Natural Convection of Water-Based Nanofluids in a Square Enclosure with Non-Uniform Heating of the Bottom Wall

Affiliation(s)

Département de Physique, Faculté des Sciences de Tunis, Campus Universitaire, El-Manar, Tunisia.

Manufacturing Engineering Department, The Public Authority for Applied Education and Training, Shuweikh, Kuwait.

Département de Physique, Faculté des Sciences de Tunis, Campus Universitaire, El-Manar, Tunisia.

Manufacturing Engineering Department, The Public Authority for Applied Education and Training, Shuweikh, Kuwait.

ABSTRACT

In this paper, a numerical study of natural convection in a square enclosure with non-uniform temperature distribution maintained at the bottom wall and filled with nanofluids is carried out using different types of nanoparticles. The remaining walls of the enclosure are kept at a lower temperature. Calculations are performed for Rayleigh numbers in the range 5 × 10^{3} ≤ *Ra* ≤ 10^{6} and different solid volume fraction of nanoparticles 0 ≤ *χ* ≤ 0.2. An enhancement in heat transfer rate is observed with the increase of nanoparticles volume fraction for the whole range of Rayleigh numbers. It is also observed that the heat transfer enhancement strongly depends on the type of nanofluids. For *Ra* = 10^{6}, the pure water flow becomes unsteady. It is observed that the increase of the volume fraction of nanoparticles makes the flow return to steady state.

KEYWORDS

Natural Convection; Unsteady State; Nanofluids; Solid Volume Fraction; Heat Transfer Enhancement

Natural Convection; Unsteady State; Nanofluids; Solid Volume Fraction; Heat Transfer Enhancement

Cite this paper

N. Ben-Cheikh, A. Chamkha, B. Ben-Beya and T. Lili, "Natural Convection of Water-Based Nanofluids in a Square Enclosure with Non-Uniform Heating of the Bottom Wall,"*Journal of Modern Physics*, Vol. 4 No. 2, 2013, pp. 147-159. doi: 10.4236/jmp.2013.42021.

N. Ben-Cheikh, A. Chamkha, B. Ben-Beya and T. Lili, "Natural Convection of Water-Based Nanofluids in a Square Enclosure with Non-Uniform Heating of the Bottom Wall,"

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[23] I. E. Sarris, I. Lekakis and N. S. Vlachos, “Natural Convection in a 2D Enclosure with Sinusoidal Upper Wall Temperature,” Numerical Heat Transfer, Part A, Vol. 42, No. 5, 2002, pp. 513-530. doi:10.1080/10407780290059675

[24] M. Corcione, “Effects of the Thermal Boundary Conditions at the Sidewalls upon Natural Convection in Rectangular Enclosures Heated from Below and Cooled from Above,” International Journal of Heat Mass Transfer, Vol. 42, No. 2, 2003, pp. 199-208.

[25] S. Roy and T. Basak, “Finite Element Analysis of Natural Convection Flows in a Square Cavity with Non-Uniformly Heated Wall(s),” International Journal of Engineering Science, Vol. 43, No. 8-9, 2005, pp. 668-680. doi:10.1016/j.ijengsci.2005.01.002

[26] M. Sathiyamoorthy, T. Basak, S. Roy and I. Pop, “Steady Natural Convection Flows in a Square Cavity with Linearly Heated Side Wall(s),” International Journal of Heat Mass Transfer, Vol. 50, No. 3-4, 2007, pp. 766-775. doi:10.1016/j.ijheatmasstransfer.2006.06.019

[27] E. Natarajan, T. Basak and S. Roy, “Natural Convection Flows in a Trapezoidal Enclosure with Uniform and Non-Uniform Heating of Bottom Wall,” International Journal of Heat Mass Transfer, Vol. 51, No. 3-4, 2008, pp. 747-756. doi:10.1016/j.ijheatmasstransfer.2007.04.027

[28] T. Basak, S. Roy, P. K. Sharma and I. Pop, “Analysis of Mixed Convection Flows within a Square Cavity with Uniform and Non-Uniform Heating of Bottom Wall,” International Journal of Thermal Sciences, Vol. 48, No. 5, 2009, pp. 891-912. doi:10.1016/j.ijthermalsci.2008.08.003

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[32] S. V. Patankar, “Numerical Heat Transfer and Fluid Flow,” McGraw-Hill, New York, 1980.

