Preserving the rheological equation of Eyring-Powell fluid through non-similar approach: a numerical analysis by BSCM

To preserve the rheological equation of the non-Newtonian Eyring-Powell (EP) fluid, present mixed convection problem is simplified via non-similar approach, as opposed to the widely used similarity technique, while the dynamics are numerically investigated through bivariate spectral collocation method (BSCM). Studies identify that variations in free stream velocity, surface mass transfer, wall temperature, buoyancy forces, magnetization, chemical reactions, etc are factors responsible for the non-similar boundary layer problem (N-SBLP). However, the assumptions in this study including dissipative heat, a Darcian medium, non-Newtonian fluid, nonlinear buoyancy, convective heat transfer, chemical reaction rates, and Soret–Dufour effects give rise to the N-SBLP, thus necessitating the use of the non-similar technique. The numerical method adopts a modified spectral Chebyshev-based collocation method (a bi-discretization scheme) known as the BSCM, capable of handling systems of partial differential equations (PDEs). The governing mathematical model of the flow, heat, and mass transfer is presented in the form of PDEs, transformed into dimensionless N-SBLP equations, and solved numerically. The results of the physical quantities confirm the preservation of the rheological properties of the EP fluid, as demonstrated in the corresponding figures and tables. The findings highlight the successful application of the non-similar approach and BSCM to the N-SBLP of EP fluid. A rise in the Dufour number indicates a stronger influence of mass diffusion on thermal energy transfer, while increasing the Eyring-Powell fluid’s dimensionless parameters and quadratic buoyancy enhances fluid motion, improves mass transfer, reduces temperature profiles, and thins boundary layers due to stronger non-Newtonian and convective effects.