Prandtl Number Effects on the Entropy Generation During the Transient Mixed Convection in a Square Cavity Heated from Below

This numerical study considers the mixed convection, heat transfer and the entropy generation within a square cavity partially heated from below with moving cooled vertical sidewalls. All the other horizontal sides of the cavity are assumed adiabatic. The governing equations, in stream function–vorticity form, are discretized and solved using the finite difference method. Numerical simulations are carried out, by varying the Richardson number, to show the impact of the Prandtl number on the thermal, flow fields, and more particularly on the entropy generation. Three working fluid, generally used in practice, namely mercury (Pr = 0.0251), air (Pr = 0.7296) and water (Pr = 6.263) are investigated and compared. Predicted streamlines, isotherms, entropy generation, as well as average Nusselt numbers are presented. The obtained results reveal that the impact of the Prandtl number is relatively significant both on the heat transfer performance and on the entropy generation. The average Nusselt number increase with increasing Prandtl number. Its value varies thereabouts from 3.7 to 3.8 for mercury, from 5.5 to 13 for air and, from 12.5 to 15 for water. In addition, it is found that the total average entropy generation is significantly higher in the case of mercury (Pr«1) and water (Pr»1) than in the case of air (Pr~1). Its value varies approximately from 700 to 1100 W/m3 K for mercury, from 200 to 500 W/m3 K for water and, from 0.03 to 5 W/m3 K for air

New Approach to Compute Accurately the Entropy Generation Due to Natural Convection in a Square Cavity

The idea to carry out an exercise to compare the calculation of entropy generation for unsteady natural convection in a square cavity with vertical sides that are maintained at different temperatures was motived by the observation, in the literature, of inaccurate or often erroneous results concerning the values of this significant physical entity. It then appeared necessary to reconsider this problem in order to ensure its consistent assessment. The new approach that we propose allows a direct access to the value of the entropy generation by considering the exact values of the thermophysical properties of the working fluid, which depends on the Prandtl and the Rayleigh numbers