MHD Convection of an Al2O3–Cu/Water Hybrid Nanofluid in an Inclined Porous Cavity with Internal Heat Generation/Absorption

Document Type : Research Article


1 Institute of Research and Development, Duy Tan University, Da Nang 550000, VIETNAM

2 Institute of Theoretical and Applied Research (ITAR), Duy Tan University, Hanoi 100000, VIETNAM

3 Department of Engineering, West Tehran Branch, Islamic Azad University, Tehran, IRAN

4 Department of Mathematics, Aswan University, Faculty of Science, Aswan, 81528, EGYPT

5 Energy and Sustainable Development Research Center, Semnan Branch, Islamic Azad University, Semnan, I.R. IRAN


In Present communication, the transference of the hybrid nanofluids due to the natural propulsive like shrinkage and relaxation of the flexible walls and the motion has serious applications in several embryonic technologies. Stimulated by the multi-disciplinary development and study of this trend, a mathematical model is suggested to explore the numerical simulation of the hybrid nanofluid flow inside a slant porous cavity to determine the impact of volume fraction, Rayleigh number, heat generation and heat source length, and location on magneto-free convective with entropy analysis. The governing nonlinear problem is converted into non-dimensional partial equations via suitably adjusted transformations. The Successive Under-Relaxation (SUR) technique has been incorporated to find solutions to the non-linear problem. Variation in entropy generation and heat transfer characteristics and thermal performance criteria has been noted for various fluid parameters.  The results are plotted graphically. The outcomes indicate that the thermal performance reduces more in the case of high volume fraction in comparison with low concentration. The addition of nanoparticles for several Rayleigh numbers causes the thermal performance to be declined.


