A numerical investigation of mixed convection due to a copper–water nanofluid in an enclosure is presented. The mixed convection is governed by moving the upper lid of the enclosure and imposing a vertical temperature gradient. The transport equations for fluid and heat are modeled by using the Boussinesq approximation. A modified form of the control volume based SIMPLET algorithm is used for the solution of the transport equations. The fluid flow and heat transfer characteristics are studied for a wide range of Reynolds number and Grashof number so as to have the Richardson number greater or less than 1. The nanoparticle volume fraction is considered up to 20%. Heat flow patterns are analyzed through the energy flux vector. The rate of enhancement in heat transfer due to the addition of nanoparticles is analyzed. The entropy generation and Bejan number are evaluated to demonstrate the thermodynamic optimization of the mixed convection. We have obtained the enhancement rate in heat transfer and entropy generation in nanofluid for a wide range of parameter values.
Issue Section:
Natural and Mixed Convection
References
1.
Eastman
, J. A.
, Choi
, S. U. S.
, Li
, S.
, Yu
, W.
, and Thompson
, L. J.
, 2001
, “Anomalously Increased Effective Thermal Conductivities of Ethylene Glycol-Based Nanofluids Containing Copper Nanoparticles
,” Appl. Phys. Lett.
, 78
(6), pp. 718
–720
.2.
Xuan
, Y.
, and Li
, Q.
, 2003
, “Investigation on Convective Heat Transfer and Flow Features of Nanofluids
,” ASME J. Heat Transfer
, 125
(1
), pp. 151
–155
.3.
Buongiorno
, J.
, 2006
, “Convective Transport in Nanofluids
,” ASME J. Heat Transfer
, 128
(3
), pp. 240
–250
.4.
Das
, S. K.
, Choi
, S. U. S.
, Yu
, W.
, and Pradet
, T.
, 2007
, Nanofluids: Science and Technology
, Wiley
, New York
.5.
Kakaç
, S.
, and Pramuanjaroenkij
, A.
, 2009
, “Review of Convective Heat Transfer Enhancement With Nanofluids
,” Int. J. Heat Mass Transfer
, 52
(13–14
), pp. 3187
–3196
.6.
Wong
, K. V.
, and Leon
, O. D.
, 2010
, “Applications of Nanofluids: Current and Future
,” Adv. Mech. Eng.
, 2
, p. 519659
.7.
Saidur
, R.
, Leong
, K. Y.
, and Mohammad
, H. A.
, 2011
, “A Review on Applications and Challenges of Nanofluids
,” Renewable Sustainable Energy Rev.
, 15
(3
), pp. 1646
–1668
.8.
Wen
, D.
, Lin
, G.
, Vafaei
, S.
, and Zhang
, K.
, 2007
, “Review of Nanofluids for Heat Transfer Applications
,” Particuology
, 7
(2
), pp. 141
–150
.9.
Mahian
, O.
, Kianifar
, A.
, Kalogirou
, S. A.
, Pop
, I.
, and Wongwises
, S.
, 2013
, “A Review of the Applications of Nanofluids in Solar Energy
,” Int. J. Heat Mass Transfer
, 57
(2
), pp. 582
–594
.10.
Celli
, M.
, 2013
, “Non-Homogeneous Model for a Side Heated Square Cavity Filled With a Nanofluid
,” Int. J. Heat Fluid Flow
, 44
, pp. 327
–335
.11.
Mojarrad
, M. S.
, Keshavarz
, A.
, and Shokouhi
, A.
, 2013
, “Nanofluids Thermal Behavior Analysis Using a New Dispersion Model Along With Single-Phase
,” Heat Mass Transfer
, 49
(9
), pp. 1333
–1343
.12.
Nield
, D. A.
, and Kuznetsov
, A. V.
, 2009
, “The Cheng–Minkowycz Problem for Natural Convective Boundary-Layer Flow in a Porous Medium Saturated by a Nanofluid
,” Int. J. Heat Mass Transfer
, 52
(25–26
), pp. 5792
–5795
.13.
Kuznetsov
, A. V.
, and Nield
, D. A.
, 2010
, “Natural Convective Boundary-Layer Flow of a Nanofluid Past a Vertical Plate
,” Int. J. Therm. Sci.
, 49
(2
), pp. 243
–247
.14.
Kuznetsov
, A. V.
, and Nield
, D. A.
, 2011
, “Double-Diffusive Natural Convective Boundary-Layer Flow of a Nanofluid Past a Vertical Plate
,” Int. J. Therm. Sci.
, 50
(5
), pp. 712
–717
.15.
Nield
, D. A.
, and Kuznetsov
, A. V.
, 2011
, “The Cheng–Minkowycz Problem for Natural Convective Boundary Layer Flow in a Porous Medium Saturated by a Nanofluid
,” Int. J. Heat Mass Transfer
, 54
(1–3
), pp. 374
–378
.16.
Kuznetsov
, A. V.
, and Nield
, D. A.
