Laminar mixed convection in a two-dimensional shallow inclined lid-driven cavity is investigated numerically. The moving cavity lid at the top is isothermally hot and the bottom is isothermally cold while the two sidewalls are insulated. The cavity aspect ratio is taken as 10. The fluid medium consists of a mixture of pure water and copper nanoparticles with volumetric concentrations of 5% and 8%. The flow Richardson number is varied from 0.1 to 10, and the cavity inclination is varied from 0 deg to 30 deg. It is found that, at any specific nanoparticle concentration, the average Nusselt number increases mildly with cavity inclination for the forced convection dominated case (Ri = 0.1) while it increases much more rapidly with inclination for natural convection dominated case (Ri = 10). Also the average Nusselt number has significant increasing trend with increasing concentration of the nanoparticles.
Issue Section:
Research Papers
References
1.
Pilkington
, L. A. B.
, 1969
, “Float Glass Process
,” Proc. R. Soc. London, Ser. A
, 314
(1516
), pp. 1
–25
.2.
Imberger
, J.
, and Hamblin
, P.
, 1982
, “Dynamics of Lakes, Reservoirs, and Cooling Ponds
,” Ann. Rev. Fluid Mech.
, 14
, pp. 153
–187
.3.
Cha
, C.
, and Jaluria
, Y.
, 1984
, “Recirculating Mixed Convection Flow for Energy Extraction
,” Int. J. Heat Mass Transfer
, 27
(10
), pp. 1801
–1812
.4.
Roy
, B.
, 1992
, Crystal Growth From Melts Applications to Growth of Groups 1 and 2 Crystals
, Wiley
, New York
.5.
Jaluria
, Y.
, 2001
, “Fluid Flow Phenomena in Materials Processing—The 2000 Freeman Scholar Lecture
,” ASME J. Fluids Eng.
, 123
(2
), pp. 173
–210
.6.
Torrance
, K.
, Zien
, H.
, and Davis
, R.
, 1972
, “Cavity Flows Driven by Buoyancy and Shear
,” Journal of Fluid Mechanics
, 51
(JAN25
), pp. 221
–231
.7.
Moallemi
, M.
, and Jang
, K.
, 1992
, “Prandtl Number Effects on Laminar Mixed Convection Heat-Transfer in a Lid-Driven Cavity
,” Int. J. Heat Mass Transfer
, 35
(8
), pp. 1881
–1892
.8.
Mohamad
, A. A.
, and Viskanta
, R.
, 1992
, “Laminar-Flow and Heat-Transfer in Rayleigh–Benard Convection With Shear
,” Phys. Fluids A
, 4
(10
), pp. 2131
–2140
.9.
Mohamad
, A.
, and Viskanta
, R.
, 1994
, “Flow Structures and Heat-Transfer in a Lid-Driven Cavity Filled With Liquid Gallium and Heated From Below
,” Exp. Therm. Fluid Sci.
, 9
(3
), pp. 309
–319
.10.
Mansour
, R. B.
, and Viskanta
, R.
, 1994
, “Shear-Opposed Mixed Convection Flow and Heat-Transfer in a Narrow, Vertical-Cavity
,” Int. J. Heat Fluid Flow
, 15
(6
), pp. 462
–469
.11.
Iwatsu
, R.
, Hyun
, J.
, and Kuwahara
, K.
, 1993
, “Mixed Convection in a Driven Cavity With a Stable Vertical Temperature-Gradient
,” Int. J. Heat Mass Transfer
, 36
(6
), pp. 1601
–1608
.12.
Iwatsu
, R.
, and Hyun
, J.
, 1995
, “Three-Dimensional Driven-Cavity Flows With a Vertical Temperature-Gradient
,” Int. J. Heat Mass Transfer
, 38
(18
), pp. 3319
–3328
.13.
Mohamad
, A.
, and Viskanta
, R.
, 1995
, “Flow and Heat-Transfer in a Lid-Driven Cavity Filled With a Stably Stratified Fluid
,” Appl. Math. Modell.
, 19
(8
), pp. 465
–472
.14.
Prasad
, A.
