Entropy generation in Poiseuille–Benard channel flow

Abstract

The issue of entropy generation in Poiseuille–Benard channel flow is analyzed by solving numerically the mass, momentum and energy equations with the use of the classic Boussinesq incompressible approximation. The numerical scheme is based on Control Volume Finite Element Method with the SIMPLER algorithm for pressure–velocity coupling. Results are obtained for Rayleigh numbers Ra and irreversibility φ ranging from 10 3 to 5×10 4 and from 10 −4 to 10 respectively. Variations of entropy generation and the Bejan number as a function of Ra and φ are studied. The limit value φ l for which entropy generation due to heat transfer is equal to entropy due to fluid friction is evaluated. It has been found that φ l is a decreasing function of the Rayleigh number Ra. φ l varies from 0.0015 to 0.096 when Ra decrease from 5×10 4 to 10 3. Stream lines and entropy generation maps are plotted at six times over one period at Ra =10 4 and φ=10 −3. It has been found that the maximum entropy generation is localized at areas where heat exchanged between the walls and the flow is maximum. No significant entropy production is seen in the main flow.