Natural convection of CNT-water nanofluid in an annular space between confocal elliptic cylinders with constant heat flux on inner wall

Document Type : Article

Authors

1 Energy Physics Laboratory, Department of Physics, Faculty of Exact Sciences, Mentouri Brothers Constantine1 University, Constantine, 25000, Algeria. Faculty of Sciences and Technology, Mohamed El Bachir El Ibrahimi University, Bordj Bou Arreridj, El-Anasser, 34030, Algeria.

2 Department of Mechanical Engineering, Prince Mohammad Bin Fahd University, Al-Khobar, 31952, Saudi Arabia. Prince Sultan Endowment for Energy and Environment, Prince Mohammad Bin Fahd University, Al-Khobar, 31952, Saudi Arabia.

3 Energy Physics Laboratory, Department of Physics, Faculty of Exact Sciences, Mentouri Brothers Constantine1 University, Constantine, 25000, Algeria

Abstract

In this paper, free convection heat transfer in an annulus between confocal elliptic cylinders filled with CNT-water nanofluid is investigated numerically. The inner cylinder is at constant surface heat flux while the outer wall is isothermally cooled. Equations of continuity, momentum and energy are formulated using the dimensionless form in elliptic coordinates for two-dimensional, laminar and incompressible flow under steady state condition, which is expressed in terms of vorticity and stream function. The governing equations are discretized using the control volume method. For the thermo-physical properties of CNTs, empirical correlations are used in terms of the volume fraction of nanoparticles. For the effective thermal conductivity of CNTs, a new model has been used. The study is performed for modified Rayleigh number (103Ram ≤106), volume fraction of nanoparticles (0≤ f ≤0.12). The eccentricity of the inner and outer ellipses and the angle of orientation are fixed at 0.9, 0.6 and 0°, respectively. Results are presented in the form of streamlines, isotherm contours, and distribution of temperature and local and average Nusselt numbers on solid boundaries. The results are also discussed in detail and a very good agreement exists between the present results and those from the literature.

