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

A Numerical Study on Entropy Generation in Two-Dimensional Rayleigh-Bénard Convection at Different Prandtl Number

Entropy generation in two-dimensional Rayleigh-Bénard convection at different Prandtl number (Pr) are investigated in the present paper by using the lattice Boltzmann Method. The major concern of the present paper is to explore the effects of Pr on the detailed information of local distributions of entropy generation in virtue of frictional and heat transfer irreversibility and the overall entropy generation in the whole flow field. The results of this work indicate that the significant viscous entropy generation rates (Su) gradually expand to bulk contributions of cavity with the increase of Pr, thermal entropy generation rates (Sθ) and total entropy generation rates (S) mainly concentrate in the steepest temperature gradient, the entropy generation in the flow is dominated by heat transfer irreversibility and for the same Rayleigh number, the amplitudes of Su, Sθ and S decrease with increasing Pr. It is found that that the amplitudes of the horizontally averaged viscous entropy generation rates, thermal entropy generation rates and total entropy generation rates decrease with increasing Pr. The probability density functions of Su, Sθ and S also indicate that a much thinner tail while the tails for large entropy generation values seem to fit the log-normal curve well with increasing Pr. The distribution and the departure from log-normality become robust with decreasing Pr

A Numerical Study on Entropy Generation in Two-Dimensional Rayleigh-Bénard Convection at Different Prandtl Number

Entropy generation in two-dimensional Rayleigh-Bénard convection at different Prandtl number (Pr) are investigated in the present paper by using the lattice Boltzmann Method. The major concern of the present paper is to explore the effects of Pr on the detailed information of local distributions of entropy generation in virtue of frictional and heat transfer irreversibility and the overall entropy generation in the whole flow field. The results of this work indicate that the significant viscous entropy generation rates (Su) gradually expand to bulk contributions of cavity with the increase of Pr, thermal entropy generation rates (Sθ) and total entropy generation rates (S) mainly concentrate in the steepest temperature gradient, the entropy generation in the flow is dominated by heat transfer irreversibility and for the same Rayleigh number, the amplitudes of Su, Sθ and S decrease with increasing Pr. It is found that that the amplitudes of the horizontally averaged viscous entropy generation rates, thermal entropy generation rates and total entropy generation rates decrease with increasing Pr. The probability density functions of Su, Sθ and S also indicate that a much thinner tail while the tails for large entropy generation values seem to fit the log-normal curve well with increasing Pr. The distribution and the departure from log-normality become robust with decreasing Pr