Authors
Abstract
A two-phase lattice Boltzmann model considering the interaction forces of nanofluid has been developed in this paper. It is applied to investigate the flow and natural convection heat transfer of Al2O3–H2O nanofluid in an enclosure containing internal heat generation. To understand the heat transfer enhancement mechanism of the nanofluid flow from the particle level, the lattice Boltzmann method is used because of its mesoscopic feature and numerical advantages. By using a two-component lattice Boltzmann model, the heat transfer enhancement of the nanofluid is analyzed through incorporating the different forces acting on the nanoparticles and the base fluid . The effects of interaction forces, nanoparticle volume fractions (0.0-0.05), and internal and external Rayleigh numbers (103-106) on the nanoparticle distributions and heat transfer characteristics are investigated. The average Nusselt number increases with the increase of nanoparticle volume fraction and Rayleigh number. We also compared and analyzed adding internal heat generation on the nanoparticles and the base fluid separately, and it was found that by considering heat generation on the base fluid, it mostly affects the temperature field, and by considering that on nanoparticles, it mostly affects the stream field.
Keywords
1. Rahimi-Gorji, M., Pourmehran, O., Hatami, M. and Ganji, D., “Statistical Optimization of Microchannel Heat Sink (MCHS) Geometry Cooled by Different Nanofluids Using RSM Analysis”, The European Physical Journal Plus, Vol. 130, No. 2, p. 22 , 2015.
2. Wang, B.-X., Zhou, L.-P. and Peng, X.-F., “A Fractal Model for Predicting the Effective Thermal Conductivity of Liquid with Suspension of Nanoparticles”, International Journal of Heat and Mass Transfer, Vol. 46, No. 14, pp. 2665-2672, 2003.
3. Yang, Y., Zhang, Z. G., Grulke, E. A., Anderson, W. B. and Wu, G., “Heat Transfer Properties of Nanoparticle-in-Fluid Dispersions (Nanofluids) in Laminar Flow”, International Journal of Heat and Mass Transfer, Vol. 48, No. 6, pp. 1107-1116, 2005.
4. Kole, M. and Dey, T., “Effect of Aggregation on The Viscosity of Copper Oxide–Gear Oil Nanofluids”, International Journal of Thermal Sciences, Vol. 50, No. 9, pp. 1741-1747, 2011.
5. Rahimi-Gorji, M., Pourmehran, O., Gorji-Bandpy, M. and Ganji, D., “An Analytical Investigation on Unsteady Motion of Vertically Falling Spherical Particles in Non-Newtonian Fluid by Collocation Method”, Ain Shams Engineering Journal, Vol. 6, No. 2, pp. 531-540, 2015.
6. Pourmehran, O., Rahimi-Gorji, M., Gorji-Bandpy, M. and Ganji, D., “Analytical Investigation of Squeezing Unsteady Nanofluid Flow Between Parallel Plates by LSM and CM”, Alexandria Engineering Journal, Vol. 54, No. 1, pp. 17-26, 2015.
7. Mehrjou, B., Heris, S. Z. and Mohamadifard, K., “Experimental Study of Cuo/Water Nanofluid Turbulent Convective Heat Transfer in Square Cross-Section Duct”, Experimental Heat Transfer, Vol. 28, No. 3, pp. 282-297, 2015.
8. Nazari, M., Ashouri, M., Kayhani, M. H. and Tamayol, A., “Experimental Study of Convective Heat Transfer of a Nanofluid Through a Pipe Filled with Metal Foam”, International Journal of Thermal Sciences, Vol. 88, pp. 33-39, 2015.
9. Corcione, M., Cianfrini, M. and Quintino, A., “Enhanced Natural Convection Heat Transfer of Nanofluids in Enclosures with Two Adjacent Walls Heated and the Two Opposite Walls Cooled”, International Journal of Heat and Mass Transfer, Vol. 88, pp. 902-913, 2015.
10. Bahremand, H., Abbassi, A. and Saffar-Avval, M., “Experimental and Numerical Investigation of Turbulent Nanofluid Flow in Helically Coiled Tubes Under Constant Wall Heat Flux Using Eulerian–Lagrangian Approach”, Powder Technology, Vol. 269, pp. 93-100, 2015.
11. Hatami, M., Sheikholeslami, M. and Ganji, D., “Laminar Flow and Heat Transfer of Nanofluid Between Contracting and Rotating Disks by Least Square Method”, Powder Technology, Vol. 253, pp. 769-779, 2014.
