Entropy generation in thermal convection with differentially discrete heat boundary conditions at various Rayleigh numbers (Ra) are numerically investigated using the lattice Boltzmann method. We mainly focused on the effects of Ra and discrete heat boundary conditions on entropy generation in thermal convection according to the minimal entropy generation principle. The results showed that the presence of the discrete heat source at the bottom boundary promotes the transition to a substantial convection, and the viscous entropy generation rate (Su) generally increases in magnitude at the central region of the channel with increasing Ra. Total entropy generation rate (S) and thermal entropy generation rate (Sθ) are larger in magnitude in the region with the largest temperature gradient in the channel. Our results also indicated that the thermal entropy generation, viscous entropy generation, and total entropy generation increase exponentially with the increase of Rayleigh number. It is noted that lower percentage of single heat source area in the bottom boundary increases the intensities of viscous entropy generation, thermal entropy generation and total entropy generation. Comparing with the classical homogeneous thermal convection, the thermal entropy generation, viscous entropy generation, and total entropy generation are improved by the presence of discrete heat sources at the bottom boundary.
Keywords: Rayleigh; discrete boundary conditions; entropy; heat transfer; lattice Boltzmann method.