Numerical study of hydrothermal characteristics in nano fluid using KKL model with Brownian motion

Document Type : Article

Authors

1 Department of Applied Mathematics & Statistics, Institute of Space Technology, Islamabad, 44000, Pakistan.

2 Department of Applied Mathematics & Statistics, Institute of Space Technology, Islamabad, 44000, Pakistan

Abstract

Finite element method (FEM) is used to study the hydrothermal characteristics of the nano-fluid subjected to Brownian motion. For effective thermal conductivity and effective, viscosity Koo-Kleinstreuer-Li (KKL) model is used. It is observed that the dispersion of nano-particles in Newtonian liquid causes a significant increase in the effective thermal conductivity. This results based on the dispersion of nano-particles help engineers to design an efficient thermal system. A significant role of viscous dissipation on diffusion of momentum of wall into the fluid is observed. Therefore, dissipations effects cannot be ignored while designing thermal systems. The buoyant force is responsible for the effect of electromagnetic thermal radiations on the velocity of fluid convectively heated surface enhances the rate of generation of entropy. This study also recommends that nano-fluids are the best coolants as compare to the base fluids. Imposition of magnetic field causes more entropy generation.

Keywords

Main Subjects


1. Einstein, A. Eine neue Bestimmung der Molekuldimensionen", Ann. d. Phys., 19, pp. 289-306 (1906). 2. Brinkman, H.C. The viscosity of concentrated suspensions and solutions", J. Chem. Phys., 20(4), pp. 571-581 (1952). 3. Batchelor G.K. The e_ect of Brownian motion on the bulk stress in a suspension of spherical particles", J. Fluid Mech., 83(1), p. 97 (1977). 4. Mori, Y. and Ototake, N. On the viscosity of suspensions", Chem. Eng., 20(9), pp. 488-494 (1956). 5. Wang, X., Xu, X., and Choi, S.U.S. Thermal conductivity of nanoparticle-uid mixture", J. Thermophys. Heat Transfer, 13(4), pp. 474-480 (1999). 6. Avsec, J. and Oblak, M. The calculation of thermal conductivity, viscosity and thermodynamic properties  for nanouids on the basis of statistical nanomechanics", Int. J. Heat Mass Transfer, 50(21-22), pp. 4331- 4341 (2007). 7. Masoumi, N. Sohrabi, N., and Behzadmehr, A. A new model for calculating the e_ective viscosity of nanouids", J. Phys. D Appl. Phys., 42(5), p. 55501 (2009). 8. Maxwell, J.C., A Treatise on Electricity and Magnetism, Oxford, Clarendon (1891). 9. Hamilton, R.L. and Crosser, O.K. Thermal conductivity of heterogeneous two-component systems", I & EC Fundamentals, 1, pp. 182-191 (1962). 10. Je_rey, D.J. Conduction through a random suspension of spheres", Proceedings of Royal Society, 335, pp. 355-367 (1973). 11. Bruggeman, D.A.G. Berechnung verschiedener physikalischer konstanten von heterogenen substanzen", I. Dielektrizitatskonstanten und Leitfahigkeiten der Mischkorper aus Isotropen Substanzen. Annalen der Physik. Leipzig, 24, pp. 636-679 (1935). 12. Lu, S.Y. and Liu, H.C. E_ective conductivity of composites containing aligned spheroidal inclusions of _nite conductivity", J. of Applied Physics, 79(9), pp. 6761-6769 (1996). 13. Davis, R.H. The e_ective thermal conductivity of a composite material with spherical inclusions", Int. J. of Thermophysics, 7, pp. 609-620 (1986). 14. Sastry, N.N., Bhunia, V., Sundararajan, T., and Das, S.K. Predicting the e_ective thermal conductivity of carbon nanotube based nanouids", Nanotechnology, 19, p. 055704 (2008). 