[33] B. P. Leonard, “A Stable and Accurate Convective Modelling Procedure Based on Quadratic Upstream Interpolation,” Computer Methods in Applied Mechanics and Engineering, Vol. 19, No. 1, 1979, pp. 59-98. doi:10.1016/0045-7825(79)90034-3

[34] B. P. Leonard, “Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods,” SIAM: Society for Industrial and Applied Mathematics, Philadelphia, 1994.

[35] N. B. Cheikh, B. B. Beya and T. Lili, “Benchmark Solution for Time-Dependent Natural Convection Flows with an Accelerated Full-Multigrid Method,” Numerical Heat Transfer. Part B Fundamentals, Vol. 52, No. 2, 2007, pp. 131-151.

[36] N. Ouertatani, N. B. Cheikh, B. B. Beya and T. Lili, “Numerical Simulation of Two-Dimensional Rayleigh-Bénard Convection in an Enclosure,” Comptes Rendus Mécanique, Vol. 336, No. 5, 2008, pp. 464-470. doi:10.1016/j.crme.2008.02.004

[37] P. H. Oosthuizen and J. T. Paul, “Natural Convection in a Rectangular Enclosure with Two Heated Sections on the Lower Surface,” International Journal of Heat and Fluid Flow, Vol. 26, No. 4, 2005, pp. 587-596.

[1] J. A. Eastman, U. S. Choi, S. Li, L. J. Thompson and S. Lee, “Enhanced Thermal Conductivity through the Development of Nanofluids,” In: S. Komarneni, J. C. Parker and H. J. Wollenberger, Eds., Nanophase and Nanocomposite Materials II. MRS, Materials Research Society, Pittsburg, 1997, pp. 3-11. doi:10.1016/S0017-9310(01)00175-2

[2] P. Keblinski, S. R. Phillpot, S. U.-S. Choi and J. A. Eastman, Mechanisms of Heat Flow in Suspensions of Nano-Sized Particles (Nanofluids),” International Journal of Heat Mass Transfer, Vol. 45, No. 4, 2002, pp. 855-863.

[3] B. X. Wang, H. Li and X. F. Peng, “Research on the Heat Conduction Enhancement for Liquid with Nanoparticles Suspensions, General Paper (G-1),” International Symposium on Thermal Science Engineering (TSE 2002), Beijing, 23-26 October 2002, pp. 23-26.

[4] B. X. Wang, L. P. Zhou and X. F. Peng, “A Fractal Model for Predicting the Effective Thermal Conductivity of Liquid with Suspension of Nanoparticles,” International Journal of Heat Mass Transfer, Vol. 46, No. 14, 2003, pp. 2665-2672. doi:10.1016/S0017-9310(03)00016-4

[5] R. L. Hamilton and O. K. Crosser, “Thermal Conductivity of Heterogeneous Two Component Systems,” Industrial & Engineering Chemistry Fundamentals, Vol. 1, No. 3, 1962, pp. 182-191.

[6] F. J. Wasp, “Solid-Liquid Flow Slurry Pipeline Transportation,” Translated Technical Publications, Berlin, 1977.

[7] J. C. Maxwell-Garnett, “Colours in Metal Glasses and in Metallic Films,” Philosophical Transactions the Royal Society A, Vol. 203, No. 359-371, 1904, pp. 385-420. doi:10.1098/rsta.1904.0024

[8] D. A. G. Bruggeman, “Berechnung Verschiedener Physikalischer Konstanten von Heterogenen Substanzen, I. Dielektrizitatskonstanten und Leitfahigkeiten der Mischkorper aus Isotropen Substanzen,” Annalen der Physik, Vol. 416, No. 7, 1935, pp. 636-679. doi:10.1002/andp.19354160705

[9] W. Yu and S. U. S. Choi, “The Role of Interfacial Layers in the Enhanced Thermal Conductivity of Nanofluids: A Renovated Maxwell Model,” Journal of Nanoparticle Research, Vol. 5, No. 1-2, 2003, pp. 167-171. doi:10.1023/A:1024438603801

