The Effect of Magnetic Field and Nanoparticle Shape on Heat Transfer in an Inclined Cavity with Uniform Heat Generation/Absorption
Authors
Abstract
In the present work, the effect of magnetic field, changes in the angle of inclination of the cavity and the shape of nanoparticles on the flow field and heat transfer of water-alumina with uniform heat generation/absorption is investigated by Lattice Boltzmann method (LBM). The curved wall and the diagonal walls of the cavity are at a constant temperature of hot and cold, respectively. Nanoparticle volume fraction of 0, 0.02 and 0.04, Hartmann number of 0, 15, 30, 45 and 60, heat generation/absorption coefficient of -5, 0 and +5 and inclination angle of 45, 135 and 225 degrees are studied. The high accuracy of the results compared to previous studies confirmed the correctness of the code written in Fortran language. The results shows that in all cases, increasing the Hartmann number leads to a decrease in the maximum value of the streamlines and the average Nusselt number, with the lowest effect at 225 degrees. Also increasing the strength of the magnetic field leads to an average decrease of 28, 23 and 7% of the average Nusselt number for angles of 45, 135 and 225 degrees, respectively. Increasing the heat generation/absorption coefficient is a determining factor in the effectiveness of the magnetic field and adding nanoparticles, and increasing it reduces the amount of heat transfer. On average, heat generation reduces the average Nusselt number by 71, 98, and 145 percent for the angles of 45, 135, and 225 degrees, respectively. In general, the lowest value of the average Nusselt number is related to the angle of 225 degrees, but the effect of adding nanoparticles in increasing the average Nusselt number is the highest at this angle. Generally, an increase in the percentage of nanoparticles leads to an average increase of 12% in the average Nusselt number. The effect of nanoparticle shape is more apparent with increasing their volume fraction. The highest amount of heat transfer is related to the cylindrical nanoparticles, in which the average Nusselt number is on average about 6% higher than the spherical state.
Keywords
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5. Ajay, C., and Srinivasa, A., “Unsteady MHD Natural Convective Boundary Layer Flow and Heat Transfer Over a Truncated Cone in the Presence of Pressure Work”," Journal of Applied Mathematics and Computational Mechanics, Vol. 19, pp. 5-16, 2020.
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11. Mahmoudi, A., Mejri, I., Abbassi, M. A., and Omri, A., “Analysis of MHD Natural Convection In A Nanofluid-Filled Open Cavity with Non Uniform Boundary Condition in the Presence of Uniform Heat Generation/Absorption”, Powder Technology, Vol. 269, pp. 275-289, 2015.
12. Mliki, B., Abbassi, M. A., Omri, A., and Zeghmati, B., “Augmentation of Natural Convective Heat Transfer in Linearly Heated Cavity by Utilizing Nanofluids in the Presence of Magnetic Field and Uniform Heat Generation/Absorption”, Powder Technology, Vol. 284, pp. 312-325, 2015.
13. Nemati, M., Sefid, M., and Rahmati, A. R., “Analysis of the Effect of Periodic Magnetic Field, Heat Absorption/Generation and Aspect Ratio of the Enclosure on Non-Newtonian Natural Convection”, Journal of Heat and Mass Transfer Research, Vol. 8, pp. 187-203, 2021.
14. Abu-Nada, E., and Oztop, H. F., “Effects of Inclination Angle on Natural Convection in Enclosures Filled with Cu–Water Nanofluid”, International Journal of Heat and Fluid Flow, Vol. 30, pp. 669-678, 2009.
15. Nemati, M., Mohamadzade, H., and Chamkha, A. J., “Optimal Wall Natural Convection for a Non-Newtonian Fluid with Heat Generation/Absorption and Magnetic Field in a Quarter-Oval Inclined Cavity”, Physica Scripta. Vol. 96, pp. 1252-1269, 2021.
16. Nemati, M.,and Sefid., “Using Multiple Relaxation Time Lattice Boltzmann Method to Simulate Power-Law Fluids MHD Natural Convection in Cavity with Lozenge Barrier”, Journal of Fluid Mechanics and Aerodynamics. Vol. 10, pp. 17-35, 2021.
17. Rahmati, A. R., and Hajzaman, R., “Numerical Study of Natural Convection Heat Transfer of Nanofluid in a Square Shaped Porous Media using Lattice Boltzmann Method”, Journal of Computational Methods in Engineering, Vol. 35, pp. 47-64, 2017.
18. Qi, C., Tang, J., and Wang, G., “Natural Convection of Composite Nanofluids Based on a Two-Phase Lattice Boltzmann Model”, Journal of Thermal Analysis and Calorimetry, pp. 1-11, 2020.
19. Mohamad, A. A., Lattice Boltzmann Method: Fundamentals and Engineering Applications with Computer Codes, Springer Science & Business Media, 2011.
20. Bhatnagar, P. L., Gross, E. P., and Krook, M., “A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems”, Physical Review, Vol 94, pp. 511-525, 1954.