15. Syam Sunder, L.S., Singh, M.K., and Sousa, C.M.A. Investigation of thermal conductivity and viscosity of Fe3O4 nanouid for heat transfer applications", Int. Commun. In Heat and Mass Transfer, 44, pp. 7-14 (2013). 16. Xuan, Y., Li, Q., and Hu, W. Aggregation structure and thermal conductivity of nanouids", J. of American Institute of Chemical Engineers (AIChE), 49(4), pp. 1038-1043 (2003). 17. Jang, S.P. and Choi, S.U.S. Role of Brownian motion in the enhanced thermal conductivity of nanouids", Appli. Phy. Letters, 84, pp. 4316-4318 (2004). 18. Kumar, D.H., Patel, H.E., Kumar, V.R.R., Sundararajan, T., Pradeep, T., and Das, S.K. Model for heat conduction in nanouids", Physical Review Letters, 93(14), pp. 144301-1-144301-4 (2004). 19. Koo, J. and Kleinstreuer, C. A new thermal conductivity model for nanouids", J. of Nanoparticle Research, 6(6), pp. 577-588 (2004). 20. Bhattacharya, P., Phelan, P.E., and Prasher, R. Brownian-motion-based convective conductive model for the e_ective thermal conductivity of nanouids", J. of Heat Transfer, 128, pp. 588-595 (2006). 21. Xu, J., Yu, B., Zou, M., and Xu, P. A new model for heat conduction of nanouids based on fractal distributions of nanoparticles", J. of Appli. Phy., 39, pp. 4486-4490 (2006). 22. Yu-Hua, L., Wei, Q., and Ian-Chao, F. Temperature dependence of thermal conductivity of nanouids", Chinese Physics Letters, 25(9), p. 3319 (2008). 23. Shukla, R.K. and Dhir, V.K. E_ect of Brownian motion on thermal conductivity of nanouids", J. of Heat Transfer, 130(4), pp. 042406-1-042406-13 (2008). 24. Yang, B. Thermal conductivity equations based on Brownian motion in suspensions of nanoparticles (nanouids)", J. of Heat Transfer, 130(4), pp. 042408- 1- 042408-5 (2008). 25. Sheikholeslami, M. KKL correlation for simulation of nanouid ow and heat transfer inapermeable channel", Physics Letters A., 1(137), pp. 1-9 (2014). 26. Sheikholeslami, M., Jafaryar, M., and Li, Z. Second law analysis for nanouid turbulent ow inside a circular duct in presence of twisted tape turbulators", J. of Molecular Liquids, 263, pp. 489-500 (2017). 27. Sheikholeslami, M. Application of Darcy law for nanouid ow in a porous cavity under the impact of Lorentz forces", J. of Molecular Liquids, 266, pp. 495-503 (2018). 28. Sheikholeslami, M. Solidi_cation of NEPCM under the e_ect of magnetic _eld in a porous thermal energy storage enclosure using nanoparticles", J. of Molecular Liquids, 263, pp. 303-315 (2018). 29. Sheikholeslami, M. and Rokni, H.B. CVFEM for e_ect of Lorentz forces on nanouid ow in a porous complex shaped enclosure by means of Nonequilibrium model", J. of Molecular Liquids, 254, pp. 446-462 (2018). 30. Sheikholeslami, M., Shehzad, S.A., Li, Z., and Shafee, A. Numerical modeling for alumina nanouid magnetohydrodynamic convective heat transfer in a permeable medium using Darcy law", Int. J. of Heat and Mass Transfer, 127, pp. 614-622 (2018). 31. Sheikholeslami, M., Li, Z., and Shafee, A. Lorentz forces e_ect on NEPCM heat transfer during solidi_- cation in a porous energy storage system", Int. J. of Heat and Mass Transfer, 127, pp. 665-674 (2018). 32. Sheikholeslami, M. Jafaryar, M., Saleem, S., Li, Z., Shafee, A., and Jiang, Y. Nanouid heat transfer augmentation and exergy loss inside a pipe equipped with innovative turbulators", Int. J. of Heat and Mass Transfer, 126, pp. 156-163 (2018). 33. Sheikholeslami, M., Shehzad, S.A., and Li, Z. Water based nanouid free convection heat transfer in a three dimensional porous cavity with hot sphere obstacle in existence of Lorenz forces", Int. J. of Heat and Mass Transfer, 125, pp. 375-386 (2018). 