A passive modeling strategy of steady MHD reacting flows for convectively heated shear-thinning/shear-thickening nanofluids over a horizontal elongating flat surface via Wakif’s-Buongiorno approach

In contrast to the previous traditional investigations, the present scrutinization intends principally to provide a proper differential formulation to examine realistically the shear-thinning and shear-thickening aspects of convectively heated viscoelastic nanofluids during their steady two-dimensional boundary layer flows over a stretchable horizontal surface. Besides, a third-order chemical reaction process can take place within the nanofluidic medium in the presence of an external magnetic field source. From a theoretical point of view, the constitutive rheological laws of Carreau's model have connected appropriately with the conservation equations of Wakif's-Buongiorno model to develop the simplified governing partial differential equations based on the boundary layer theory. By adopting feasible mathematical transformations and invoking the passive nanoparticles' control strategy, the leading dimensionless boundary layer equations are derived in the form of a coupled nonlinear structure of ordinary differential equations along with their boundary conditions, whose approximate solutions are computed accurately via Runge's-Kutta-Fehlberg method. In this respect, several findings are presented thereafter graphically and tabularly in different physical scenarios. As foremost results, it is found that the shear-thinning and shear-thickening tendencies have reciprocal influences on the axial velocity, the nanofluid temperature, the nanoparticles' molar concentration distribution, the skin friction coefficient, Nusselt's number, the surface temperature, and the surface molar concentration of nanoparticles when Weissenberg's number gets raised. Whist, a similar impression is witnessed for these rheological propensities when augmenting the other operating control parameters independently.