Main Subjects

[2] Yang R.-J., Hou H.-H., Wang Y.-N., Fu L.-M., Micro-Magnetofluidics in Microfluidic Systems: A Review, Sensors Actuators B Chem. 224: 1–15 (2016).
[4] Choi S.U.S., Eastman J.A., "Enhancing Thermal Conductivity of Fluids with Nanoparticles”, Argonne National Lab., IL (United States) (1995).
[5] Jani H.K., Modi K. V, A Review on Numerous Means of Enhancing Heat Transfer Rate in Solar- Thermal Based Desalination Devices, Renew. Sustain. Energy Rev., 93: 302–317 (2018).
[6] Falsafi M., Kargarsharifabad H., Numerical Study of Ferrofluid Forced Convection Heat Transfer in Tube with Magnetic Field, Iut- Jcme, 34(1): 11–25 (2015).
[7] Sheikholeslami M., Gorji-Bandpy M., Free Convection of Ferro Fluid in a Cavity Heated from below in the Presence of an External Magnetic Field, Powder Technol., 256: 490–498 (2014).
[8] Jafari A., Shahmohammadi A., Mousavi S. CFD Investigation of Gravitational Sedimentation Effect on Heat Transfer of a Nano-Ferrofluid, Iran. J. Chem. Chem. Eng. (IJCCE), 34(1): 87-96 (2015)
[9] Habibi M., Amini M., Arefmanesh A., Ghasemikafrudi E., Effects of Viscosity Variations on Buoyancy-Driven Flow from a Horizontal Circular Cylinder Immersed in Al2O3-Water Nanofluid, Iran. J. Chem. Chem. Eng. (IJCCE), 38(1):213-232 (2019).
[10] Goodarzi M, Safaei MR, Vafai K, Ahmadi G, Dahari M, Kazi SN, Jomhari N., Investigation of Nanofluid Mixed Convection in a Shallow Cavity Using a Two-Phase Mixture Model, Int. J. Therm. Sci., 75:204-220 (2014).
[11] Yousefzadeh, S., Rajabi, H., Ghajari, N., Sarafraz M.M., Akbari O.A., Goodarzi M., Numerical Investigation of Mixed Convection Heat Transfer Behavior of Nanofluid in a Cavity with Different Heat Transfer Areas, J. Therm. Anal. Calorim., 140: 2779–2803 (2020).
[12] Armaghani T., Ismael M.A., Chamkha A.J., Analysis of Entropy Generation and Natural Convection in an Inclined Partially Porous Layered Cavity Filled with a Nanofluid, Can. J. Phys., 95(3): 238–252 (2017).
[14] Sundar L.S., Singh M.K., Sousa A.C.M., Enhanced Heat Transfer and Friction Factor of MWCNT-Fe3O4/Water Hybrid Nanofluids, Int. Commun. Heat Mass Transf., 52: 73–83 (2014).
[15] Suresh S., Venkitaraj K.P.P., Selvakumar P., Chandrasekar M., Effect of Al2O3–Cu/Water Hybrid Nanofluid in Heat Transfer, Exp. Therm. Fluid Sci., 38: 54–60 (2012).
[16] Ranga Babu J.A., Kumar K.K., Srinivasa Rao S., State-of-Art Review on Hybrid Nanofluids, Renew. Sustain. Energy Rev., 77: 551–565 (2017).
[18] Suresh S., Venkitaraj K.P., Selvakumar P., Chandrasekar M., Synthesis of Al2O3-Cu/Water Hybrid Nanofluids Using Two-Step Method and Its Thermo Physical Properties, Colloids Surfaces A Physicochem. Eng. Asp., 388(1–3): 41–48 (2011).
[19] Selvakumar P., Suresh S., Use of Al2O3–Cu/Water Hybrid Nanofluid in an Electronic Heat Sink, IEEE Trans. Compon., Packag., Manuf. Technol., 2(10): 1600–1607 (2012).
[20] Shahsavar A., Saghafian M., Salimpour M.R., Shafii M.B., Experimental Investigation on Laminar Forced Convective Heat Transfer of Ferrofluid Loaded with Carbon Nanotubes under Constant and Alternating Magnetic Fields, Exp. Therm. Fluid Sci., 76: 1–11 (2016).
[21] HAN W.S., Rhi S.H., Thermal Characteristics of Grooved Heat Pipe with Hybrid Nanofluids, Therm. Sci., 15(1): 195–206 (2011).
[22] Sundar L.S., Singh M.K., Sousa A.C.M., Enhanced Heat Transfer and Friction Factor of MWCNT-Fe3O4/Water Hybrid Nanofluids, Int. Commun. Heat Mass Transf., 52: 73–83 (2014).
[23] Sarkar J., Ghosh P., Adil A., A Review on Hybrid Nano Fluids : Recent Research, Development and Applications, Renew. Sustain. Energy Rev., 43: 164–177 (2015).
