Local entropy production rates are determined from a numerical and experimental study of natural convection in an enclosure. Numerical predictions are obtained from a control-volume-based finite element formulation of the conservation equations and the Second Law. The experimental procedure combines methods of particle image velocimetry and planar laser induced fluorescence for measured velocity and temperature fields in the enclosure. An entropy based conversion algorithm in the measurement procedure is developed and compared with numerical predictions of free convection in the cavity. The predicted and measured results show close agreement. A measurement uncertainty analysis suggests that the algorithm postprocesses velocities (accurate within to give entropy production data, which is accurate within near the wall. Results are reported for free convection of air and water in a square cavity at various Rayleigh numbers. The results provide measured data for tracking spatial variations of friction irreversibility and local exergy losses.
Issue Section:
Natural and Mixed Convection
1.
De Vahl Davis
, G.
, 1983
, “Natural Convection of Air in a Square Cavity: A Benchmark Solution
,” Int. J. Numer. Methods Fluids
, 3
, pp. 249
–264
.2.
Hortmann
, M.
, Peric
, M.
, and Scheuerer
, G.
, 1990
, “Finite Volume Multigrid Predictions for Laminar Natural Convection: Benchmark Solution
,” Int. J. Numer. Methods Fluids
, 11
, pp. 189
–207
.3.
Lightstone, M. F., and Collins, W. M., 1994, “Simulation of Natural Convection of Air in a Square Cavity Using the GOTHIC Thermohydraulic Code,” Proceedings of the CNA/CNS Annual Conference, Montreal, Canada, June 5–8.
4.
Ismail
, K. A. R.
, and Scalon
, V. L.
, 2000
, “A Finite Element Free Convection Model for the Side Wall Heated Cavity
,” Int. J. Heat Mass Transfer
, 43
, pp. 1373
–1389
.5.
Bejan, A., 1996, Entropy Generation Minimization: The Method of Thermodynamic Optimization of Finite-Time Systems and Finite-Time Processes, CRC Press, Boca Raton, FL.
6.
Poulikakos
, D.
, and Bejan
, A.
, 1982
, “A Fin Geometry for Minimum Entropy Generation in Forced Convection
,” Trans. ASME
, 104
, pp. 616
–623
.7.
Zubair
, S. M.
, Kadaba
, P. V.
, and Evans
, R. B.
, 1987
, “Second-Law-Based Thermoeconomic Optimization of Two-phase Heat Exchangers
,” ASME J. Heat Transfer
, 109
, pp. 287
–294
.8.
Bejan
, A.
, 1979
, “A Study of Entropy Generation in Fundamental Convective Heat Transfer
,” Trans. ASME
, 101
, pp. 718
–725
.9.
Adeyinka, O. B., and Naterer, G. F., 2002, “Predictive Entropy Production and Measurement with Particle Image Velocimetry (PIV) for Recirculating Flows,” AIAA/ASME 8th Joint Thermophysics and Heat Transfer Conference, AIAA Paper-2002-3090, St. Louis, M., June.
10.
Moore, J., and Moore, J. G., 1983, “Entropy Production Rates from Viscous Flow Calculations Part I-A Turbulent Boundary Layer Flow,” ASME Gas Turbine Conference, ASME Paper 83-GT-70, Phoenix.
11.
Moore, J., and Moore, J. G., 1983, “Entropy Production Rates from Viscous Flow Calculations Part II—Flow in a Rectangular Elbow,” ASME Gas Turbine Conference, ASME Paper 83-GT-71, Phoenix.
12.
Drost
, M. K.
, and White
, M. D.
, 1991
, “Numerical Predictions of Local Entropy Generation in an Impinging Jet
,” ASME J. Heat Transfer
, 113
, pp. 823
–829
.13.
Kramer-Bevan, J. S., 1992, “A Tool for Analysing Fluid Flow Losses,” M.Sc. thesis, University of Waterloo.
14.
Cheng
, C. H.
, Ma
, W. P.
, and Huang
, W. H.
, 1994
, “Numerical Predictions of Entropy Generation for Mixed Convective Flows in a Vertical Channel with Transverse Fin Arrays
,” Int. J. Heat Mass Transfer
, 21
, pp. 519
–530
.15.
Sahin
, A. Z.
, 2000
, “Entropy Generation in Turbulent Liquid Flow Through a Smooth Duct Subjected to Constant Wall Temperature
,” Int. J. Heat Mass Transfer
, 43
, pp. 1469
–1478
.16.
Sahin
, A. Z.
, 2002
, “Entropy Generation and Pumping Power in a Turbulent Fluid Flow Through a Smooth Pipe Subjected to Constant Heat Flux
,” Exergy, An International Journal
, 2
, pp. 314
–321
.17.
Demirel
, Y.