21. Fu, C., Rahmani, A., Suksatan, W., Alizadeh, S. M., Zarringhalam, M., Chupradit, S., Toghraie, D., “Comprehensive Investigations of Mixed Convection of Fe–ethylene-glycol Nanofluid Inside an Enclosure with Different Obstacles Using Lattice Boltzmann Method”,Scientific Reports. Vol. 11, pp. 1-16, 2021.
22. Nemati, M., Mohamadzade, H. and Sefid, M., “Investigation the Effect of Direction of Wall Movement on Mixed Convection in Porous Enclosure with Heat Absorption/Generation and Magnetic Field”, Fluid Mechanics & Aerodynamics Journal, Vol. 9, No. 1, pp. 99-115, 2020.
23. Sathiyamoorthy, M., and Chamkha, A., “Effect of Magnetic Field on Natural Convection Flow in a Liquid Gallium Filled Square Cavity for Linearly Heated Side Wall (S)”, International Journal of Thermal Sciences, Vol. 49, pp. 1856-1865, 2010.
24. Sayehvand, H., Habibzadeh, A., and Mekanik, A., “CFD Analysis of Natural Convection Heat Transfer in a Square Cavity with Partitions Utilizing Al2O3 Nanofluid”, Powder Technology, Vol. 259, pp. 275-289, 2012.
25. Shahriari, A., and Ashorynejad, H. R., “Numerical Study of Heat Transfer and Entropy Generation of Rayleigh–Bَenard Convection Nanofluid in Wavy Cavity with Magnetic Field”, Modares Mechanical Engineering, Vol. 17, pp. 385-396, 2017.
26. Vo, D. D., Hedayat, M., Ambreen, T., Shehzad, S. A., Sheikholeslami, M., Shafee, A., and Nguyen, T. K., “Effectiveness of Various Shapes of Al2O3 Nanoparticles on The MHD Convective Heat Transportation in Porous Medium”, Journal of Thermal Analysis and Calorimetry, Vol. 139, pp. 1345-1353, 2020.
27. Chamkha, A. J., and Aly, A., “MHD Free Convection Flow of a Nanofluid Past a Vertical Plate in the Presence of Heat Generation or Absorption Effects”, Chemical Engineering Communications, Vol. 198, pp. 425-441, 2010.
2. Patel, H. E., Das, S. K., Sundararajan, T., Sreekumaran Nair, A., George, B., and Pradeep, T., “Thermal Conductivities of Naked and Monolayer Protected Metal Nanoparticle Based Nanofluids: Manifestation of Anomalous Enhancement and Chemical Effects”, Applied Physics Letters, Vol. 83, pp. 2931-2933, 2003.
3. Sheikhzadeh, G. A., Aghaei, A., and Soleimani, S., “Effect of Nanoparticle Shape on Natural Convection Heat Transfer in a Square Cavity with Partitions Using Water-Sio2 Nanofluid”, Transport Phenomena in Nano and Micro Scales, Vol. 6, pp. 27-38, 2018.
4. Gireesh, B., and Sindhu, S., “MHD Natural Convection Flow of Casson Fluid in an Annular Microchannel Containing Porous Medium with Heat Generation/Absorption”, Nonlinear Engineering, Vol. 9, pp. 223-232, 2020.
5. Ajay, C., and Srinivasa, A., “Unsteady MHD Natural Convective Boundary Layer Flow and Heat Transfer Over a Truncated Cone in the Presence of Pressure Work”," Journal of Applied Mathematics and Computational Mechanics, Vol. 19, pp. 5-16, 2020.
6. Aly, A. M., and Raizah, Z., “Incompressible Smoothed Particle Hydrodynamics Simulation of Natural Convection in a Nanofluid-Filled Complex Wavy Porous Cavity with Inner Solid Particles”, Physica A: Statistical Mechanics and Its Applications, Vol. 537, pp. 122-132, 2020.
7. Dogonchi, A., Tayebi, T., Chamkha, A. J., and Ganji, D., “Natural Convection Analysis in a Square Enclosure with a Wavy Circular Heater Under Magnetic Field and Nanoparticles”, Journal of Thermal Analysis and Calorimetry, Vol. 139, pp. 661-671, 2020.
8. Ma, Y., Mohebbi, R., Rashidi, M., Yang, Z., and Sheremet, M. A., “Numerical Study of MHD Nanofluid Natural Convection in a Baffled U-Shaped Enclosure”, International Journal of Heat and Mass Transfer, Vol. 130, pp. 123-134, 2019.
9. Jami, M., Mezrhab, A., Bouzidi, M. H., and Lallemand, P., “Lattice Boltzmann Method Applied to the Laminar Natural Convection in an Enclosure with a Heat-Generating Cylinder Conducting Body”,International Journal of Thermal Sciences, Vol. 46, pp. 38-47, 2007.