[24] Mehryan S.A.M., Izadpanahi E., Ghalambaz M., Chamkha A.J., Mixed Convection Flow Caused by an Oscillating Cylinder in a Square Cavity Filled with Cu–Al2O3/Water Hybrid Nanofluid, J. Therm. Anal. Calorim., 137(3): 965–982
[25] Ismael M.A., Armaghani T., Chamkha A.J., Mixed Convection and Entropy Generation in a Lid-Driven Cavity Filled with a Hybrid Nanofluid and Heated by a Triangular Solid, Heat Transf. Res., 49(17): 1645–1665 (2018).
[26] Zhou P., Zhong Y., Wang H., Fan L., Dong L., Li F., Long Q., Zheng T., Behavior of Fe/Nano-Si Particles Composite Electrodeposition with a Vertical Electrode System in a Static Parallel Magnetic Field, Electrochim. Acta., 111: 126–135 (2013).
[27] Mehryan S.A.M., Kashkooli F.M., Ghalambaz M., Chamkha A.J., Free Convection of Hybrid Al2O3-Cu Water Nanofluid in a Differentially Heated Porous Cavity, Adv. Powder Technol., 28(9): 2295–2305 (2017).
[28] Nield D.A., Bejan A., Convection in Porous Media, Springer (2006).
[29] Kaviany M., Principles of Heat Transfer in Porous Media, Springer Science & Business Media (2012).
[30] Siavashi M., Yousofvand R., Rezanejad S., Nanofluid and Porous Fins Effect on Natural Convection and Entropy Generation of Flow Inside a Cavity, Adv. Powder Technol., 29(1): 142–156 (2018).
[31] Leong J.C., Lai F.C., Mixed Convection in a Rotating Concentric Annulus with a Porous Sleeve, J. Thermophys. Heat Transf., 33(2): 483–494 (2019).
[32] Das D., Roy M., Basak T., Studies on Natural Convection within Enclosures of Various (Non-Square) Shapes – A Review, Int. J. Heat Mass Transf., 106: 356–406 (2017).
[33] Muasavi S., Shahnazari M. Investigation of Natural Convection in a Vertical Cavity Filled with an Anisotropic Porous Media, Iran. J. Chem. Chem. Eng. (IJCCE), 27(2):39-45 (2008).
[34] Tong T.W., Subramanian E., Natural Convection in Rectangular Enclosures Partially Filled with a Porous Medium, Int. J. heat fluid flow., 7(1): 3–10 (1986).
[35] Mahdi R.A., Mohammed H.A., Munisamy K.M., Saeid N.H., Review of Convection Heat Transfer and Fluid Flow in Porous Media with Nanofluid, Renew. Sustain. Energy Rev., 41: 715–734 (2015).
[36] Kasaeian A., Azarian R.D., Mahian O., Kolsi L., Chamkha A.J., Wongwises S., Pop I., Nanofluid Flow and Heat Transfer in Porous Media: A Review of the Latest Developments, Int. J. Heat Mass Transf., 107: 778–791 (2017).
[37] Hatami M., Zhou J., Geng J., Song D., Jing D., Optimization of a Lid-Driven T-Shaped Porous Cavity to Improve the Nanofluids Mixed Convection Heat Transfer, J. Mol. Liq., 231: 620–631 (2017).
[38] Selimefendigil F., Ismael M.A., Chamkha A.J., Mixed Convection in Superposed Nanofluid and Porous Layers in Square Enclosure with Inner Rotating Cylinder, Int. J. Mech. Sci., 124125: 95–108 (2017).
[40] Mohebbi R., Mehryan S.A.M., Izadi M., Mahian O., Natural Convection of Hybrid Nanofluids inside a Partitioned Porous Cavity for Application in Solar Power Plants, J. Therm. Anal. Calorim., 137(5): 1719–1733 (2019).
[41] Karimdoost Yasuri A., Izadi M., Hatami H. Numerical Study of Natural Convection in a Square Enclosure Filled by Nanofluid with a Baffle in the Presence of Magnetic Field, Iran. J. Chem. Chem. Eng. (IJCCE), 38(5): 209-220 (2019).
[42] Bahmani A., Kargarsharifabad H., New Integral Solutions for Magnetohydrodynamic Free Convection of Power-Law Fluids Over a Horizontal Plate, Iran. J. Sci. Technol. - Trans. Mech. Eng. Online (2020).
[43] Bahmani A., Kargarsharifabad H., Magnetohydrodynamic Free Convection of Non-Newtonian Power-Law Fluids over a Uniformly Heated Horizontal Plate, Therm. Sci., 24(2B): 1323–1334 (2020).