, 1999
, “Irreversibility Profiles in a Circular Couette Flow of Temperature Dependence Materials
,” Int. Commun. Heat Mass Transfer
, 26
, pp. 75
–83
.18.
Mahmud
, S.
, and Fraser
, R. A.
, 2002
, “Thermodynamic Analysis of Flow and Heat Transfer Inside Channel with Two Parallel Plates
,” Exergy, An International Journal
, 2
, pp. 140
–146
.19.
Mahmud
, S.
, and Fraser
, R. A.
, 2002
, “Analysis of Entropy Generation Inside Concentric Cylinder Annuli With Relative Rotation
,” Int. J. Therm. Sci.
, 42
, pp. 513
–521
.20.
Baytas
, A. C.
, 1997
, “Optimization in an Enclosure for Minimum Entropy Generation in Natural Convection
,” J. Non-Equilib. Thermodyn.
, 22
(2
), pp. 145
–155
.21.
Baytas
, A. C.
, 2000
, “Entropy Generation for Natural Convection in an Inclined Porous Cavity
,” Int. J. Heat Mass Transfer
, 43
, pp. 2089
–2099
.22.
Megherbi
, M.
, Abbassi
, H.
, and Brahim
, A. B.
, 2003
, “Entropy Generation at the Onset of Natural Convection
,” Int. J. Heat Mass Transfer
, 46
(18
), pp. 3441
–3450
.23.
Abu-Hijleh
, B. A.
, and Heilen
, W. N.
, 1999
, “Entropy Generation Due to Laminar Natural Convection Over a Heated Rotating Cylinder
,” Int. J. Heat Mass Transfer
, 42
, pp. 4225
–4233
.24.
Meyer, K. E., Larsen, P. S., Guillard, F., and Westergaard, C. H., 2002, “Temperature and Velocity Fields in Natural Convection by PIV and LIF,” 11th International Symposium on Application of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, July.
25.
Coolen
, M. C. J.
, Kieft
, R. N.
, Rindt
, C. C. M.
, and Van Steenhoven
, A. A.
, 1999
, “Application of 2-D LIF Temperature Measurement in Water using a Nd:YAG Laser
,” Exp. Fluids
, 27
, pp. 420
–426
.26.
Adeyinka, O. B., 2002, “Entropy and Second Law Optimization in Computational Thermofluids with Laser Based Measurements.,” M.Sc. thesis, University of Manitoba.
27.
Naterer, G. F., 2002, Heat Transfer in Single and Multiphase Systems, CRC Press, Boca Raton, FL.
28.
Adeyinka
, O. B.
, and Naterer
, G. F.
, 2002
, “Apparent Entropy Difference with Heat and Fluid Flow Irreversibilities
,” Numer. Heat Transfer, Part B
, 42
, pp. 411
–436
.29.
Schneider, G. E., 1988, “Elliptic Systems: Finite Element Method I,” in Handbook of Numerical Heat Transfer, W. J. Minkoycz, E. M. Sparrow, G. E. Schneider, and R. H. Pletcher, eds., J Wiley, New York.
30.
Westerweel, J., 2002, “Introduction to PIV,” Dantec Dynamics website: www.dantecmt.com June.
31.
Mallinson
, G. D.
, and De Vahl Davis
, G.
, 1977
, “Three Dimensional Natural Convection in a Box: A Numerical Study
,” J. Fluid Mech.
, 83
(1
), pp. 1
–31
.32.
Hamady
, F. J.
, and Lloyd
, J. R.
, 1989
, “Study of Local Convection Heat Transfer in an Inclined Enclosure
,” Int. J. Heat Mass Transfer
, 32
(9
), pp. 1697
–1708
.33.
FlowMap Particle Image Velocimetry Instrumentation: Installation and User Guide, Dantec Dynamics, Demark, 1998.
34.
Sheng
, J.
, Meng
, H.
, and Fox
, R. O.
, 2000
, “A Large Eddy PIV Method for Turbulence Dissipation Rate Estimation
,” Chem. Eng. Sci.
, 55
, pp. 4423
–4434
.35.
Liu
, Z. C.
, Landreth
, C. C.
, Adrain
, R. J.
, and Hanratty
, T. J.
, 1991
, “High Resolution Measurement of Turbulent Structure in a Channel with Particle Image velocimetry
,” Exp. Fluids
, 10
, pp. 301
–312
.36.
Naterer
, G. F.
, and Camberos
, J. A.
, 2003
, “Entropy and the Second Law in Fluid Flow and Heat Transfer Simulation
,” AIAA Journal of Thermophysics and Heat Transfer
, 17
(3
), pp. 360
–371
.37.
AIAA-Standard-S017-1995, 1995, “Assessment of Experimental Uncertainty with Application to Wind Tunnel Testing,” American Institute of Aeronautics and Astronautics, Washington, DC.
Copyright © 2005
by ASME
You do not currently have access to this content.
