Numerical study of the porous cavity with different square size vanes with a high focus on Nusselt number

This study extensively analyzes various regular and irregular vanes in pipe porous cavities on natural convection, thermal entropy generation, stream function, and temperature distribution in fluid and solid phases. The finite element method (FEM) is employed to study stream function, temperature distribution in the fluid phase and solid phase, and various γ for Nu_f, ave and Nu_s, ave in SR, TR, SIR, and TIR. In the present study, a significant contribution of this research is the investigation into the effects of regular versus irregular vanes in the context of enclosures formed by pipe porous cavities that the SIR specimen has the most influence on stream function and thermal effect in the fluid phase and solid phase that aims to enhance system performance and optimize energy efficiency. In addition, the significant influence of geometrical parameters constitutes many heated obstacles in the middle of SIR, various heated vanes in the left of SIR, and employed Ra and ε in the analysis of Nu_f, ave and Nu_s, ave in SIR are carried out to investigate the percentage discrepancies obtained, notably 89.35 % and 89.72 %, respectively. In validation, the calculation in results was adapted accurately to the finite element method's stream function, the temperature distribution in the fluid phase and solid phase, and various γ for Nu_f, ave and Nu_s, ave which means that the percentage differences in obtaining results reached under 1 %. Numerical results revealed that the Hartman number has a significant influence in S_htf, ave,  S_hts, ave,  Ty_ave, Nu_f, ave and Nu_s, ave in TR, SR, TIR, and SIR.