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Natural convection of nanofluid in a wavy cavity in the presence of magnetic field on variable heat surface temperature

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Abstract

A numerical analysis has been performed to investigate the laminar natural convection heat characteristics in a wavy cavity filled with CuO/water nanofluid. One of the sinusoidal walls (BC) is at the volatile high temperature and the opposite wavy surface is at a stable low temperature and the two other walls are considered flat and insulated while the uniform magnetic field is considered. Performing the analysis, the governing equations are given in terms of the stream function-vorticity formulation. In order to solve the nondimensionalized equations, discretizing with second-order accurate central difference method is performed then the successive under relaxation method with appropriate boundary conditions is considered. To validate the numerical model, various comparisons with previously published studies have been conducted and the results are in a good agreement. The main objective is to survey the effects of the Rayleigh number, Hartmann number, and nanoparticles volume fraction on the fluid flow and heat transfer characteristics. The results are illustrated in contours of stream function, constant temperature, and Nusselt number. The results show that the presence of the magnetic field the local Nusselt number decreases at the hot wall. Moreover, the enhancement in the heat transfer performance increases with an increasing nanoparticle concentration. However, for all values of Rayleigh number, the presence of nanoparticles leads to significant enhancement in heat transfer and the increase of Rayleigh number causes the heat transfer mechanism to change from conduction to convection.

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References

  1. X. Wang, D. Li and H. Jiao, Heat transfer enhancement of Cu-water nanofluids considering Brownian motion of nanoparticles in a singular cavity, Journal of Information and Computational Science, 9 (5) (2012) 1223–1235.

    Google Scholar 

  2. O. Manca, S. Nardini, D. Ricci and S. Tamburrino, Numeri-cal investigation on mixed convection in triangular crosssection ducts with nanofluids, Advanced in Mechanical Engineering, 7 (1) (2015) 13.

    Article  Google Scholar 

  3. J. Guiet, M. Reggio and P. Vasseeur, Natural convection of nanofluids in square enclosure with a protruding heat, Advanced in Mechanical Engineering, 4 (2012) (167296) 11.

    Article  Google Scholar 

  4. J. Rahmannezhad, A. Ramezani and M. Kalteh, Numerical investigation of magnetic field effects on mixed convection flow in a nanofluid-filled lid driven cavity, Int. J. of Engineering, 26 (10) (2013) 1213–1224.

    Google Scholar 

  5. E. Abu-Nada, 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 Transf., 132 (5) (2010) 052401.

    Article  Google Scholar 

  6. E. Abu-Nada, Effects of variable viscosity and thermal conductivity of Al2O3-water nanofluid on heat transfer enhancement in natural convection, Int. J. Heat Fluid Flow, 30 (2009) 679–690.

    Article  Google Scholar 

  7. 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, J. Enhanced Heat Transf., 15 (4) (2008) 273–287.

    Article  Google Scholar 

  8. 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, Int. J. Heat Mass Transfer, 51 (17-18) (2008) 4506–4516.

    Article  MATH  Google Scholar 

  9. A. Al-Amiri, K. Khanafer, J. Bull and I. Pop, Effect of sinusoidal wavy bottom surface on mixed convection heat transfer in a lid-driven cavity, International Journal of Heat and Mass Transfer, 50 (2007) 1771–1780.

    Article  MATH  Google Scholar 

  10. C. C. Cho, C. L. Chen and C. K. Chen, Mixing of non-Newtonian fluids in wavy serpentine microchannel using electro kinetically-driven flow, Electrophoresis, 33 (5) (2012) 743–750.

    Article  Google Scholar 

  11. E. Abu-Nada and H. F. Oztop, Numerical analysis of Al2O3/water nanofluids natural convection in a wavy walled cavity, Numerical Heat Transfer, Part A: Applications, 59 (5) (2011) 403–419.

    Google Scholar 

  12. C. C. Cho, C. L. Chen and C. K. Chen, Natural convection heat transfer performance in complex-wavy wall enclosed cavity filled with nanofluid, Int. J. Therm. Sci., 60 (2012) 255–263.