, and Koseff
, J.
, 1996
, “Combined Forced and Natural Convection Heat Transfer in a Deep Lid Driven Cavity Flow
,” Int. J. Heat Fluid Flow
, 17
(5
), pp. 460
–467
.15.
Lee
, S. C.
, and Chen
, C. K.
, 1996
, “Finite Element Solutions of Laminar and Turbulent Mixed Convection in a Driven Cavity
,” Int. J. Numer. Methods Fluids
, 23
(1
), pp. 47
–64
.16.
Alleborn
, N.
, Raszillier
, H.
, and Durst
, F.
, 1999
, “Lid-Driven Cavity With Heat and Mass Transport
,” Int. J. Heat Mass Transfer
, 42
(5
), pp. 833
–853
.17.
Chamkha
, A.
, and Al-Naser
, H.
, 2001
, “Double-Diffusive Convection in an Inclined Porous Enclosure With Opposing Temperature and Concentration Gradients
,” Int. J. Therm. Sci.
, 40
(3
), pp. 227
–244
.18.
Chamkha
, A.
, 2002
, “Hydromagnetic Combined Convection Flow in a Vertical Lid-Driven Cavity With Internal Heat Generation or Absorption
,” Numer. Heat Transfer, Part A
, 41
(5
), pp. 529
–546
.19.
Shankar
, P.
, Meleshko
, V.
, and Nikiforovich
, E.
, 2002
, “Slow Mixed Convection in Rectangular Containers
,” J. Fluid Mech.
, 471
, pp. 203
–217
.20.
Oztop
, H.
, and Dagtekin
, I.
, 2004
, “Mixed Convection in Two-Sided Lid-Driven Differentially Heated Square Cavity
,” Int. J. Heat Mass Transfer
, 47
(8–9
), pp. 1761
–1769
.21.
Waheed
, M. A.
, 2009
, “Mixed Convective Heat Transfer in Rectangular Enclosures Driven by a Continuously Moving Horizontal Plate
,” Int. J. Heat Mass Transfer
, 52
(21–22
), pp. 5055
–5063
.22.
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
.23.
Cheng
, T. S.
, 2011
, “Characteristics of Mixed Convection Heat Transfer in a Lid-Driven Square Cavity With Various Richardson and Prandtl Numbers
,” Int. J. Therm. Sci.
, 50
(2
), pp. 197
–205
.24.
Bettaibi
, S.
, Kuznik
, F.
, and Sediki
, E.
, 2014
, “Hybrid Lattice Boltzmann Finite Difference Simulation of Mixed Convection Flows in a Lid-Driven Square Cavity
,” Phys. Lett. A
, 378
(32–33
), pp. 2429
–2435
.25.
Al-Mudhaf
, A.
, and Chamkha
, A. J.
, 2004
, “Natural Convection of Liquid Metals in an Inclined Enclosure in the Presence of a Magnetic Field
,” Int. J. Fluid Mech. Res.
, 31
(3
), pp. 221
–243
.26.
Ogut
, E.
, 2008
, “Mixed Convection in an Inclined and Lid-Driven Rectangular Enclosure Heated and Cooled on Adjacent Walls
,” Trans. Can. Soc. Mech. Eng.
, 32
(2
), pp. 213
–226
.27.
Ogut
, E. B.
, 2010
, “Mixed Convection in an Inclined Lid-Driven Enclosure With a Constant Flux Heater Using Differential Quadrature (DQ) Method
,” Int. J. Phys. Sci.
, 5
(15
), pp. 2287
–2303
.28.
Darzi
, A. A. R.
, Farhadi
, M.
, and Sedighi
, K.
, 2011
, “Mixed Convection Simulation of Inclined Lid Driven Cavity Using Lattice Boltzmann Method
,” Iran. J. Sci. Technol.
, 35
(M1
), pp. 73
–83
.29.
Karimipour
, A.
, Nezhad
, A. H.
, and D'Orazio
, A.
, 2013
, “The Effects of Inclination Angle and Prandtl Number on the Mixed Convection in the Inclined Lid Driven Cavity Using Lattice Boltzmann Method
,” J. Theor. Appl. Mech.