, 2013
, “The Cheng–Minkowycz Problem for Natural Convective Boundary Layer Flow in a Porous Medium Saturated by a Nanofluid: A Revised Model
,” Int. J. Heat Mass Transfer
, 65
, pp. 682
–685
.17.
Nield
, D. A.
, and Kuznetsov
, A. V.
, 2014
, “Forced Convection in a Parallel-Plate Channel Occupied by a Nanofluid or a Porous Medium Saturated by a Nanofluid
,” Int. J. Heat Mass Transfer
, 70
, pp. 430
–433
.18.
Ahmad
, S.
, Rohni
, A. M.
, and Pop
, I.
, 2011
, “Blasius and Sakiadis Problems in Nanofluids
,” Acta Mech.
, 218
(3–4
), pp. 195
–204
.19.
Magyari
, E.
, 2011
, “Comment on the Homogeneous Nanofluid Models Applied to Convective Heat Transfer Problems
,” Acta Mech.
, 222
(3–4
), pp. 381
–385
.20.
Khanafer
, K.
, Vafai
, K.
, and Lightstone
, M.
, 2003
, “Buoyancy-Driven Heat Transfer Enhancement in a Two-Dimensional Enclosure Utilizing Nanofluids
,” Int. J. Heat Mass Transfer
, 46
(19
), pp. 3639
–3653
.21.
Jou
, R. Y.
, and Tzeng
, S. C.
, 2006
, “Numerical Research of Nature Convective Heat Transfer Enhancement Filled With Nanofluids in Rectangular Enclosures
,” Int. Commun. Heat Mass Transfer
, 33
(6
), pp. 727
–736
.22.
Oztop
, H. F.
, and Abu-Nada
, E.
, 2008
, “Numerical Study of Natural Convection in Partially Heated Rectangular Enclosures Filled With Nanofluids
,” Int. J. Heat Fluid Flow
, 29
(5
), pp. 1326
–1336
.23.
Maïga
, S. E. B.
, Palm
, S. J.
, Nguyen
, C. T.
, Roy
, G.
, and Galanis
, N.
, 2008
, “Heat Transfer Enhancement by Using Nanofluids in Forced Convection Flows
,” Int. J. Heat Fluid Flow
, 26
(4
), pp. 530
–546
.24.
Tiwari
, R. K.
, and Das
, M. K.
, 2007
, “Heat Transfer Augmentation in a Two Sided Lid-Driven Differentially Heated Square Cavity Utilizing Nanofluids
,” Int. J. Heat Mass Transfer
, 50
(9–10
), pp. 2002
–2018
.25.
Abu-Nada
, E.
, and Chamkha
, A. J.
, 2010
, “Mixed Convection Flow in a Lid-Driven Inclined Square Enclosure Filled With a Nanofluid
,” Eur. J. Mech. B/Fluids
, 29
(6
), pp. 472
–482
.26.
Talebi
, F.
, Mahmoudi
, A. H.
, and Shahi
, M.
, 2010
, “Numerical Study of Mixed Convection Flows in a Square Lid-Driven Cavity Utilizing Nanofluid
,” Int. Commun. Heat Mass Transfer
, 37
(1
), pp. 79
–90
.27.
Mahmoodi
, M.
, 2011
, “Mixed Convection Inside Nanofluid Filled Rectangular Enclosures With Moving Bottom Wall
,” Therm. Sci.
, 15
(3), pp. 889
–903
.28.
Chamkha
, A. J.
, and Abu-Nada
, E.
, 2012
, “Mixed Convection Flow in Single and Double-Lid Driven Square Cavities Filled With Water–Al2O3 Nanofluid: Effect of Viscosity Models
,” Eur. J. Mech. B/Fluids
, 36
, pp. 82
–96
.29.
Khorasanizadeh
, H.
, Nikfar
, M.
, and Amani
, J.
, 2013
, “Entropy Generation of Cu–Water Nanofluid Mixed Convection in a Cavity
,” Eur. J. Mech. B/Fluids
, 37
, pp. 143
–152
.30.
Nayak
, R. K.
, Bhattacharyya
, S.
, and Pop
, I.
, 2015
, “Numerical Study on Mixed Convection and Entropy Generation of Cu–Water Nanofluid in a Differentially Heated Skewed Enclosure
,” Int. J. Heat Mass Transfer
, 85
, pp. 620
–634
.31.
Kimura
, S.
, and Bejan
, A.
, 1983
, “The Heatline Visualization of Convective Heat Transfer
,” ASME J. Heat Transfer
, 105
(4
), pp. 916
–919
.32.
Bello-Ochende
, F. L.
, 1988
, “A Heat Function Formulation for Thermal Convection in a Square Cavity
,” Comput. Methods Appl. Mech. Eng.
, 68
(2
), pp. 141
–149
.33.
Costa
, V. A. F.
, 1999
, “Unification of the Streamline, Heatline and Massline Methods for the Visualization of Two-Dimensional Transport Phenomena
,” Int. J. Heat Mass Transfer
, 42
(1
), pp. 27
–33
.34.
Deng
, Q. H.
, and Tang
, G. F.
