Variable viscosity effects on the flow of MHD hybrid nanofluid containing dust particles over a needle with Hall current—a Xue model exploration

This study scrutinizes the flow of engine oil-based suspended carbon nanotubes magneto-hydrodynamics (MHD) hybrid nanofluid with dust particles over a thin moving needle following the Xue model. The analysis also incorporates the effects of variable viscosity with Hall current. For heat transfer analysis, the effects of the Cattaneo-Christov theory and heat generation/absorption with thermal slip are integrated into the temperature equation. The Tiwari-Das nanofluid model is used to develop the envisioned mathematical model. Using similarity transformation, the governing equations for the flow are translated into ordinary differential equations. The bvp4c method based on Runge-Kutta is used, along with a shooting approach. Graphs are used to examine and depict the consequences of significant parameters on involved profiles. The results revealed that the temperature of the fluid and boundary layer thickness is diminished as the solid volume fraction is raised. Also, with an enhancement in the variable viscosity parameter, the velocity distribution becomes more pronounced. The results are substantiated by assessing them with an available study.