, 51
(2
), pp. 447
–462
.30.
Mekroussi
, S.
, Nehari
, D.
, and Bouzit
, M.
, 2013
, “Analysis of Mixed Convection in an Inclined Lid-Driven Cavity With a Wavy Wall
,” J. Mech. Sci. Technol.
, 27
(7
), pp. 2181
–2190
.31.
Sivasankaran
, S.
, Sivakumar
, V.
, and Hussein
, A. K.
, 2013
, “Numerical Study on Mixed Convection in an Inclined Lid-Driven Cavity With Discrete Heating
,” Int. Commun. Heat Mass Transfer
, 46
, pp. 112
–125
.32.
Cheng
, T. S.
, and Liu
, W.-H.
, 2014
, “Effects of Cavity Inclination on Mixed Convection Heat Transfer in Lid-Driven Cavity Flows
,” Comput. Fluids
, 100
, pp. 108
–122
.33.
Sivakumar
, V.
, and Sivasankaran
, S.
, 2014
, “Mixed Convection in an Inclined Lid-Driven Cavity With Non-Uniform Heating on Both Sidewalls
,” ASME J. Appl. Mech. Tech. Phys.
, 55
(4
), pp. 634
–649
.34.
Hajmohammadi
, M. R.
, Maleki
, H.
, and Lorenzini
, G.
, 2015
, “Effects of Cu and Ag Nano-Particles on Flow and Heat Transfer From Permeable Surfaces
,” Adv. Powder Technol.
, 26
(1
), pp. 193
–199
.35.
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
, 29
(6
), pp. 472
–482
.36.
Mansour
, M. A.
, Mohamed
, R. A.
, and Abd-Elaziz
, M. M.
, 2010
, “Numerical Simulation of Mixed Convection Flows in a Square Lid-Driven Cavity Partially Heated From Below Using Nanofluid
,” Int. Commun. Heat Mass Transfer
, 37
(10
), pp. 1504
–1512
.37.
Muthtamilselvan
, M.
, Kandaswamy
, P.
, and Lee
, J.
, 2010
, “Heat Transfer Enhancement of Copper–Water Nanofluids in a Lid-Driven Enclosure
,” Commun. Nonlinear Sci. Numer. Simul.
, 15
(6
), pp. 1501
–1510
.38.
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
.39.
Alinia
, M.
, Ganji
, D. D.
, and Gorji-Bandpy
, M.
, 2011
, “Numerical Study of Mixed Convection in an Inclined Two Sided Lid Driven Cavity Filled With Nanofluid Using Two-Phase Mixture Model
,” Int. Commun. Heat Mass Transfer
, 38
(10
), pp. 1428
–1435
.40.
Kahveci
, K.
, and Ogut
, E. B.
, 2011
, “Mixed Convection of Water-Based Nanofluids in a Lid-Driven Square Enclosure With a Heat Source
,” Heat Transfer Res.
, 42
(8
), pp. 711
–735
.41.
Mahmoodi
, M.
, 2011
, “Mixed Convection Inside Nanofluid Filled Rectangular Enclosures With Moving Bottom Wall
,” Therm. Sci.
, 15
(3
), pp. 889
–903
.42.
Arani
, A. A. A.
, Sebdani
, S. M.
, and Mahmoodi
, M.
, 2012
, “Numerical Study of Mixed Convection Flow in a Lid-Driven Cavity With Sinusoidal Heating on Sidewalls Using Nanofluid
,” Superlattices Microstruct.
, 51
(6
), pp. 893
–911
.43.
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
, 36
, pp. 82
–96
.44.
Mansour
, M. A.
, and Ahmed
, S. E.
, 2012
, “Mixed Convection Flows in a Square Lid-Driven Cavity With Heat Source at the Bottom Utilising Nanofluid
,” Can. J. Chem. Eng.
, 90
(1
), pp. 100
–110
.45.
Rahman
, M. M.
, Billah
, M. M.
, and Hasanuzzaman
, M.