12. Sheikholeslami, M., Gorji-Bandpy, M. and Vajravelu, K., “Lattice Boltzmann Simulation of Magnetohydrodynamic Natural Convection Heat Transfer of Al2O3–Water Nanofluid in a Horizontal Cylindrical Enclosure with an Inner Triangular Cylinder”, International Journal of Heat and Mass Transfer, Vol. 80, pp. 16-25, 2015.
13. Sheikholeslami, M. and Ellahi, R., “Three Dimensional Mesoscopic Simulation of Magnetic Field Effect on Natural Convection of Nanofluid”, International Journal of Heat and Mass Transfer, Vol. 89, pp. 799-808, 2015.
14. Sheikholeslami, M., Gorji-Bandpy, M., Ganji, D. and Soleimani, S., “MHD Natural Convection in a Nanofluid Filled Inclined Enclosure with Sinusoidal Wall Using CVFEM”, Neural Computing and Applications, Vol. 24, No. 3-4, pp. 873-882, 2014.
15. Sheikholeslami, M., Gorji-Bandpay, M. and Ganji, D., “Magnetic Field Effects on Natural Convection Around a Horizontal Circular Cylinder Inside a Square Enclosure Filled with Nanofluid”, International Communications in Heat and Mass Transfer, Vol. 39, No. 7, pp. 978-986, 2012.
16. Sheikholeslami, M., Rashidi, M. and Ganji, D., "Effect of Non-Uniform Magnetic Field on Forced Convection Heat Transfer of Fe3O4–Water Nanofluid”, Computer Methods in Applied Mechanics and Engineering, Vol. 294, pp. 299-312, 2015.
17. Sheikholeslami, M. and Rashidi, M., “Ferrofluid Heat Transfer Treatment in the Presence of Variable Magnetic Field”, The European Physical Journal Plus, Vol. 130, No. 6, p. 115, 2015.
18. Sheikholeslami, M. and Rashidi, M. M., “Effect of Space Dependent Magnetic Field on Free Convection of Fe3O4–Water Nanofluid”, Journal of the Taiwan Institute of Chemical Engineers, Vol. 56, pp. 6-15, 2015.
19. Sheikholeslami, M. and Ganji, D., “Entropy Generation of Nanofluid in Presence of Magnetic Field using Lattice Boltzmann Method”, Physica A: Statistical Mechanics and Its Applications, Vol. 417, pp. 273-286, 2015.
20. Chen, S. and Doolen, G. D., “Lattice Boltzmann Method for Fluid Flows”, Annual Review of Fluid Mechanics, Vol. 30, No. 1, pp. 329-364, 1998.
21. Xuan, Y., Yu, K. and Li, Q., “Investigation on Flow and Heat Transfer of Nanofluids by the Thermal Lattice Boltzmann Model”, Progress in Computational Fluid Dynamics, an International Journal, Vol. 5, No. 1-2, pp. 13-19 , 2004.
22. Guo, Y., Qin, D., Shen, S. and Bennacer, R., “Nanofluid Multi-Phase Convective Heat Transfer in Closed Domain: Simulation with Lattice Boltzmann Method", International Communications in Heat and Mass Transfer, Vol. 39, No. 3, pp. 350-354, 2012.
23. Mliki, B., Abbassi, M. A. and Omri, A., Zeghmati, B., “Effects of Nanoparticles Brownian Motion in a Linearly/Sinusoidally Heated Cavity with MHD Natural Convection in the Presence of Uniform Heat Generation/Absorption”, Powder Technology, Vol. 295, pp. 69-83, 2016.
24. Qi, C., Liang, L. and Rao, Z., “Study on the Flow and Heat Transfer of Liquid Metal Based Nanofluid with Different Nanoparticle Radiuses using Two-Phase Lattice Boltzmann Method", International Journal of Heat and Mass Transfer, Vol. 94, pp. 316-326, 2016.
25. Garoosi, F. and Talebi, F., “Numerical Analysis of Conjugate Natural and Mixed Convection Heat Transfer of Nanofluids in a Square Cavity using the Two-Phase Method”, Advanced Powder Technology, Vol. 28, No. 7, pp. 1668-1695, 2017.
