A numerical and theoretical analysis of the viscous fluid across a vertical cone in the presence of joule heating and magnetic impacts is organized in this segment of the work; this study involves numerous applications in the science, engineering, and industrial fields. The flow model is designed in the form of mathematical equations, and for the sake of numerical solution simplicity, a nondimensionalization process is performed and the earned nonsimilarity equations are solved numerically via the bivariate Chebyshev spectral collocation quasi-linearization method. A schematic illustration of the obtained results at various streamwise locations of the flow profiles for variations of the governing parameters are exhibited in the results and discussions section; we observed that the velocity can be controlled by the magnetic impact. Moreover, skin friction, mass and heat transfer rate are also illustrated in tabular form. To authenticate the accuracy of the present computations a comparison with prior computation is organized; the residual analysis study is also depicted, which determines the convergence of the formulated numerical simulation.