[10] K. Khanafer, K. Vafai and M. Lightstone, “Buoyancy Driven Heat Transfer Enhancement in a Two-Dimensional Enclosure Utilizing Nanofluids,” International Journal of Heat Mass Transfer, Vol. 46, No. 19, 2003, pp. 3639-3653. doi:10.1016/S0017-9310(03)00156-X

[11] S. P. Jang and S. U. S. Choi, “Free Convection in a Rectangular Cavity (Benard Convection) with Nanofluids,” Proceedings of the IMECE, Anaheim, 13-19 November 2004, pp. 147-153.

[12] R. Y. Jou and S. C. Tzeng, “Numerical Research of Nature Convective Heat Transfer Enhancement Filled with Nanofluids in Rectangular Enclosures,” International Communications in Heat and Mass Transfer, Vol. 33, No. 6, 2006, pp. 727-736. doi:10.1016/j.icheatmasstransfer.2006.02.016

[13] A. K. Santra, S. Sen and N. Chakraborty, “Study of Heat Transfer Augmentation in a Differentially Heated Square Cavity Using Copper-Water Nanofluid,” International Journal of Thermal Sciences, Vol. 47, No. 9, 2008, pp. 1113-1122. doi:10.1016/j.ijthermalsci.2007.10.005

[14] K. S. Hwang, J. H. Lee and S. P. Jang, “Buoyancy-Driven Heat Transfer of Water-Based Al

[15] S. P. Jang and S. U. S. Choi, “The Role of Brownian Motion in the Enhanced Thermal Conductivity of Nanofluids,” Applied Physics Letters, Vol. 84, No. 21, 2004, pp. 4316-4318. doi:10.1063/1.1756684

[16] X.-Q. Wang, A. S. Mujumdar and C. Yap, “Free Convection Heat Transfer in Horizontal and Vertical Rectangular Cavities Filled with Nanofluids,” International Heat Transfer Conference IHTC-13, Sydney, 13-18 August 2006, 12 p.

[17] A. K. Santra, S. Sen and N. Chakraborty, “Study of Heat Transfer Characteristics of Copper-Water Nanofluid in a Differentially Heated Square Cavity with Different Viscosity Models,” Journal of Enhanced Heat Transfer, Vol. 15, No. 4, 2008, pp. 273-287. doi:10.1615/JEnhHeatTransf.v15.i4.10

[18] C. J. Ho, M. W. Chen and Z. W. Li, “Numerical Simulation of Natural Convection of Nanofluid in a Square Enclosure: Effects Due to Uncertainties of Viscosity and Thermal Conductivity,” International Journal of Heat Mass Transfer, Vol. 51, No. 17-18, 2008, pp. 4506-4516. doi:10.1016/j.ijheatmasstransfer.2007.12.019

[19] H. F. Oztop and E. Abu-Nada, “Numerical Study of Natural Convection in Partially Heated Rectangular Enclosures Filled with Nanofluids,” International Journal of Heat and Fluid Flow, Vol. 29, No. 5, 2008, pp. 1326- 1336. doi:10.1016/j.ijheatfluidflow.2008.04.009

[20] S. M. Aminossadati and B. Ghasemi, “Natural Convection Cooling of a Localised Heat Source at the Bottom of a Nanofluid-Filled Enclosure,” European Journal of Mechanics B/Fluids, Vol. 28, No. 5, 2009, pp. 630-640. doi:10.1016/j.euromechflu.2009.05.006

[21] E. B. Ogut, “Natural Convection of Water-Based Nano-Fluids in an Inclined Enclosure with a Heat Source,” International Journal of Thermal Sciences, Vol. 48, No. 11, 2009, pp. 2063-2073. doi:10.1016/j.ijthermalsci.2009.03.014

[22] B. Ghasemi and S. M. Aminossadati, “Periodic Natural Convection in a Nanofluid-Filled Enclosure with Oscillating Heat Flux,” International Journal of Thermal Sciences, Vol. 49, No. 1, 2010, pp. 1-9. doi:10.1016/j.ijthermalsci.2009.07.020

[23] I. E. Sarris, I. Lekakis and N. S. Vlachos, “Natural Convection in a 2D Enclosure with Sinusoidal Upper Wall Temperature,” Numerical Heat Transfer, Part A, Vol. 42, No. 5, 2002, pp. 513-530. doi:10.1080/10407780290059675

[24] M. Corcione, “Effects of the Thermal Boundary Conditions at the Sidewalls upon Natural Convection in Rectangular Enclosures Heated from Below and Cooled from Above,” International Journal of Heat Mass Transfer, Vol. 42, No. 2, 2003, pp. 199-208.