, 2002
, “Numerical Visualization of Mass and Heat Transport for Conjugate Natural Convection/Heat Conduction by Streamline and Heatline
,” Int. J. Heat Mass Transfer
, 45
(11
), pp. 2373
–2385
.35.
Basak
, T.
, Roy
, S.
, Sharma
, P. K.
, and Pop
, I.
, 2009
, “Analysis of Mixed Convection Flows Within a Square Cavity With Uniform and Non-Uniform Heating of Bottom Wall
,” Int. J. Therm. Sci.
, 48
(5
), pp. 891
–912
.36.
Varol
, Y.
, Oztop
, H. F.
, Mobedi
, M.
, and Pop
, I.
, 2010
, “Visualization of Heat Flow Using Bejan's Heatline Due to Natural Convection of Water Near 4 °C in Thick Walled Porous Cavity
,” Int. J. Heat Mass Transfer
, 53
(9–10
), pp. 1691
–1698
.37.
Guo
, Z. Y.
, Li
, D. Y.
, and Wang
, B. X.
, 1998
, “A Novel Concept for Convective Heat Transfer Enhancement
,” Int. J. Heat Mass Transfer
, 41
(14
), pp. 2221
–2225
.38.
Bejan
, A.
, 2014
, “Heatlines (1983) Versus Synergy (1998)
,” Int. J. Heat Mass Transfer
, 81
, pp. 654
–658
.39.
Hooman
, K.
, 2010
, “Energy Flux Vector as New Tool for Convection Visualization
,” Int. J. Numer. Method Heat Fluid Flow
, 20
(2
), pp. 240
–249
.40.
Bejan
, A.
, 1996
, Entropy Generation Minimization
, CRC Press
, Boca Raton, FL
.41.
Bejan
, A.
, 1979
, “A Study of Entropy Generation in Fundamental Convective Heat Transfer
,” ASME J. Heat Transfer
, 101
(4
), pp. 718
–725
.42.
Baytaş
, A. C.
, 2000
, “Entropy Generation for Natural Convection in an inclined Porous cavity
,” Int. J. Heat Mass Transfer
, 43
(12
), pp. 2089
–2099
.43.
Magherbi
, M.
, Abbassi
, H.
, and Brahim
, B. A.
, 2003
, “Entropy Generation at the Onset of Natural Convection
,” Int. J. Heat Mass Transfer
, 46
(18
), pp. 3441
–3450
.44.
Varol
, Y.
, Oztop.
, H. F.
, and Koca
, A.
, 2008
, “Entropy Generation Due to Conjugate Natural Convection in Enclosures Bounded by Vertical Solid Walls With Different Thicknesses
,” Int. Commun. Heat Mass Transfer
, 35
(5
), pp. 648
–656
.45.
Ilis
, G. G.
, Mobedi
, M.
, and Sunden
, B.
, 2008
, “Effect of Aspect Ratio on Entropy Generation in a Rectangular Cavity With Differentially Heated Vertical Walls
,” Int. Commun. Heat Mass Transfer
, 35
(6
), pp. 696
–703
.46.
Sheng
, Y.
, Shoukri
, M.
, Sheng
, G.
, and Wood
, P.
, 1998
, “A Modification to the Simple Method for Buoyancy-Driven Flows
,” Numer. Heat Transfer, Part B: Fundam.
, 33
(1
), pp. 65
–78
.47.
Brinkman
, H. C.
, 1952
, “The Viscosity of Concentrated Suspensions and Solution
,” J. Chem. Phys
, 20
, pp. 571
–581
.48.
Sarkar
, S.
, Ganguly
, S.
, and Dalal
, A.
, 2013
, “Buoyancy Driven Flow and Heat Transfer of Nanofluids Past a Square Cylinder in Vertically Upward Flow
,” Int. J. Heat Mass Transfer
, 59
, pp. 433
–450
.49.
Abu-Nada
, E.
, 2010
, “Effects of Variable Viscosity and Thermal Conductivity of CuO–Water Nanofluid on Heat Transfer Enhancement in Natural Convection: Mathematical Model and Simulation
,” ASME J. Heat Transfer
, 132
(5
), p. 052401
.50.
Koo
, J.
, and Kleinstreuer
, C.
, 2004
, “A New Thermal Conductivity Model for Nanofluids
,” J. Nanopart. Res.
, 6
(6
), pp. 577
–588
.51.
Prasher
, R.
, Bhattacharyya
, P.
, and Phelan
, P. E.
, 2005
, “Thermal Conductivity of Nanoscale Colloidal Solutions (Nanofluids)
,” Phys. Rev. Lett.
, 94
, p. 025901
.52.
Leonard
, B. P.
, 1979
, “A Stable and Accurate Convective Modelling Procedure Based on Quadratic Upstream Interpolation
,” Comput. Methods Appl. Mech. Eng.
, 19
(1
), pp. 59
–98
.53.
Cheng
, T. S.
, and Liu
, W. H.
, 2010
, “Effect of Temperature Gradient Orientation on the Characteristics of Mixed Convection Flow in a Lid-Driven Square Cavity
,” Comput. Fluids
, 39
(6
), pp. 965
–978
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