Hydrodynamic analysis of nanofluids flow over 45° inclined porous square cylinder using Darcy–Brinkman–Forchheimer model

Various engineering applications commonly involve the flow of nanofluids over a porous 45° inclined square cylinder. Therefore, the current study is to assess the impact of the Darcy parameter (Da), nanoparticle volume fraction (ϕ), and Reynolds number (Re) on the momentum transport characteristics over the 45° inclined porous square cylinder. The governing equations were solved numerically using the Darcy–Brinkman–Forchheimer model for different values of Da ( ${10}^{-6}\le \mathrm{Da}\le {10}^{-2}$), nanoparticle volume fraction ϕ ( $0.01\le \varphi \le 0.05$), and Reynolds number Re ( $1\le \mathrm{Re}\le 40$). The results for each parameter were visualized using streamline plots, velocity profiles within the porous cylinder, and vorticity contours. Complex flow behaviors were observed between Da = 10⁻³–10⁻², flow separation detached and disappeared at the cylinder's downstream side at critical Darcy number. Drag and pressure coefficents are used to represent the global and local parameter of the flow fields. The pressure coefficient on the surface of the cylinder showed an inverse relationship with the nanoparticles volume fraction and Darcy number. The strength of the drag coefficient decreased with the addition of nanoparticles to the base fluid, with a decreasing trend observed for Da = 10⁻⁴–10⁻² and no change observed for Da = 10⁻⁶–10⁻⁴. At last, the comparative analysis has been conducted between a porous square cylinder at 0° inclined and another 45° inclined.