34. Sheikholeslami, M., Darzi, M., and Li, Z. Experimental investigation for entropy generation and energy loss of nano-refrigerant condensation process", Int. J. of Heat and Mass Transfer, 125, pp. 1087-1095 (2018). 35. Sheikholeslami, M., Darzi, M., and Sadoughi, M.K. Heat transfer improvement and pressure drop during condensation of refrigerant-based nanouid; an experimental procedure", Int. J. of Heat and Mass Transfer, 122, pp. 643-650 (2018). 36. Sheikholeslami, M., Shehzad, S.A., Abbasi, F.M., and Li, Z. Nanouid ow and forced convection heat transfer due to Lorentz forces in a porous lid driven cubic enclosure with hot obstacle", Comput. Methods Appl. Mech. Engrg., 338, pp. 491-505 (2018). 37. Sheikholeslami, M. CuO-water nanouid ow due to magnetic _eld inside a porous media considering Brownian motion", J. of Molecular Liquids, 249, pp. 921-929 (2018). 38. Sheikholeslami, M., Li, Z., and Shafee, A. Lorentz forces e_ect on NEPCM heat transfer during solidi_- cation in a porous energy storage system", Int. J. of Heat and Mass Transfer, 127, pp. 665-674 (2018). 39. Malvandi, A., Safaei, M.R., A_ash, M.H.K., and Ganji, D.D. MHD mixed convection in a vertical annulus _lled with Al2O3-water nanouid considering nanoparticle migration", J. of Magnetism and Magnetic Materials, 382, pp. 296-306 (2015). 40. Domairry, G. and Hatami, M. Squeezing Cu-water nanouid ow analysis between parallel plates by DTM-Pade method", J. of Molecular Liquids, 193, pp. 37-44 (2014). 41. Alinia, M., Ganji, D.D., and Gorji-Bandpy, M. Numerical study of mixed convection in an inclined two sided lid driven cavity _lled with nanouid using twophase mixture model", Int. Commun. in Heat and Mass Transfer, 38, pp. 1428-1435 (2011). 42. Hatami, M., Sheikholeslami, M., Hosseini, M., and Domiri Ganji, D. Analytical investigation of MHD nanouid ow in non-parallel walls", J. of Molecular Liquids, 194, pp. 251-259 (2014). 43. Ahmadi, A.R., Zahmatkesh, A., Hatami, M., and Ganji, D.D. A comprehensive analysis of the ow and heat transfer for a nanouid over an unsteady stretching at plate", Powder Technology, 258, pp. 125-133 (2014). 44. Malvandi, A., Hedayati, F., and Domairry, G. Stagnation point ow of a nanouid toward an exponentially stretching sheet with nonuniform heat generation/ absorption", J. of Thermodynamics, 2013, pp. 1-12 (2013). 45. Khorasanizadeh, H., Amani, J., and Nikfar, M. Numerical investigation of Cu-water nanouid natural convection and entropy generation within a cavity with an embedded conductive ba_e", Scientia Iranica, 19(6), pp. 1996-2003 (2012). 46. Sheikholeslami, M. and Gangi, D.D. MHD ow in a permeable channel _lled with nanouid", Scientia Iranica, 21(1), pp. 203-212 (2014). 47. Hosseinzadeh, Kh., Afsharpanah, F., Zamani, S., Gholinia, M., and Ganji, D.D. A numerical investigation on ethylene glycoltitanium dioxide nanouid convective ow over a stretching sheet in presence of heat generation/absorption", Case Studies in Thermal Engineering, 12, pp. 228-236 (2018). 48. Ghadikolaei, S.S., Hosseinzadeh, Kh., Ganji, D.D., and Jafari, B. Nonlinear thermal radiation e_ect on magneto Casson nanouid ow with Joule heating e_ect over an inclined porous stretching sheet", Case Studies in Thermal Engineering, 12, pp. 176-187 (2018). 49. Amiri, A.J., Ardahaie, S.S., Amooie, A., Hosseinzadeh, Kh., and Ganji, D.D. Investigating the e_ect of adding nanoparticles to the blood ow in presence of magnetic _eld in a porous blood arterial", Informatics in Medicine Unlocked, 10, pp. 71-81 (2017). 