Abstract
In this investigation, we have examined the flow and thermal characteristics of MHD Casson nanofluid in a square enclosure with non-uniform heat source at the bottom wall using the Brinkman model. Finite volume technique is employed to solve system of nonlinear partial differential equations. Impact of the governing parameters on the local Nusselt number, streamlines and isotherms has been demonstrated. Two counter rotating vortices are seen in the streamlines which result from the buoyancy caused by the variations in fluid temperature along the side of the enclosure with non-uniform temperature distribution. An increase in the Raleigh number results in a sharp rise in the temperature in the middle of the enclosure, whereas the thermal distribution becomes steeper near the enclosure walls. It has been noted that, for higher values of the Rayleigh number, effect of the magnetic field (quantified by the Hartman number) becomes prominent as a force of retardation.
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References
E. Abu-Nada, H.F. Oztop, I. Pop, Buoyancy induced flow in a nano-fluid filled enclosure partially exposed to forced convection. Superlattices Microstruct. 51, 381–395 (2012)
S.U.S. Choi, Enhancing Thermal Conductivity of Fluids with Nanoparticles. Developments and Applications of Non-Newtonian Flows, vol 66 (ASME, New York, 1995), pp 99–105
S.U.S. Choi, Nano-fluids: from vision to reality through research. J. Heat Transf. 131(3), 1–9 (2009)
A. Akbarinia, M. Abdolzadeh, R. Laura, Critical investigation of heat transfer enhancement using nano-fluids in micro channels with slip and non-slip flow regimes. Appl. Therm. Eng. 31(4), 556–565 (2010)
S.M.S. Murshed, C.A.N. de Castro, M.J.V. Lourenco, M.L.M. Lopes, F.J.V. Santos, A review of boiling and convective heat transfer with nanofluids. Renew. Sustain. Energy Rev. 15, 2342–2354 (2011)
W. Yu, D.M. France, J.L. Routbort, S.U.S. Choi, Review and comparison of nano-fluid thermal conductivity and heat transfer enhancements. Heat Transf. Eng. 29(5), 432–460 (2008)
G. de Vahl Davis, Natural convection of air in a square cavity: a bench mark numerical solution. Int. J. Numer. Methods Fluids 3(3), 249–264 (1983)
N. Casson, A flow equation for pigment-oil suspensions of the printing ink type, in Rheology of disperse systems, ed. by C.C. Mill (Pergamon Press, Oxford, 1959), pp. 84–104
A.J. Chamkha, Chamkha Natural convection flow under magnetic field in a square cavity for uniformly linearly heated adjacent walls. Int. J. Numer. Methods Heat Fluid Flow 22, 677–698 (2012)
S.A. Hossain, M.A. Alim, S.K. Saha, A finite element analysis on MHD free convection flow in open square cavity containing heated circular cylinder. Am. J. Comput. Math. 5, 41–54 (2015)
A. Kamran, S. Hussain, M. Sagheer, N. Akmal, A numerical study of magnetohydrodynamics flow in Casson nanofluid combined with Joule heating and slip boundary conditions. Results Phy. 7, 3037–3048 (2017)
N.T. Eldabe, M.E. Gabr, S.A. Zaher, Boundary layer flow of MHD Casson nano-fluid with heat and mass transfer through porous medium over a semi infinite moving plate. J. Interpol. Approx. Sci. Comp. 2, 21–34 (2018)
F. Mabood, K. Das, Outlining the impact of melting on MHD Casson fluid flow past a stretching sheet in a porous medium with radiation. Heliyon 5, 1–23 (2019)
M. Sheikholeslami, Z. Shah, A. Tassaddiq, A. Shafee, I. Khan, Application of electric field for augmentation of ferrofluid heat transfer in an enclosure including double moving walls. IEEE Access 21048–21056 (2019)