[25] S. Roy and T. Basak, “Finite Element Analysis of Natural Convection Flows in a Square Cavity with Non-Uniformly Heated Wall(s),” International Journal of Engineering Science, Vol. 43, No. 8-9, 2005, pp. 668-680. doi:10.1016/j.ijengsci.2005.01.002

[26] M. Sathiyamoorthy, T. Basak, S. Roy and I. Pop, “Steady Natural Convection Flows in a Square Cavity with Linearly Heated Side Wall(s),” International Journal of Heat Mass Transfer, Vol. 50, No. 3-4, 2007, pp. 766-775. doi:10.1016/j.ijheatmasstransfer.2006.06.019

[27] E. Natarajan, T. Basak and S. Roy, “Natural Convection Flows in a Trapezoidal Enclosure with Uniform and Non-Uniform Heating of Bottom Wall,” International Journal of Heat Mass Transfer, Vol. 51, No. 3-4, 2008, pp. 747-756. doi:10.1016/j.ijheatmasstransfer.2007.04.027

[28] T. Basak, S. Roy, P. K. Sharma and I. Pop, “Analysis of Mixed Convection Flows within a Square Cavity with Uniform and Non-Uniform Heating of Bottom Wall,” International Journal of Thermal Sciences, Vol. 48, No. 5, 2009, pp. 891-912. doi:10.1016/j.ijthermalsci.2008.08.003

[29] H. C. Brinkman, “The Viscosity of Concentrated Suspensions and Solution,” Journal of Chemical Physics, Vol. 20, No. 4, 1952, pp. 571-581. doi:10.1063/1.1700493

[30] J. Maxwell, “A Treatise on Electricity and Magnetism,” 2nd Edition, Oxford University Press, Cambridge, 1904.

[31] Y. Achdou and J. L. Guermond, “Convergence Analysis of a Finite Element Projection Lagrange-Galerkin Method for the Incompressible Navier-Stokes Equations,” SIAM Journal on Numerical Analysis, Vol. 37, No. 3, 2000, pp. 799-826. doi:10.1137/S0036142996313580

[32] S. V. Patankar, “Numerical Heat Transfer and Fluid Flow,” McGraw-Hill, New York, 1980.

[33] B. P. Leonard, “A Stable and Accurate Convective Modelling Procedure Based on Quadratic Upstream Interpolation,” Computer Methods in Applied Mechanics and Engineering, Vol. 19, No. 1, 1979, pp. 59-98. doi:10.1016/0045-7825(79)90034-3

[34] B. P. Leonard, “Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods,” SIAM: Society for Industrial and Applied Mathematics, Philadelphia, 1994.

[35] N. B. Cheikh, B. B. Beya and T. Lili, “Benchmark Solution for Time-Dependent Natural Convection Flows with an Accelerated Full-Multigrid Method,” Numerical Heat Transfer. Part B Fundamentals, Vol. 52, No. 2, 2007, pp. 131-151.

[36] N. Ouertatani, N. B. Cheikh, B. B. Beya and T. Lili, “Numerical Simulation of Two-Dimensional Rayleigh-Bénard Convection in an Enclosure,” Comptes Rendus Mécanique, Vol. 336, No. 5, 2008, pp. 464-470. doi:10.1016/j.crme.2008.02.004

[37] P. H. Oosthuizen and J. T. Paul, “Natural Convection in a Rectangular Enclosure with Two Heated Sections on the Lower Surface,” International Journal of Heat and Fluid Flow, Vol. 26, No. 4, 2005, pp. 587-596.