Impact of activation energy on hybrid nanofluid flow dynamics at stagnation point in porous media: A Darcy-Forchheimer and bio-convective approach

This article presents the stagnation point and the boundary layer flow for Williamson Hybrid Nanofluids over a stretching cylinder substrate situated within a porous medium. The analysis for heat and mass transfer concerning convective boundary conditions is presented. The primary governing equations are solved using established boundary layer approximations. Consequently, when the principal variables of the Williamson fluid Hybrid Nanofluid model are treated as analogous, the governing equations for this model are transformed into ordinary differential equations. For the numerical solutions, the widely recognized numerical method “Bvp4c” is employed within MATLAB software. The residual squared error is also computed for precision of numerical solutions. Both tabular and graphical representations of the comparative results are presented. Hybrid nanofluids find practical applications in various sectors, including the automotive industry, transportation systems, military, healthcare, microfluidics, and other industrial fields. An increase in the buoyancy parameter, Williamson fluid coefficient, and curvature parameter results in an enhancement of the fluid’s velocity, whereas the velocity distribution diminishes with rising porosity, stretching parameters, and Forchheimer effects. Consistent with previous research, the temperature profile of both basic and hybrid nanofluids decreases as the values of the Prandtl parameters increase. Additionally, the fluid temperature exhibits an upward trend in response to variations in the curvature parameter for both nano and hybrid nanofluids. Moreover, the mobility of swimming cells diminishes as the Peclet number increases. To ensure graph convergence, the range for η is set from 0 to 7. The results obtained have been validated against existing literature for accuracy.