[45] Gireesha B.J., Shankaralingappa B.M., Prasannakumar B.C., Nagaraja B., MHD Flow and Melting Heat Transfer of Dusty Casson Fluid over a Stretching Sheet with Cattaneo–Christov Heat Flux Model, Int. J. Ambient Energy. Online: 1–9 (2020).
[46] Hajatzadeh Pordanjani A., Aghakhani S., Karimipour A., Afrand M., Goodarzi   M. Investigation of Free Convection Heat Transfer and Entropy Generation of Nanofluid Flow inside a Cavity Affected by Magnetic Field and Thermal Radiation, J. Therm. Anal. Calorim., 137: 997–1019 (2019)
[47] Mahmoudi A.H., Pop I., Shahi M., Talebi F., MHD Natural Convection and Entropy Generation in a Trapezoidal Enclosure Using Cu – Water Nanofluid, Comput. FLUIDS, 72: 46–62 (2013).
[48] Mahmoudi A.H., Abu-Nada E., Combined Effect of Magnetic Field and Nanofluid Variable Properties on Heat Transfer Enhancement in Natural Convection, Numer. Heat Transf. Part A Appl., 63(6): 452–472 (2013).
[49] Mejri I., Mahmoudi A., MHD Natural Convection in a Nanofluid-Filled Open Enclosure with a Sinusoidal Boundary Condition, Chem. Eng. Res. Des., 98: 1–16 (2015).
[50] Aminossadati S.M., Raisi  a., Ghasemi B., Effects of Magnetic Field on Nanofluid Forced Convection in a Partially Heated Microchannel, Int. J. Non. Linear. Mech., 46(10): 1373–1382 (2011).
[51] Rashad A.M., Armaghani T., Chamkha A.J., Mansour M.A., Entropy Generation and MHD Natural Convection of a Nanofluid in an Inclined Square Porous Cavity: Effects of a Heat Sink and Source Size and Location, Chinese J. Phys., 56(1): 193–211 (2018).
[53] Sajjadi H., Delouei A.A., Izadi M., Mohebbi Rjij., Investigation of MHD Natural Convection in a Porous Media by Double MRT Lattice Boltzmann Method Utilizing MWCNT–Fe3O4/Water Hybrid Nanofluid, Int. J. Heat Mass Transf., 132: 1087–1104 (2019).
[54] Izadi M., Maleki N.M., Pop I., Mehryan S.A.M., Natural Convection of a Hybrid Nanofluid Subjected to Non-Uniform Magnetic Field within Porous Medium Including Circular Heater, Int. J. Numer. Methods Heat Fluid Flow., 29(4): 1211–1231 (2019).
[55] Bejan A., A Study of Entropy Generation in Fundamental Convective Heat Transfer, J. Heat Transfer., 101(4): 718 (1979).
[56] Bejan A., Second-Law Analysis in Heat Transfer and Thermal Design, Adv. Heat Transfer., 15: 1-58 (1982).
[59] Berrehal H., Mabood F., Makinde O.D., Entropy-Optimized Radiating Water/FCNTs Nanofluid Boundary-Layer Flow with Convective Condition, Eur. Phys. J. Plus., 135(7): 535 (2020).
[60] Aghaei A., Sheikhzadeh G.A., Goodarzi M., Hasani H., Damirchi H., Afrand M., Effect of Horizontal and Vertical Elliptic Baffles inside an Enclosure on the Mixed Convection of a MWCNTs-Water Nanofluid and its Entropy Generation, Eur. Phys. J. Plus, 133: 486 (2018).
[61] Goodarzi M, Safaei MR, Oztop HF, Karimipour A, Sadeghinezhad E, Dahari M, Kazi SN, Jomhari N. Numerical Study of Entropy Generation Due to Coupled Laminar and Turbulent Mixed Convection and Thermal Radiation in an Enclosure Filled with a Semitransparent Medium, Sci. World J., 2014: 761745 (2014).
[62] Ismael M.A., Armaghani T., Chamkha A.J., Conjugate Heat Transfer and Entropy Generation in a Cavity Filled with a Nanofluid-Saturated Porous Media and Heated by a Triangular Solid, J. Taiwan Inst. Chem. Eng., 59: 138–151 (2016).
[64] Chamkha A.J., Rashad A.M., Mansour M.A., Armaghani T., Ghalambaz M., Effects of Heat Sink and Source and Entropy Generation on MHD Mixed Convection of a Cu-Water Nanofluid in a Lid-Driven Square Porous Enclosure with Partial Slip, Phys. Fluids., 29(5): 52001 (2017).
[65] Chamkha A.J., Rashad A.M., Armaghani T., Mansour M.A., Effects of Partial Slip on Entropy Generation and MHD Combined Convection in a Lid-Driven Porous Enclosure Saturated with a Cu–Water Nanofluid, J. Therm. Anal. Calorim., 132(2): 1291–1306 (2018).