26. Sheikholeslami, M., Hayat, T. and Alsaedi, A., “Numerical Simulation for Forced Convection Flow of MHD Cuo-H2O Nanofluid Inside a Cavity by Means of LBM”, Journal of Molecular Liquids, Vol. 249, pp. 941-948, 2018.
27. Bondareva, N. S., Sheremet, M. A., Oztop, H. F. and Abu-Hamdeh, N., “Free Convection in an Open Triangular Cavity Filled with a Nanofluid Under the Effects of Brownian Diffusion, Thermophoresis and Local Heater”, Journal of Heat Transfer, Vol. 140, No. 4, pp. 042502(1)-042502(12), 2018.
28. Li, A. and Ahmadi, G., “Dispersion and Deposition of Spherical Particles From Point Sources in a Turbulent Channel Flow”, Aerosol Science and Technology, Vol. 16, No. 4, pp. 209-226, 1992.
29. Sheikholeslami, M., Gorji-Bandpy, M. and Ganji, D., “Investigation of Nanofluid Flow and Heat Transfer in Presence of Magnetic Field using KKL Model", Arabian Journal for Science and Engineering, Vol. 39, No. 6, pp. 5007-5016, 2014.
30. Xuan, Y. and Roetzel, W., “Conceptions for Heat Transfer Correlation of Nanofluids”, International Journal of Heat and Mass Transfer, Vol. 43, No. 19, pp. 3701-3707 , 2000.
31. Krieger, I. M. and Dougherty, T. J., “A Mechanism For Non‐Newtonian Flow in Suspensions of Rigid Spheres”, Transactions of the Society of Rheology, Vol. 3, No. 1, pp. 137-152, 1959.
32. Thomas, D. G., “Transport Characteristics of Suspension: VIII. a Note on the Viscosity of Newtonian Suspensions of Uniform Spherical Particles”, Journal of Colloid Science, Vol. 20, No. 3, pp. 267-277, 1965.
33. Eastman, J. A., Phillpot, S., Choi, S. and Keblinski, P., “Thermal Transport in Nanofluids”, Annual Review of Materials Research, Vol. 34, pp. 219-246, 2004.
34. Oztop, H. F. and Abu-Nada, E., “Numerical Study of Natural Convection in Partially Heated Rectangular Enclosures Filled with Nanofluids”, International Journal of Heat and Fluid Flow, Vol. 29, No. 5, pp. 1326-1336, 2008.
35. Krane, R., “Some Detailed Field Measurements for a Natural Convection Flow in a Vertical Square Enclosure", Proceedings of the First ASME-JSME Thermal Engineering Joint Conference, Vol. 1, pp. 323-329, 1983.
36. Khanafer, K., Vafai, K. and Lightstone, M., “Buoyancy-Driven Heat Transfer Enhancement in a Two-Dimensional Enclosure Utilizing Nanofluids”, International Journal of Heat and Mass Transfer, Vol. 46, No. 19, pp. 3639-3653, 2003.
2. Wang, B.-X., Zhou, L.-P. and Peng, X.-F., “A Fractal Model for Predicting the Effective Thermal Conductivity of Liquid with Suspension of Nanoparticles”, International Journal of Heat and Mass Transfer, Vol. 46, No. 14, pp. 2665-2672, 2003.
3. Yang, Y., Zhang, Z. G., Grulke, E. A., Anderson, W. B. and Wu, G., “Heat Transfer Properties of Nanoparticle-in-Fluid Dispersions (Nanofluids) in Laminar Flow”, International Journal of Heat and Mass Transfer, Vol. 48, No. 6, pp. 1107-1116, 2005.
4. Kole, M. and Dey, T., “Effect of Aggregation on The Viscosity of Copper Oxide–Gear Oil Nanofluids”, International Journal of Thermal Sciences, Vol. 50, No. 9, pp. 1741-1747, 2011.
5. Rahimi-Gorji, M., Pourmehran, O., Gorji-Bandpy, M. and Ganji, D., “An Analytical Investigation on Unsteady Motion of Vertically Falling Spherical Particles in Non-Newtonian Fluid by Collocation Method”, Ain Shams Engineering Journal, Vol. 6, No. 2, pp. 531-540, 2015.
6. Pourmehran, O., Rahimi-Gorji, M., Gorji-Bandpy, M. and Ganji, D., “Analytical Investigation of Squeezing Unsteady Nanofluid Flow Between Parallel Plates by LSM and CM”, Alexandria Engineering Journal, Vol. 54, No. 1, pp. 17-26, 2015.
