This study presents a comprehensive numerical investigation into laminar natural convection within a porous square enclosure, focusing on the intricate interplay between buoyancy forces and porous matrix permeability. Simulations were executed across a broad parameter space, encompassing Rayleigh numbers from 10 3 to 10 6 and Darcy numbers ranging from 10 -1 to 10 -5 , while systematically varying the linear heating position H S along the left vertical boundary. The thermal and hydrodynamic behavior was characterized using streamline, isotherm, and heatline visualizations, complemented by a rigorous second-law analysis involving entropy generation components and the Bejan number. A primary finding indicates that permeability serves as a more decisive factor in modulating heat transfer rates than the Rayleigh number, with increased porous resistance significantly suppressing flow velocities. Thermodynamic optimization, evaluated through the Energy Coefficient of Performance (ECOP), identified the uppermost heating configuration (H S = 1) as the most efficient regime, yielding maximized heat transfer alongside minimized irreversibility. Conversely, the highest thermodynamic losses were observed at H S = 0.25. The results further reveal that in low-permeability regimes (Da=10 -5 ), the total entropy production is almost entirely dominated by thermal gradients, whereas the sensitivity of the ECOP to heating positions diminishes at higher Rayleigh numbers. • Natural convection and entropy generations in a porous cavity were numerically investigated. • Permeability is more decisive in heat transfer modulation than the Rayleigh number. • Uppermost heating (H S =1) maximizes the ECOP by inducing thermal stratification. • Total entropy converges to heat-transfer-related losses at low Darcy numbers. • Maximum irreversibility occurs at the H S =0.25 heating position. • Darcy-Brinkman resistance suppresses flow velocities and frictional entropy.
Birol Şahi̇n (Sun,) studied this question.