This study investigates the effects of an unsteady mixed convection nanofluid flow in a rotating vertical cone submerged in spinning nanofluid. Our analysis considered the impacts of heat flux, chemical reactions, and thermal radiation, with the thermal and concentration Biot numbers serving as constraints at the boundary. The governing unsteady and coupled partial differential equations were solved through appropriate similarity transformations, addressing the nonlinear terms inherent in these equations. The spectral quasi-linearisation method (SQLM) was employed to solve the higher-order nonlinear differential equations. This study elucidates and assesses the impact of diverse physical constraints and parameters through the use of graphical representations. Notably, the temperature distribution of the liquefied substance was intensified as the thermal and solutal Biot numbers increased.

The present work illustrates the variable viscosity of dust nanofluid runs over a permeable stretched sheet with thermal radiation. The problem has been modelled mathematically introducing the mixed convective condition and magnetic effect. Additionally analysis of entropy generation and Bejan number provides the fine points of the flow. The of model equations are transformed into non-linear ordinary differential equations which are then transformed into linear form using the spectral quasi-linearization method (SQLM) for direct Taylor series expansions that can be applied to non-linear terms in order to linearize them. The spectral collocation approach is then applied to solve the resulting linearized system of equations. The validity of our model is established using relative entropy generation analysis. A convergence schematic was obtained graphically. Consequence of various parameters on flow features have been delivered via graphs. Some important findings reported in this study that entropy generation analysis have significant impact in controlling the rate of heat transfer in the boundary layer region. The paper acquires realistic numerical explanations for rapidly convergent solutions using the Spectral quasi-linearization method. Convergence of the numerical solutions was monitored using the convergence graph. The initial guess values are automatically satisfied the boundary conditions. The resulting equations are then integrated using the Spectral quasi-linearization methods. The influence of radiation, heat and mass parameters on the flow are made appropriately via graphs. The effects of varying certain physical parameters of interest are examined and presented.