7. Mehrjou, B., Heris, S. Z. and Mohamadifard, K., “Experimental Study of Cuo/Water Nanofluid Turbulent Convective Heat Transfer in Square Cross-Section Duct”, Experimental Heat Transfer, Vol. 28, No. 3, pp. 282-297, 2015.
8. Nazari, M., Ashouri, M., Kayhani, M. H. and Tamayol, A., “Experimental Study of Convective Heat Transfer of a Nanofluid Through a Pipe Filled with Metal Foam”, International Journal of Thermal Sciences, Vol. 88, pp. 33-39, 2015.
9. Corcione, M., Cianfrini, M. and Quintino, A., “Enhanced Natural Convection Heat Transfer of Nanofluids in Enclosures with Two Adjacent Walls Heated and the Two Opposite Walls Cooled”, International Journal of Heat and Mass Transfer, Vol. 88, pp. 902-913, 2015.
10. Bahremand, H., Abbassi, A. and Saffar-Avval, M., “Experimental and Numerical Investigation of Turbulent Nanofluid Flow in Helically Coiled Tubes Under Constant Wall Heat Flux Using Eulerian–Lagrangian Approach”, Powder Technology, Vol. 269, pp. 93-100, 2015.
11. Hatami, M., Sheikholeslami, M. and Ganji, D., “Laminar Flow and Heat Transfer of Nanofluid Between Contracting and Rotating Disks by Least Square Method”, Powder Technology, Vol. 253, pp. 769-779, 2014.
12. Sheikholeslami, M., Gorji-Bandpy, M. and Vajravelu, K., “Lattice Boltzmann Simulation of Magnetohydrodynamic Natural Convection Heat Transfer of Al2O3–Water Nanofluid in a Horizontal Cylindrical Enclosure with an Inner Triangular Cylinder”, International Journal of Heat and Mass Transfer, Vol. 80, pp. 16-25, 2015.
13. Sheikholeslami, M. and Ellahi, R., “Three Dimensional Mesoscopic Simulation of Magnetic Field Effect on Natural Convection of Nanofluid”, International Journal of Heat and Mass Transfer, Vol. 89, pp. 799-808, 2015.
14. Sheikholeslami, M., Gorji-Bandpy, M., Ganji, D. and Soleimani, S., “MHD Natural Convection in a Nanofluid Filled Inclined Enclosure with Sinusoidal Wall Using CVFEM”, Neural Computing and Applications, Vol. 24, No. 3-4, pp. 873-882, 2014.
15. Sheikholeslami, M., Gorji-Bandpay, M. and Ganji, D., “Magnetic Field Effects on Natural Convection Around a Horizontal Circular Cylinder Inside a Square Enclosure Filled with Nanofluid”, International Communications in Heat and Mass Transfer, Vol. 39, No. 7, pp. 978-986, 2012.
16. Sheikholeslami, M., Rashidi, M. and Ganji, D., "Effect of Non-Uniform Magnetic Field on Forced Convection Heat Transfer of Fe3O4–Water Nanofluid”, Computer Methods in Applied Mechanics and Engineering, Vol. 294, pp. 299-312, 2015.
17. Sheikholeslami, M. and Rashidi, M., “Ferrofluid Heat Transfer Treatment in the Presence of Variable Magnetic Field”, The European Physical Journal Plus, Vol. 130, No. 6, p. 115, 2015.
18. Sheikholeslami, M. and Rashidi, M. M., “Effect of Space Dependent Magnetic Field on Free Convection of Fe3O4–Water Nanofluid”, Journal of the Taiwan Institute of Chemical Engineers, Vol. 56, pp. 6-15, 2015.
19. Sheikholeslami, M. and Ganji, D., “Entropy Generation of Nanofluid in Presence of Magnetic Field using Lattice Boltzmann Method”, Physica A: Statistical Mechanics and Its Applications, Vol. 417, pp. 273-286, 2015.
20. Chen, S. and Doolen, G. D., “Lattice Boltzmann Method for Fluid Flows”, Annual Review of Fluid Mechanics, Vol. 30, No. 1, pp. 329-364, 1998.
21. Xuan, Y., Yu, K. and Li, Q., “Investigation on Flow and Heat Transfer of Nanofluids by the Thermal Lattice Boltzmann Model”, Progress in Computational Fluid Dynamics, an International Journal, Vol. 5, No. 1-2, pp. 13-19 , 2004.