[66] Mansour M.A., Ahmed S.E., Chamkha A.J., Entropy Generation Optimization for MHD Natural Convection of a Nanofluid in Porous Media-Filled Enclosure with Active Parts and Viscous Dissipation, Int. J. Numer. Methods Heat Fluid Flow., 27(2): 379–399 (2017).
[67] Rashad A.M., Armaghani T., Chamkha A.J., Mansour M.A., Entropy Generation and MHD Natural Convection of a Nanofluid in an Inclined Square Porous Cavity: Effects of a Heat Sink and Source Size and Location, Chinese J. Phys., 56(1): 193–211 (2018).
[68] Sheikholeslami M., Hatami M., Ganji D.D., Numerical Investigation of Nanofluid Spraying on an Inclined Rotating Disk for Cooling Process, J. Mol. Liq., 211: 577–583 (2015).
[69] Chamkha A.J., Mansour M.A., Rashad A.M., Kargarsharifabad H., Armaghani T., Magnetohydrodynamic Mixed Convection and Entropy Analysis of Nanofluid in Gamma-Shaped Porous Cavity, J. Thermophys. Heat Transf., 34(4): 836–847 (2020).
[70] Prasad V., Kulacki F.A., Keyhani M., Natural Convection in Porous Media, J. Fluid Mech., 150: 89–119 (1985).
[71] Mahmud S., Fraser R.A., Magnetohydrodynamic Free Convection and Entropy Generation in a Square Porous Cavity, Int. J. Heat Mass Transf., 47(14–16): 3245–3256 (2004).
[72] Ho C.J., Huang J.B., Tsai P.S., Yang Y.M., Preparation and Properties of Hybrid Water-Based Suspension of Al2O3 Nanoparticles and MEPCM Particles as Functional Forced Convection Fluid, Int. Commun. Heat Mass Transf., 37(5): 490–494 (2010).
[73] Khanafer K., Vafai K., Lightstone M., Buoyancy-Driven Heat Transfer Enhancement in a Two-Dimensional Enclosure Utilizing Nanofluids, Int. J. Heat Mass Transf., 46(19): 3639–3653 (2003).
[74] Maxwell J.C., "A Treatise on Electricity and Magnetism", Clarendon Press (1881).
[75] Sheikholeslami M., Bandpy M.G., Ellahi R., Zeeshan A., Simulation of MHD CuO–Water Nanofluid Flow and Convective Heat Transfer Considering Lorentz Forces, J. Magn. Magn. Mater., 369: 69–80 (2014).
[76] Takabi B., Shokouhmand H., Effects of Al2O3–Cu/Water Hybrid Nanofluid on Heat Transfer and Flow Characteristics in Turbulent Regime, Int. J. Mod. Phys., 26(4): 1–25 (2015).
[77] Brinkman H.C., The Viscosity of Concentrated Suspensions and Solutions, J. Chem. Phys., 20(4): 571 (1952).
[78] Pourmehran O., Rahimi-Gorji M., Hatami M., Sahebi S.A.R., Domairry G., Numerical Optimization of Microchannel Heat Sink (MCHS) Performance Cooled by KKL Based Nanofluids in Saturated Porous Medium, J. Taiwan Inst. Chem. Eng., 55: 49–68 (2015).
[80] Goodarzi M, Safaei MR, Karimipour A, Hooman K, Dahari M, Kazi SN, Sadeghinezhad E., Comparison of the Finite Volume and Lattice Boltzmann Methods for Solving Natural Convection Heat Transfer Problems Inside Cavities and Enclosures, Abstr. Appl. Anal., 2014: 762184 (2014)
[82] Dogonchi A.S., Hatami M., Domairry G., Motion Analysis of a Spherical Solid Particle in Plane Couette Newtonian Fluid Flow, Powder Technol., 274: 186–192 (2015).
[84] Hatami M., Ganji D.D., Motion of a Spherical Particle in a Fluid Forced Vortex by DQM and DTM, Particuology, 16: 206–212 (2014).
[87] Bahmani A., Kargarsharifabad H., Laminar Natural Convection of Power-Law Fluids over a Horizontal Heated Flat Plate, Heat Transf. Res., 48(3): 1044–1066 (2019).
[88] Aminossadati S.M., Ghasemi B., Natural Convection Cooling of a Localised Heat Source at the Bottom of a Nanofluid-Filled Enclosure, Eur. J. Mech. B/Fluids. 28(5): 630–640 (2009).
[89] M. Sheikholeslami M., Gorji Bandpy M., Ellahi R., Zeeshan A., Simulation of MHD CuO–Water Nanofluid Flow and Convective Heat Transfer Considering Lorentz Forces, J. of Mag. Magnetic Material., 369: 69-80 (2014).