Applications of triadic hybridized-cross nanomaterials suspended in engine oil using quadratic and linear convection with magnetic dipole

This work comprises the contribution of buoyancy forces, linear and quadratic convection on cross Nano fluid under the effects of dipole effects with chemical reaction. The flow of a cross model (CM) with mass and thermal transport has been modeled in Cartesian coordinates for the two-dimensional fluid flow problem. Temperature gradient effects have been incorporated in mass transport and concentration gradient impacts in thermal transport phenomenon with chemical reaction. The governing laws are derived under boundary layer principle (BLP) in the conformation of coupled nonlinear partial differential equations. Afterwards, coupled partial differential equations are converted into a scheme of ordinary differential equations (ODEs) by incorporating the similarity transformation. The nonlinear modeled equations are solved numerically with the aid of finite element scheme as well as analysis of grid independent is reported based on the reliability of the utilized approach. Several graphs and tables have been prepared to observe the bearing of multiple emerging parameters regarding velocity, temperature as well as concentration fields. Comparison has been made to confirm the efficiency of a finite element scheme. It is perceived that higher values of a Schmidt number control the fluid concentration. Moreover, velocity is diminished against higher values of Weissenberg parameter.