    Article  Google Scholar 

  13. M. Esmaeilpour and M. Abdollahzadeh, Free convection and entropy generation of nanofluid inside an enclosure with different patterns of vertical wavy walls, International Journal of Thermal Sciences, 52 (2012) 127–136.

    Article  Google Scholar 

  14. C.-C. Cho, C.-L. Chen and C.-K. Chen, Mixed convection heat transfer performance of water-based nanofluids in liddriven cavity with wavy surfaces, International Journal of Thermal Sciences, 68 (2013) 181e190.

    Article  Google Scholar 

  15. E. Abu-Nada and A. J. Chamkha, Mixed convection flow of a nanofluid in a lid-driven cavity with a wavy wall, International Communications in Heat and Mass Transfer, 57 (2014) 36–47.

    Article  Google Scholar 

  16. C.-C. Cho, Heat transfer and entropy generation of natural convection in nanofluid-filled square cavity with partiallyheated wavy surface, International Journal of Heat and Mass Transfer, 77 (2014) 818–827.

    Article  Google Scholar 

  17. M. A. Sheremet, I. Popc and A. Shenoy, Unsteady free convection in a porous open wavy cavity filled with a nanofluid using Buongiorno's mathematical model, International Communications in Heat and Mass Transfer, 67 (2015) 66–72.

    Article  Google Scholar 

  18. M. A. Sheremet, I. Pop and N. Bachok, Effect of thermal dispersion on transient natural convection in a wavy-walled porous cavity filled with a nanofluid: Tiwari and Das’ nanofluid model, International Journal of Heat and Mass Transfer, 92 (2016) 1053–1060.

    Article  Google Scholar 

  19. R. K. Tiwari and M. K. Das, Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluids, Int. J. Heat Mass Transfer, 50 (2007) 2002–2018.

    Article  MATH  Google Scholar 

  20. A. H. Mahmoudi, I. Pop and M. Shahi, Effect of magnetic field on natural convection in a triangular enclosure filled with nanofluid, Int. J. Thermal Science, 59 (2012) 12–140.

    Article  Google Scholar 

  21. M. A. A. Hamad, I. Pop and A. I. Md Ismail, Magnetic field effects on free convection flow of a nanofluid past a vertical semi-infinite flat plate, Nonlinear Analysis: Real World Applications, 12 (3) (2011) 1338–1346.

    Article  MathSciNet  MATH  Google Scholar 

  22. S. Selimli, Z. Recebli and E. Arcaklioglu, MHD numerical analyses of hydrodynamically developing laminar liquid lithium duct flow, International Journal of Hydrogen Energy, 40 (2015) 15358–15364.

    Article  Google Scholar 

  23. Z. Recebli, S. Selimli and E. Gedik, Three dimensional numerical analysis of magnetic field effect on Convective heat transfer during the MHD steady state laminar flow of liquid lithium in a cylindrical pipe, Computers & Fluids, 88 (2013) 410–417.

    Article  MathSciNet  Google Scholar 

  24. S. Selimli, Z. Recebli and E. Arcaklioglu, Combined effects of magnetic and electrical field on the hydrodynamic and thermophysical parameters of magnetoviscous fluid flow, International Journal of Heat and Mass Transfer, 86 (2015) 426–432.

    Article  Google Scholar 

  25. M. Sheikholeslami, M. Gorji-Bandpy, D. D. Ganji and S. Soleimani, Natural convection heat transfer in a cavity with sinusoidal wall filled with CuO-water nanofluid in presence of magnetic field, Journal of the Taiwan Institute of Chemical Engineers, 45 (1) (2014) 40–49.

    Article  Google Scholar 

  26. M. M. Rashidi, M. Nasiri, M. Khezerloo and N. Laraqi, Numerical investigation of magnetic field effect on mixed convection heat transfer of nanofluid in a channel with sinusoidal walls, Journal of Magnetism and Magnetic Materials, 40 (1) (2016) 159–168.