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Main Subjects


Refrences:
1.Abu-Nada, E. and Chamkha, A.J. E_ect of nanouid variable properties on natural convection in enclosures _lled with a CuO-EG-water nanouid", Int. J. Therm. Sci., 49(12), pp. 2339-2352 (2010).
2. Abu-Nada, E. and Chamkha, A.J. Mixed convection ow in a lid-driven inclined square enclosure _lled with a nanouid", Eur. J. Mech. B/Fluids, 29(6), pp. 472- 482 (2010).
3. Basak, T. and Chamkha, A.J. Heatline analysis on natural convection for nanouids con_ned within square cavities with various thermal boundary conditions", Int. J. Heat Mass Transfer, 55(21-22), pp. 5526-5543 (2012).
4. Chamkha, A.J. and Abu-Nada, E. Mixed convection ow in single-and double-lid driven square cavities _lled with water-Al2O3 nanouid: E_ect of viscosity models", Eur. J. Mech. B/Fluids, 36, pp. 82-96 (2012). 5. Tayebi, T., Djezzar, M., and Saadaoui, K. E_ect of sinusoidal thermal boundary condition on natural convection in a cavity _lled with Cu-water nanouid", J. Nanouids, 2(2), pp. 120-126 (2013). 6. Chamkha, A.J. and Ismael, M.A. Conjugate heat transfer in a porous cavity _lled with nanouids and heated by a triangular thick wall", Int. J. Therm. Sci., 67, pp. 135-151 (2013). 7. Chamkha, A.J. and Ismael, M.A. Natural convection in di_erentially heated partially porous layered cavities _lled with a nanouid", Numer. Heat Transfer, Part A, 65(11), pp. 1089-1113 (2014). 8. Alinia, M., Gorji-Bandpy, M., Ganji, D.D., Soleimani, S., Ghasemi, E., and Darvan, A. Two-phase natural convection of SiO2-water nanouid in an inclined square enclosure", Scientia Iranica, B, 21(5), pp. 1643- 1654 (2014). 9. Tayebi, T. and Djezzar, M. Numerical study of natural convection ow in a square cavity with linearly heating on bottom wall using copper-water nanouid", J. Nanouids, 4(1), pp. 38-49 (2015). 10. Sheremet, M.A. and Pop, I. Mixed convection in a liddriven square cavity _lled by a nanouid: Buongiorno's mathematical model", Appl. Math. Comput., 266, pp. 792-808 (2015). 11. Sheremet, M.A., Pop, I., and Bachok, N. E_ect of thermal dispersion on transient natural convection in a wavy-walled porous cavity _lled with a nanouid" Tiwari and Das' nanouid model", Int. J. Heat Mass Transfer, 92, pp. 1053-1060 (2016). 12. Kamali, R. and Binesh, A. Numerical investigation of heat transfer enhancement using carbon nanotubebased non-Newtonian nanouids", Int. Commun. Heat Mass Transfer, 37(8), pp. 1153-1157 (2010). 13. Xu, X., Li, H., and Xian, G. Energy dissipation behaviors of surface treated multi-walled carbon nanotubes-based nanouid", Mater. Lett., 66(1), pp. 176-178 (2012). 14. Harish, S., Ishikawa, K., Einarsson, E., Aikawa, S., Chiashi, S., Shiomi, J., and Maruyama, S. Enhanced thermal conductivity of ethylene glycol with singlewalled carbon nanotube inclusions", Int. J. Heat Mass Transfer, 55(13-14), pp. 3885-3890 (2012). 15. Kumaresan, V., Velraj, R., and Das, S.K. Convective heat transfer characteristics of secondary refrigerant based CNT nanouids in a tubular heat exchanger", Int. J. Refrigeration, 35(8), pp. 2287-2296 (2012). 16. Youse_, T., Veisy, F., Shojaeizadeh, E., and Zinadini, S. An experimental investigation on the e_ect of MWCNT-H2O nanouid on the e_ciency of at-plate solar collectors", Exp. Therm Fluid Sci., 39, pp. 207- 212 (2012). 17. Kumaresan, V., Khader, S.M.A., Karthikeyan, S., and Velraj, R. Convective heat transfer characteristics of CNT nanouids in a tubular heat exchanger of various lengths for energy e_cient cooling/heating system", Int. J. Heat Mass Transfer, 60, pp. 413-421 (2013). 18. Halelfadl, S., Estell_e, P., Aladag, B., Doner, N., and Mar_e, T. Viscosity of carbon nanotubes water-based nanouids: Inuence of concentration and temperature", Int. J. Therm. Sci., 71, pp. 111-117 (2013). 19. Rahman, M.M, Mojumder, S., Saha, S., Mekhilef, S., and Saidur, R. E_ect of solid volume fraction and tilt angle in a quarter circular solar thermal collectors _lled with CNT-water nanouid", Int. Commun. Heat Mass Transfer, 57, pp. 79-90 (2014). 20. Rahman, M.M.,  Oztop, H.F., Steele, M., Naim, A.G., Al-Salem, K., and Ibrahim, T.A. Unsteady natural convection and statistical analysis in a CNT-water _lled cavity with non-isothermal heating", Int. Commun. Heat Mass Transfer, 64, pp. 50-60 (2015). 21. Tayebi, T., Ferhat, C.E., Rezig, N., and Djezzar, M. Free convection in a carbon nanotube-water nanouid _lled enclosure with power-law variation wall temperature", J. Nanouids, 5(4), pp. 531-542 (2016). 22. Al-Rashed, A.A., Kolsi, L., Kalidasan, K., Malekshah, E.H., Borjini, M.N., and Kanna, P.R. Second law analysis of natural convection in a CNT-water nanouid _lled inclined 3D cavity with incorporated Ahmed body", Int. J. Mech. Sci, 130, pp. 399-415 (2017). 23. Al-Rashed, A.A., Aich, W., Kolsi, L., Mahian, O., Hussein, A.K., and Borjini, M.N. E_ects of movableba _e on heat transfer and entropy generation in a cavity saturated by CNT suspensions: three-dimensional modeling", Entropy, 19(5), p. 200 (2017). 24. Parvin, S., Nasrin, R., Alim, M., Hossain, N., and Chamkha, A.J. Thermal conductivity variation on natural convection ow of water-alumina nanouid in an annulus", Int. J. Heat Mass Transfer, 55(19-20), pp. 5268-5274 (2012). 25. Nasrin, R., Alim, M., and Chamkha, A.J. E_ect of viscosity variation on natural convection ow of wateralumina nanouid in an annulus with internal heat generation", Heat Tran. Asian Res., 41(6), pp. 536- 552 (2012). 