22. Guo, Y., Qin, D., Shen, S. and Bennacer, R., “Nanofluid Multi-Phase Convective Heat Transfer in Closed Domain: Simulation with Lattice Boltzmann Method", International Communications in Heat and Mass Transfer, Vol. 39, No. 3, pp. 350-354, 2012.
23. Mliki, B., Abbassi, M. A. and Omri, A., Zeghmati, B., “Effects of Nanoparticles Brownian Motion in a Linearly/Sinusoidally Heated Cavity with MHD Natural Convection in the Presence of Uniform Heat Generation/Absorption”, Powder Technology, Vol. 295, pp. 69-83, 2016.
24. Qi, C., Liang, L. and Rao, Z., “Study on the Flow and Heat Transfer of Liquid Metal Based Nanofluid with Different Nanoparticle Radiuses using Two-Phase Lattice Boltzmann Method", International Journal of Heat and Mass Transfer, Vol. 94, pp. 316-326, 2016.
25. Garoosi, F. and Talebi, F., “Numerical Analysis of Conjugate Natural and Mixed Convection Heat Transfer of Nanofluids in a Square Cavity using the Two-Phase Method”, Advanced Powder Technology, Vol. 28, No. 7, pp. 1668-1695, 2017.
26. Sheikholeslami, M., Hayat, T. and Alsaedi, A., “Numerical Simulation for Forced Convection Flow of MHD Cuo-H2O Nanofluid Inside a Cavity by Means of LBM”, Journal of Molecular Liquids, Vol. 249, pp. 941-948, 2018.
27. Bondareva, N. S., Sheremet, M. A., Oztop, H. F. and Abu-Hamdeh, N., “Free Convection in an Open Triangular Cavity Filled with a Nanofluid Under the Effects of Brownian Diffusion, Thermophoresis and Local Heater”, Journal of Heat Transfer, Vol. 140, No. 4, pp. 042502(1)-042502(12), 2018.
28. Li, A. and Ahmadi, G., “Dispersion and Deposition of Spherical Particles From Point Sources in a Turbulent Channel Flow”, Aerosol Science and Technology, Vol. 16, No. 4, pp. 209-226, 1992.
29. Sheikholeslami, M., Gorji-Bandpy, M. and Ganji, D., “Investigation of Nanofluid Flow and Heat Transfer in Presence of Magnetic Field using KKL Model", Arabian Journal for Science and Engineering, Vol. 39, No. 6, pp. 5007-5016, 2014.
30. Xuan, Y. and Roetzel, W., “Conceptions for Heat Transfer Correlation of Nanofluids”, International Journal of Heat and Mass Transfer, Vol. 43, No. 19, pp. 3701-3707 , 2000.
31. Krieger, I. M. and Dougherty, T. J., “A Mechanism For Non‐Newtonian Flow in Suspensions of Rigid Spheres”, Transactions of the Society of Rheology, Vol. 3, No. 1, pp. 137-152, 1959.
32. Thomas, D. G., “Transport Characteristics of Suspension: VIII. a Note on the Viscosity of Newtonian Suspensions of Uniform Spherical Particles”, Journal of Colloid Science, Vol. 20, No. 3, pp. 267-277, 1965.
33. Eastman, J. A., Phillpot, S., Choi, S. and Keblinski, P., “Thermal Transport in Nanofluids”, Annual Review of Materials Research, Vol. 34, pp. 219-246, 2004.
34. Oztop, H. F. and Abu-Nada, E., “Numerical Study of Natural Convection in Partially Heated Rectangular Enclosures Filled with Nanofluids”, International Journal of Heat and Fluid Flow, Vol. 29, No. 5, pp. 1326-1336, 2008.
35. Krane, R., “Some Detailed Field Measurements for a Natural Convection Flow in a Vertical Square Enclosure", Proceedings of the First ASME-JSME Thermal Engineering Joint Conference, Vol. 1, pp. 323-329, 1983.
36. Khanafer, K., Vafai, K. and Lightstone, M., “Buoyancy-Driven Heat Transfer Enhancement in a Two-Dimensional Enclosure Utilizing Nanofluids”, International Journal of Heat and Mass Transfer, Vol. 46, No. 19, pp. 3639-3653, 2003.
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