50. Ghadikolaei, S.S., Hosseinzadeh, Kh., Yassari, M., Sadeghi, H., and Ganji, D. D. Boundary layer analysis of micropolar dusty uid with TiO2 nanoparticles in a porous medium under the e_ect of magnetic _eld and thermal radiation over a stretching sheet", Journal of Molecular Liquids, 244, pp. 374-389 (2017). 51. Ghadikolaei, S.S., Hosseinzadeh, Kh., Hatami, M., and Ganji, D.D. MHD boundary layer analysis for micropolar dusty uid containing hybrid nanoparticles (Cu, Al2O3) over a porous medium", Journal of Molecular Liquids, 268, pp. 813-823 (2018). 52. Ghadikolaei, S.S., Hosseinzadeh, Kh., and Ganji, D.D. Investigation on three dimensional squeezing ow of mixture base uid (ethylene glycol-water) suspended by hybrid nanoparticle (Fe3O4 - Ag) dependent on shape factor", Journal of Molecular Liquids, 262, pp. 376-388 (2018). 53. Ghadikolaei, S.S., Hosseinzadeh, Kh., Ganji, D.D., and Hatami, M. Fe3O4 -(CH2OH)2 nanouid analysis in a porous medium under MHD radiative boundary layer and molecular dusty uid", Journal of Molecular Liquids, 258, pp. 172-185 (2018). 54. Ghadikolaei, S.S., Hosseinzadeh, Kh., Hatami, M., Ganji, D.D., and Armin, M. Investigation for squeezing ow of ethylene glycol (C2H6O2) carbon nanotubes (CNTs) in rotating stretching channel with nonlinear thermal radiation", Journal of Molecular Liquids, 263, pp. 10-21 (2018). 55. Ghadikolaei, S.S., Hosseinzadeh, K.H., and Ganji, D.D. MHD raviative boundary layer analysis of micropolar dusty uid with graphene oxide (Go)-engine oil nanoparticles in a porous medium over a stretching sheet with joule heating e_ect", Powder Technology, 338, pp. 425-437 (2018). 56. Hosseinzadeh, Kh., Amiri, A.J., Ardahaie, S.S., and Ganji, D.D. E_ect of variable Lorentz forces on nanouid ow in movable parallel plates utilizing analytical method", Case Studies in Thermal Engineering, 10, pp. 595-610 (2017). 57. Sheikholeslami, M., Hatami, M., and Domairry, G. Numerical simulation of two phase unsteady nanouid ow and heat transfer between parallel plates in presence of time dependent magnetic _eld", J. of the Taiwan Institute of Chemical Engineers, 46, pp. 43-50 (2015). 58. Bejan, A. Entropy generation minimization, the new thermodynamics of _nite-size devices and _nite-time processes", J. Appl. Phys., 79, pp. 1191-1218 (1996). 59. Bhatti, M.M., Rashidi, M.M., and Pop, I. Entropy generation with nonlinear heat and mass transfer on MHD boundary layer over a moving surface using SLM", Nonlinear Eng., 6, pp. 43-52 (2017). 60. Armaghania, T., Kasaeipoora, A., Alavib, N., and Rashidic, M.M. Numerical investigation of wateralumina nanouid natural convection heat transfer and entropy generation in a based L-shaped cavity", J. Mol. Liq., 223, pp. 243-251 (2016). 61. Bianco, V., Nardini, S., and Manca, O. Enhancement of heat transfer and entropy generation analysis of nanouids turbulent convection ow in square section tubes", Nanoscale Research Letters, 6, p. 252 (2011). 62. Butt, A.S. and Ali, A.A. Computational study of entropy generation in magnetohy-drodynamic ow and heat transfer over an unsteady stretching permeable sheet", The European Physical J. Plus, 129, pp. 1-13 (2014). 63. Das, S., Chakraborty, S., Jana, R.N., and Makinde, O.D. Entropy analysis of unsteady magneto-nanouid ow past accelerating stretching sheet with convective boundary condition", Appl. Math. Mech. -Engl. Ed., 36(12), pp. 1593-1610 (2015). 64. Abolbashari, M.H., Freidoonimehr, N., Nazari, F., and Rashidi, M.M. Entropy analysis for an unsteady MHD ow past a stretching permeable surface in nano- uid", Powder Technology, 267, pp. 256-267 (2014).