10. Mliki, B., Abbassi, M. A., Omri, A., and 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.
11. Mahmoudi, A., Mejri, I., Abbassi, M. A., and Omri, A., “Analysis of MHD Natural Convection In A Nanofluid-Filled Open Cavity with Non Uniform Boundary Condition in the Presence of Uniform Heat Generation/Absorption”, Powder Technology, Vol. 269, pp. 275-289, 2015.
12. Mliki, B., Abbassi, M. A., Omri, A., and Zeghmati, B., “Augmentation of Natural Convective Heat Transfer in Linearly Heated Cavity by Utilizing Nanofluids in the Presence of Magnetic Field and Uniform Heat Generation/Absorption”, Powder Technology, Vol. 284, pp. 312-325, 2015.
13. Nemati, M., Sefid, M., and Rahmati, A. R., “Analysis of the Effect of Periodic Magnetic Field, Heat Absorption/Generation and Aspect Ratio of the Enclosure on Non-Newtonian Natural Convection”, Journal of Heat and Mass Transfer Research, Vol. 8, pp. 187-203, 2021.
14. Abu-Nada, E., and Oztop, H. F., “Effects of Inclination Angle on Natural Convection in Enclosures Filled with Cu–Water Nanofluid”, International Journal of Heat and Fluid Flow, Vol. 30, pp. 669-678, 2009.
15. Nemati, M., Mohamadzade, H., and Chamkha, A. J., “Optimal Wall Natural Convection for a Non-Newtonian Fluid with Heat Generation/Absorption and Magnetic Field in a Quarter-Oval Inclined Cavity”, Physica Scripta. Vol. 96, pp. 1252-1269, 2021.
16. Nemati, M.,and Sefid., “Using Multiple Relaxation Time Lattice Boltzmann Method to Simulate Power-Law Fluids MHD Natural Convection in Cavity with Lozenge Barrier”, Journal of Fluid Mechanics and Aerodynamics. Vol. 10, pp. 17-35, 2021.
17. Rahmati, A. R., and Hajzaman, R., “Numerical Study of Natural Convection Heat Transfer of Nanofluid in a Square Shaped Porous Media using Lattice Boltzmann Method”, Journal of Computational Methods in Engineering, Vol. 35, pp. 47-64, 2017.
18. Qi, C., Tang, J., and Wang, G., “Natural Convection of Composite Nanofluids Based on a Two-Phase Lattice Boltzmann Model”, Journal of Thermal Analysis and Calorimetry, pp. 1-11, 2020.
19. Mohamad, A. A., Lattice Boltzmann Method: Fundamentals and Engineering Applications with Computer Codes, Springer Science & Business Media, 2011.
20. Bhatnagar, P. L., Gross, E. P., and Krook, M., “A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems”, Physical Review, Vol 94, pp. 511-525, 1954.
21. Fu, C., Rahmani, A., Suksatan, W., Alizadeh, S. M., Zarringhalam, M., Chupradit, S., Toghraie, D., “Comprehensive Investigations of Mixed Convection of Fe–ethylene-glycol Nanofluid Inside an Enclosure with Different Obstacles Using Lattice Boltzmann Method”,Scientific Reports. Vol. 11, pp. 1-16, 2021.
22. Nemati, M., Mohamadzade, H. and Sefid, M., “Investigation the Effect of Direction of Wall Movement on Mixed Convection in Porous Enclosure with Heat Absorption/Generation and Magnetic Field”, Fluid Mechanics & Aerodynamics Journal, Vol. 9, No. 1, pp. 99-115, 2020.
23. Sathiyamoorthy, M., and Chamkha, A., “Effect of Magnetic Field on Natural Convection Flow in a Liquid Gallium Filled Square Cavity for Linearly Heated Side Wall (S)”, International Journal of Thermal Sciences, Vol. 49, pp. 1856-1865, 2010.
24. Sayehvand, H., Habibzadeh, A., and Mekanik, A., “CFD Analysis of Natural Convection Heat Transfer in a Square Cavity with Partitions Utilizing Al2O3 Nanofluid”, Powder Technology, Vol. 259, pp. 275-289, 2012.
25. Shahriari, A., and Ashorynejad, H. R., “Numerical Study of Heat Transfer and Entropy Generation of Rayleigh–Bَenard Convection Nanofluid in Wavy Cavity with Magnetic Field”, Modares Mechanical Engineering, Vol. 17, pp. 385-396, 2017.
26. Vo, D. D., Hedayat, M., Ambreen, T., Shehzad, S. A., Sheikholeslami, M., Shafee, A., and Nguyen, T. K., “Effectiveness of Various Shapes of Al2O3 Nanoparticles on The MHD Convective Heat Transportation in Porous Medium”, Journal of Thermal Analysis and Calorimetry, Vol. 139, pp. 1345-1353, 2020.
27. Chamkha, A. J., and Aly, A., “MHD Free Convection Flow of a Nanofluid Past a Vertical Plate in the Presence of Heat Generation or Absorption Effects”, Chemical Engineering Communications, Vol. 198, pp. 425-441, 2010.
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