26. Matin, M.H. and Pop, I. Natural convection ow and heat transfer in an eccentric annulus _lled by Copper nanouid", Int. J. Heat Mass Transfer, 61, pp. 353- 364 (2013). 27. Mehrizi, A.A., Farhadi, M., and Shayamehr, S. Natural convection ow of Cu-Water nanouid in horizontal cylindrical annuli with inner triangular cylinder using lattice Boltzmann method", Int. Commun. Heat Mass Transfer, 44, pp. 147-156 (2013). 28. Izadi, M., Shahmardan, M., and Behzadmehr, A. Richardson number ratio e_ect on laminar mixed convection of a nanouid ow in an annulus", Int. J. Comput. Methods Eng. Sci. Mech., 14(4), pp. 304-316 (2013). 29. Sheikholeslami, M., Gorji-Bandpy, M., and Ganji, D. Natural convection in a nanouid _lled concentric annulus between an outer square cylinder and an inner elliptic cylinder", Scientia Iranica, B, 20(4), pp. 1241- 1253 (2013). 30. Matin, M.H. and Pop, I. Numerical study of mixed convection heat transfer of a nanouid in an eccentric annulus", Numer. Heat Transfer, Part A, 65(1), pp. 84-105 (2014). 31. Seyyedi, S., Dayyan, M., Soleimani, S., and Ghasemi, E. Natural convection heat transfer under constant heat ux wall in a nanouid _lled annulus enclosure", Ain Shams Eng. J., 6(1), pp. 267-280 (2015). 32. Arbaban, M. and Salimpour, M. Enhancement of laminar natural convective heat transfer in concentric annuli with radial _ns using nanouids", Heat Mass Transfer., 51(3), pp. 353-362 (2015). 33. Mokhtari Moghari, R., Talebi, F., Rafee, R., and Shariat, M. Numerical study of pressure drop and thermal characteristics of Al2O3-water nanouid ow in horizontal annuli", Heat Transfer Eng., 36(2), pp. 166-177 (2015). 34. Tayebi, T., Djezzar, M., Bouzerzour, A., Azzouz, K., and Khan, Z.H. Numerical simulation of natural convection of water based nanouids in horizontal eccentric cylindrical annuli", J. Nanouids, 5(2), pp. 253-263 (2016). 35. Tayebi, T. and Chamkha, A.J. Natural convection enhancement in an eccentric horizontal cylindrical annulus using hybrid nanouids", Numer. Heat Transfer, Part A, 71(11), pp. 1159-1173 (2017). 36. Lee, J.H. and Lee, T.S. Natural convection in the annuli between horizontal confocal elliptic cylinders", Int. J. Heat Mass Transfer, 24(10), pp. 1739-1742 (1981). 37. Schreiber, W.C. and Singh, S.N. Natural convection between confocal horizontal elliptical cylinders", Int. J. Heat Mass Transfer, 28(4), pp. 807-822 (1985). 38. Elshamy, M., Ozisik, M., and Coulter, J. Correlation for laminar natural convection between confocal horizontal elliptical cylinders", Numer. Heat Transfer, 18(1), pp. 95-112 (1990). 39. Cheng, C.-H. and Chao, C.-C. Numerical prediction of the buoyancy-driven ow in the annulus between horizontal eccentric elliptical cylinders", Numer. Heat Transfer Part A Applications, 30(3), pp. 283-303 (1996). 40. Mota, J., Esteves, I., Portugal, C., Esperan_ca, J., and Saatdjian, E. Natural convection heat transfer in horizontal eccentric elliptic annuli containing saturated porous media", Int. J. Heat Mass Transfer, 43(24), pp. 4367-4379 (2000). 41. Hirose, K., Hachinohe, T., and Ishii, Y. Natural convection heat transfer in eccentric horizontal annuli between a heated outer tube and a cooled inner tube with di_erent orientation: The case of an elliptical outer tube", Heat Tran. Asian Res., 30(8), pp. 624- 635 (2001). 42. Zhu, Y., Shu, C., Qiu, J., and Tani, J. Numerical simulation of natural convection between two elliptical cylinders using DQ method", Int. J. Heat Mass Transfer, 47(4), pp. 797-808 (2004). 43. Zerari, K., Afrid, M., and Groulx, D. Forced and mixed convection in the annulus between two horizontal confocal elliptical cylinders", Int. J. Therm. Sci., 74, pp. 126-144 (2013). 44. Bouras, A., Djezzar, M., Naji, H., and Ghernoug, C. Numerical computation of double-di_usive natural convective ow within an elliptic-shape enclosure", Int. Commun. Heat Mass Transfer., 57, pp. 183-192 (2014). 45. Izadi, M., Behzadmehr, A., and Jalali-Vahida, D. Numerical study of developing laminar forced convection of a nanouid in an annulus", Int. J. Therm. Sci., 48(11), pp. 2119-2129 (2009). 46. Dawood, H., Mohammed, H., and Munisamy, K. Heat transfer augmentation using nanouids in an elliptic annulus with constant heat ux boundary condition", Case Stud. Therm. Eng., 4, pp. 32-41 (2014). 47. Tayebi, T., Chamkha, A.J., Djezzar, M., and Bouzerzour, A. Natural convective nanouid ow in an annular space between confocal elliptic cylinders", J. Thermal Sci. Eng. Appl., 9(1), 011010, pp. 1-9 (2017). 48. Tayebi, T. and Chamkha, A.J. Free convection enhancement in an annulus between horizontal confocal elliptical cylinders using hybrid nanouids", Numer. Heat Transfer, Part A, 70(10), pp. 1141-1156 (2016). 49. Moon, P. and Spencer, D., Field Theory Handbook, New York, Springer Verlag (1971). 50. Brinkman, H. The viscosity of concentrated suspensions and solutions", J. Chem. Phys., 20(4), pp. 571- 581 (1952). 51. Xue, Q. Model for thermal conductivity of carbon nanotube-based composites", Physica B: Condensed Matter, 368(1-4), pp. 302-307 (2005). 52. Patankar, S., Numerical Heat Transfer and Fluid Flow, New York, CRC Press (1980). 53. Nogotov, E.F. Applications of numerical heat transfer", NASA, Washington, DC, NASA STI/Recon Technical Report A, Report No. 7914672 (1978). 54. Pop, E., Mann, D., Wang, Q., Goodson, K., and Dai, H. Thermal conductance of an individual singlewall carbon nanotube above room temperature", Nano Lett., 6(1), pp. 96-100 (2006). 55. Zhang, S., Xia, M., Zhao, S., Xu, T., and Zhang, E. Speci_c heat of single-walled carbon nanotubes", Phys. Rev. B., 68(7), p. 075415 (2003).