P. Umadevi, N. Nithyadevi, Magneto convection of water based nanofluids inside an enclosure having uniform heat generation and various thermal boundaries. J. Nigeri. Math. Soc. 35, 82–92 (2016)
A.I. Alsabery, M.A. Sheremet, A.J. Chamkha, I. Hashim, MHD convective heat transfer in a discretely heated square cavity with conductive inner block using two-phase nanofluid model. Sci. Rep. 8, 1–17 (2018)
S. Mahjabin, MdA Alim, Effect of hartmann number on free convective flow of MHD fluid in a square cavity with a heated cone of different orientation. Am. J. Comput. Math. 8, 314–325 (2018)
A.H. Bhuiyan, M.A. Alim, Md.N. Uddin, Effect of hartmann number on free convective flow in a square cavity with different positions of heated square block. World Acad. Sci. Eng. Technol. Int. J. Math. Comput. Phy. Elect. Comp. Eng. 8(2), 385–390 (2014)
S.M. Aminossasati, B. Ghasemi, Natural convection cooling of a localised heat source at the bottom of a nano-fluid filled enclosure. Euro. J. Mech. B/Fluid 28, 630–640 (2009)
H.F. Oztop, E. Abu-Nada, Numerical study of natural convection in partially heated rectangular enclosures filled with nano-fluids. Int. J. Heat Fluid Flow 29, 1326–1336 (2008)
I. Mejri, A. Mahmoudi, M.A. Abbassi, A. Omri, MHD natural convection in a nanofluid filled enclosure with non-uniform heating on both side walls. Tech. Sci. Press 10(1), 83–114 (2014)
I. Mejri, A. Mahmoudi, M.A. Abbassi, A. Omri, Lattice Boltzmann simulation of MHD natural convection in a nanofluid filled enclosure with non-Uniform heating on both side walls. World Acad. Sci. Eng. Tech. Int. J. Phy. Nucl. Sci. Eng. 8(1), 28–44 (2014)
M. Ghalambaz, A. Doostani, E. Izadpanahi, A.J. Chamkha, Conjugate natural convection flow of Ag–MgO/water hybrid nanofluid in a square cavity. J. Therm. Anal. Calorim. (2019). https://doi.org/10.1007/s10973-019-08617-7(0123456789)
T. Tayebi, A.J. Chamkha, Entropy generation analysis due to MHD natural convection flow in a cavity occupied with hybrid nanofluid and equipped with a conducting hollow cylinder. J. Therm. Anal. Calorim. (2019). https://doi.org/10.1007/s10973-019-08651-5
A. Bhattacharyya, G.S. Seth, R. Kumar, A.J. Chamkha, Simulation of Cattaneo-Christov heat flux on the flow of single and multi-walled carbon nanotubes between two stretchable coaxial rotating disks. J. Therm. Anal. Calorim. (2019). https://doi.org/10.1007/s10973-019-08644-4
A.I. Alsabery, M.A. Ismael, A.J. Chamkha, I. Hashim, Effect of nonhomogeneous nanofluid model on transient natural convection in a non-Darcy porous cavity containing an inner solid body. Int. Commun. Heat Mass Transf. 110 (2020)
E. Khodabandeh, D. Toghraie, A. Chamkha, R. Mashayekhi, O. Akbariand, S.A. Rozati, Energy saving with using of elliptic pillows in turbulent flow of two-phase water-silver nanofluid in a spiral heat exchanger. Int. J. Numer. Methods Heat Fluid Flow (2018)
T. Tayebi, A.J. Chamkha, Entropy generation analysis during MHD natural convection flow of hybrid nanofluid in a square cavity containing a corrugated conducting block. Int. J. Numer. Methods Heat Fluid Flow 30(3), 1115–1136 (2020)
D. Toghraie, R. Mashayekhi, H. Arasteh, S. Sheykhi, M. Niknejadi, A.J. Chamkha, Two-phase investigation of water-Al2O3 nanofluid in a micro concentric annulus under non-uniform heat flux boundary conditions. Int. J. Numer. Methods Heat Fluid Flow (2019). https://doi.org/10.1108/hff-11-2018-0628