, 2012
, “Heat Transfer Enhancement of Nanofluids in a Lid-Driven Square Enclosure
,” Numer. Heat Transfer, Part A
, 62
(12
), pp. 973
–991
.46.
Salari
, M.
, Tabar
, M. M.
, and Tabar
, A. M.
, 2012
, “Mixed Convection of Nanofluid Flows in a Square Lid-Driven Cavity Heated Partially From Both the Bottom and Side Walls
,” Numer. Heat Transfer, Part A
, 62
(2
), pp. 158
–177
.47.
Cho
, C.
, Chen
, C.
, and Chen
, C.
, 2013
, “Mixed Convection Heat Transfer Performance of Water-Based Nanofluids in Lid-Driven Cavity With Wavy Surfaces
,” Int. J. Therm. Sci.
, 68
, pp. 181
–190
.48.
Esfe
, M. H.
, Ghadi
, A. Z.
, and Noroozi
, M. J.
, 2013
, “Numerical Simulation of Mixed Convection Within Nanofluid-Filled Cavities With Two Adjacent Moving Walls
,” Trans. Can. Soc. Mech. Eng.
, 37
(4
), pp. 1073
–1089
.49.
Fereidoon
, A.
, Saedodin
, S.
, and Esfe
, M. H.
, 2013
, “Evaluation of Mixed Convection in Inclined Square Lid-Driven Cavity Filled With Al2O3/Water Nano-Fluid
,” Eng. Appl. Comput. Fluid Mech.
, 7
(1
), pp. 55
–65
.50.
Hussein
, A. K.
, Ahmed
, S. E.
, and Mohammed
, H. A.
, 2013
, “Mixed Convection of Water-Based Nanofluids in a Rectangular Inclined Lid-Driven Cavity Partially Heated From Its Left Side Wall
,” J. Comput. Theor. Nanosci.
, 10
(9
), pp. 2222
–2233
.51.
Li
, D.
, Wang
, X.
, and Feng
, H.
, 2013
, “Fully HOC Scheme for Mixed Convection Flow in a Lid-Driven Cavity Filled With a Nanofluid
,” Adv. Appl. Math. Mech.
, 5
(1
), pp. 55
–77
.52.
Mansour
, M. A.
, and Ahmed
, S. E.
, 2013
, “Mixed Convection in Double Lid-Driven Enclosures Filled With Al2O3–Water Nanofluid
,” J. Thermophys. Heat Transfer
, 27
(4
), pp. 707
–718
.53.
Abu-Nada
, E.
, and Chamkha
, A. J.
, 2014
, “Mixed Convection Flow of a Nanofluid in a Lid-Driven Cavity With a Wavy Wall
,” Int. Commun. Heat Mass Transfer
, 57
, pp. 36
–47
.54.
Esfe
, M. H.
, Akbari
, M.
, and Toghraie
, D.
, 2014
, “Effect of Nanofluid Variable Properties on Mixed Convection Flow and Heat Transfer in an Inclined Two-Sided Lid-Driven Cavity With Sinusoidal Heating on Sidewalls
,” Heat Transfer Res.
, 45
(5
), pp. 409
–432
.55.
Faridzadeh
, M. R.
, Semiromi
, D. T.
, and Niroomand
, A.
, 2014
, “Analysis of Laminar Mixed Convection in an Inclined Square Lid-Driven Cavity With a Nanofluid by Using an Artificial Neural Network
,” Heat Transfer Res.
, 45
(4
), pp. 361
–390
.56.
Heydari
, M. R.
, Esfe
, M. H.
, and Hajmohammad
, M. H.
, 2014
, “Mixed Convection Heat Transfer in a Double Lid-Driven Inclined Square Enclosure Subjected to Cu–Water Nanofluid With Particle Diameter of 90 Nm
,” Heat Transfer Res.
, 45
(1
), pp. 75
–95
.57.
Karimipour
, A.
, Esfe
, M. H.
, and Safaei
, M. R.
, 2014
, “Mixed Convection of Copper–Water Nanofluid in a Shallow Inclined Lid Driven Cavity Using the Lattice Boltzmann Method
,” Physica A
, 402
, pp. 150
–168
.58.
