Effect of a Sinusoidal Temperature Profile on Entropy Generation Due to Double-Diffusive Natural Convection in a Square Partly Porous Cavity

In this paper, entropy generation due to double-diffusive natural convection inside a partly porous enclosure under sinusoidal wall heating is numerically analyzed. The resulting dimensionless coupled partial differential equations are discretized using the finite volume method (FVM), while the pressure–velocity coupling is handled using the SIMPLE algorithm. To ensure the validity of the results obtained from the in-house FORTRAN code, a comparison is made with previous numerical and experimental works. The results of the study indicate that the dimensionless thickness of the porous layer (⁠$Δ$⁠), the thermal conductivity ratio (⁠$Rk$⁠), the angle of inclination of the cavity (⁠$α$⁠), and the buoyancy ratio (⁠$N$⁠) are critical factors in determining local distribution and global maximum value of entropy generation due to heat transfer and fluid friction. In contrast, their effect on entropy generation induced by concentration is insignificant, except for the buoyancy ratio parameter, where an enhancement of the global maximum of entropy generation is observed by increasing $N$⁠. Moreover, it is found that $Sψ (max)$ experiences a sharp decline as Δ varies from 0.2 to 0.8, resulting in a reduction of about 67% for the case with $N=10$ and 83% for the case with $N=1$⁠. These results highlight the importance of carefully controlling system parameters to minimize energy losses and maximize system efficiency in heat transfer and fluid flow systems.