    Article  Google Scholar 

  27. J. C. Maxwell, A treatise on electricity and magnetism, London: Oxford University Press (1904).

    MATH  Google Scholar 

  28. S. M. S. Murshed, K. C. Leong and C. Yang, Enhanced thermal conductivity of TiO2-water based nanofluids, Int. J. Thermal Sci., 44 (4) (2005) 367–373.

    Article  Google Scholar 

  29. E. V. Timofeeva, J. L. Routbort and D. Singh, Particle shape effects on thermo physical properties of alumina nano fluids, J. Appl. Phys., 106 (014304) (2009) 10.

    Google Scholar 

  30. B. C. Pak and Y. I. Cho, Hydrodynamic and heat transfer study ofdispersed fluids with submicron metallic oxide particles, Exp Heat Transfer Int. J., 11 (2) (1998) 151–170.

    Article  Google Scholar 

  31. H. C. Brinkman, The viscosity of concentrated suspensions and solution, J. Chem. Phys., 20 (1952) 571–581.

    Article  Google Scholar 

  32. M. Sheikholeslami, S. Soleimani, M. Gorji-Bandpy, D. D. Ganji and S. M. Seyyedi, Natural convection of nanofluids in an enclosure between acircular and a sinusoidal cylinder in the presence of magnetic field, Int. Commun Heat Mass Transfer, 39 (9) (2012) 1435–1443.

    Article  Google Scholar 

  33. J. Koo and C. Kleinstreuer, Laminar nanofluid flow in microheat-sinks, Int. J. Heat Mass Transfer, 48 (2005) 2652–2661.

    Article  MATH  Google Scholar 

  34. K. Khanafer, K. Vafai and M. Lightstone, Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids, International Journal of Heat and Mass Transfer, 46 (2003) 3639–3653.

    Article  MATH  Google Scholar 

  35. G. Barakos and E. Mitsoulis, Natural convection flow in a square cavity revisited: Laminar and turbulent models with wall functions, Int. J. Numerical Methods Fluids, 18 (1994) 695–719.

    Article  MATH  Google Scholar 

  36. T. Fusegi, J. M. Hyun, K. Kuwahara and B. Farouk, A numerical study of three-dimensional natural convection in a differentially heated cubical enclosure, Int. J. Heat Mass Transfer, 34 (1991) 1543–1557.

    Article  Google Scholar 

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Authors and Affiliations

  1. Faculty of Mechanical Engineering, University of Guilan, Rasht, Iran

    Korosh Javaherdeh

  2. Department of Mechanical Engineering, University Campus 2, University of Guilan, Rasht, Iran

    Mehdi Moslemi & Mona Shahbazi

Authors
  1. Korosh Javaherdeh
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  2. Mehdi Moslemi
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  3. Mona Shahbazi
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Corresponding author

Correspondence to Korosh Javaherdeh.

Additional information

Recommended by Associate Editor Ji Hwan Jeong

Mehdi Moslemi received his Master of Science in Mechanical Engineering from From University of guilan in 2010. He is a Ph.D. student of Mechanical Engineering at University of guilan. His research interests include heat transfer in wavy plate and cavity and channel and non Newtonian fluids and nanofluids.

Korosh Javaherdeh received his Master of Science in Mechanical Engineering from in Institute National Polytechnique de Lorraine 1993 and his Ph.D. in Mechanical Engineering from Nancy University in 1997. He was appointed as an Associate Professor in Mechanical Engineering at University of guilan in 2014. His general research interests are in the areas heat transfer in wavy plate and cavity and channel and non- Newtonian fluids and nanofluids, numerical and experimental heat transfer.

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Javaherdeh, K., Moslemi, M. & Shahbazi, M. Natural convection of nanofluid in a wavy cavity in the presence of magnetic field on variable heat surface temperature. J Mech Sci Technol 31, 1937–1945 (2017). https://doi.org/10.1007/s12206-017-0342-7

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  • DOI: https://doi.org/10.1007/s12206-017-0342-7

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