneo–Christov heat flux on MHD flow of hybrid nanofluid over a varying thickness stretching surface

The study of nanofluids and hybrid nanofluids is gaining conceivable importance due to their characteristics of being so useful in various daily life applications. This study deals with the motion of an electro conductive, incompressible magneto-hydrodynamic (MHD) hybrid nanofluid across a stretched surface of variable thickness. The objective of this study is motivated by a number of manufacturing and machine-building applications. However, no attempt has been made to establish MHD flow of hybrid nanofluid along a stretching sheet (a sheet with variable thickness) while keeping an eye on the impact of Hall current. In real-life situations, variable-thickness sheets are crucial in the creation of flexible containers and, additionally, in the layout and production of aerospace wings and auto body components. This study extends our fundamental knowledge of fluid dynamics and heat transmission in intricate systems. Recognizing how magnetic effects, nanofluid traits and heat conduction interplay can help researchers make valuable developments and breakthroughs in the areas of fluid mechanics and heat transfer. Hall effects are vital for applications including conductive fluids or plasma as they provide a more precise understanding of the movement of charged nanoparticles in the presence of a magnetic field. For hybrid nanofluid, we mixed the nanoparticles of titanium dioxide and copper (TiO2–Cu) into the water. Due to the low noxiousness and chemical strength of titanium dioxide-based nanoparticles, they have great uses in research. We also consider the effects of Cattaneo–Christov heat flux to analyze the heat transfer of nanoparticles and Hall current effects, which make the flow three-dimensional. For both fundamental research and real-world applications, it is of the utmost importance to take into account the Hall effects and Cattaneo–Christov heat flux in the MHD flow analysis of hybrid nanofluid over stretched surface. It makes it possible to describe the phenomenon more precisely and can enhance the effectiveness and efficiency of numerous technical procedures. By using appropriate transformations, the equations that govern the flow are transformed into a system of non-dimensional ordinary differential equations. The non-dimensional system of equations has been solved numerically by using the ND Solve command in Mathematica Software, which is based on a multistep predictor-corrector method. For velocity and temperature profiles, the interplay of numerous developing parameters on flow is depicted graphically. The Hall parameter enhances the axial velocity but reduces the transverse velocity, while the magnetic field has the opposite effects. The temperature increases with the volume fraction of nanoparticles but decreases with the thermal relaxation parameter.