Muthtamilselvan
, M.
, and Doh
, D. H.
, 2014
, “Mixed Convection of Heat Generating Nanofluid in a Lid-Driven Cavity With Uniform and Non-Uniform Heating of Bottom Wall
,” Appl. Math. Modell.
, 38
(13
), pp. 3164
–3174
.59.
Nasrin
, R.
, Alim
, M. A.
, and Chamkha
, A. J.
, 2014
, “Modeling of Mixed Convective Heat Transfer Utilizing Nanofluid in a Double Lid-Driven Chamber With Internal Heat Generation
,” Int. J. Numer. Methods Heat Fluid Flow
, 24
(1
), pp. 36
–57
.60.
Ogut
, E. B.
, and Kahveci
, K.
, 2014
, “Mixed Convection of Water-Based Nanofluids in a Square Enclosure Heated and Cooled on Adjacent Walls
,” Prog. Comput. Fluid Dyn.
, 14
(5
), pp. 328
–340
.61.
Sivasankaran
, S.
, and Pan
, K. L.
, 2014
, “Natural Convection of Nanofluids in a Cavity With Nonuniform Temperature Distributions on Side Walls
,” Numer. Heat Transfer, Part A
, 65
(3
), pp. 247
–268
.62.
Sharif
, M. A. R.
, 2007
, “Laminar Mixed Convection in Shallow Inclined Driven Cavities With Hot Moving Lid on Top and Cooled From Bottom
,” Appl. Therm. Eng.
, 27
(5–6
), pp. 1036
–1042
.63.
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
.64.
Brinkman
, H. C.
, 1952
, “The Viscosity of Concentrated Suspensions and Solutions
,” J. Chem. Phys.
, 20
, p. 571
.65.
Ho
, C. J.
, Chen
, M. W.
, and Li
, Z. W.
, 2008
, “Numerical Simulation of Natural Convection of Nanofluid in a Square Enclosure: Effects Due to Uncertainties of Viscosity and Thermal Conductivity
,” Int. J. Heat Mass Transfer
, 51
(17–18
), pp. 4506
–4516
.66.
Aminossadati
, S. M.
, and Ghasemi
, B.
, 2009
, “Natural Convection Cooling of a Localised Heat Source at the Bottom of a Nanofluid-Filled Enclosure
,” Eur. J. Mech. B
, 28
(5
), pp. 630
–640
.67.
Chon
, C.
, Kihm
, K.
, and Lee
, S.
, 2005
, “Empirical Correlation Finding the Role of Temperature and Particle Size for Nanofluid (Al2O3) Thermal Conductivity Enhancement
,” Appl. Phys. Lett.
, 87
(15
), p. 153107
.68.
Masoumi
, N.
, Sohrabi
, N.
, and Behzadmehr
, A.
, 2009
, “A New Model for Calculating the Effective Viscosity of Nanofluids
,” J. Phys. D: Appl. Phys.
, 42
(5
), p. 055501
.69.
Gul
, R.
, Khan
, Z. H.
, and Khan
, W. A.
, 2009
, “Heat Transfer From Solids With Variable Thermal Conductivity and Uniform Internal Heat Generation Using Homotopy Perturbation Method
,” ASME
Paper No. HT2008-56449.70.
Khan
, Z. H.
, Gul
, R.
, and Khan
, W. A.
, 2009
, “Effect of Variable Thermal Conductivity on Heat Transfer From a Hollow Sphere With Heat Generation Using Homotopy Perturbation Method
,” ASME
Paper No. HT2008-56448.71.
He
, J.
, 2003
, “Homotopy Perturbation Method: A New Nonlinear Analytical Technique
,” Appl. Math. Comput.
, 135
(1
), pp. 73
–79
.72.
Hajmohammadi
, M. R.
, and Nourazar
, S. S.
, 2014
, “Conjugate Forced Convection Heat Transfer From a Heated Flat Plate of Finite Thickness and Temperature-Dependent Thermal Conductivity
,” Heat Transfer Eng.
, 35
(9
), pp. 863
–874
.Copyright © 2015 by ASME
You do not currently have access to this content.