F. Selimefendigil, A.J. Chamkha, MHD mixed convection of nanofluid in a three dimensional vented cavity with surface corrugation and inner rotating cylinder. Int. J. Numer. Methods Heat Fluid Flow (2019). https://doi.org/10.1108/hff-10-2018-0566
F. Selimefendigil, H.F. Öztop, A.J. Chamkha, Role of magnetic field on forced convection of nanofluid in a branching channel. Int. J. Numer. Methods Heat Fluid Flow (2019). https://doi.org/10.1108/hff-10-2018-0568
H.M. Sadeghi, M. Babayan, A.J. Chamkha, Investigation of using multi-layer PCMs in the tubularheat exchanger with periodic heat transfer boundary condition. Int. J. Heat and Mass Trans. (2019). https://doi.org/10.1016/j.ijheatmasstransfer.2019.118970
Y. Menni, A.J. Chamkha, N. Massarotti, H. Ameur, N. Kaid, Hydrodynamic and thermal analysis of water, ethylene glycol and water-ethylene glycol as base fluids dispersed by aluminum oxide nano-sized solid particles. Int. J. Numer. Methods Heat Fluid Flow (2019). https://doi.org/10.1108/hff-10-2019-0739
G. Rasool, T. Zhang, A. J. Chamkha, A. Shafiq, I. Tlili, G. Shahzadi, Entropy generation and consequences of binary chemical reaction on MHD Darcy–Forchheimer Williamson nanofluid flow over nonlinearly stretching surface. Entropy 22(18) (2020). https://doi.org/10.3390/e22010018
M. Ghalambaz, A.J. Chamkha, D. Wen, Natural convective flow and heat transfer of nano-encapsulated phase change materials (NEPCMs) in a cavity. Int. J. Heat Mass Transf. 138, 738–749 (2019)
A.I. Alsabery, R. Mohebbi, A.J. Chamkha, I. Hashim, Effect of local thermal non-equilibrium model on natural convection in a nanofluid-filled wavy-walled porous cavity containing inner solid cylinder. Chem. Eng. Sci. 201(29), 247–263 (2019)
A.S. Dogonchi, T. Armaghani, A.J. Chamkha, D.D. Ganji, Natural convection analysis in a cavity with an inclined elliptical heater subject to shape factor of nanoparticles and magnetic field. Arab. J. Sci. Eng. (2019). https://doi.org/10.1007/s13369-019-03956-x
A.I. Alsabery, M.A. Ismael, A.J. Chamkha, I. Hashim, Effects of two-phase nanofluid model on MHD mixed convection in a lid-driven cavity in the presence of conductive inner block and corner heater. J. Therm. Anal. Calorim. (2018). https://doi.org/10.1007/s10973-018-7377.V
S.A.M. Mehryan, E. Izadpanahi, M. Ghalambaz, A.J. Chamkha, Mixed convection flow caused by an oscillating cylinder in a square cavity filled with Cu–Al2O3/water hybrid nanofluid. J. Therm. Anal. Calorim. https://doi.org/10.1007/s10973-019-08012-2
J. Raza, F.M. Oudina, A.J. Chamkha, Magnetohydrodynamic flow of molybdenum disulfide nanofluid in a channel with shape effects. Multidiscip. Model. Mater. Struct. 15(4), 737–757 (2019)
Y. Menni, A. Azzi1, A. J. Chamkha, Enhancement of convective heat transfer in smooth air channels with wall-mounted obstacles in the flow path. J. Therm. Anal. Calorim. https://doi.org/10.1007/s10973-018-7268-x
Z. Li, M. Ramzan, A. Shafee, S. Saleem, Q.M. Al-Mdallal, A.J. Chamkha, Numerical approach for nanofluid transportation due to electric force in a porous enclosure. Micro system Tech. https://doi.org/10.1007/s00542-018-4153-2
I. Zahan, R. Nasrin, M.A. Alim, MHD effect on conjugate heat transfer in a nano-fluid filled rectangular enclosure. J. Petrol. Sci. E 3(3), 114–123 (2018)
Y. El Hammami, M. El Hattab, R. Mir, T. Mediouni, Numerical study of natural convection of nanofluid in a square enclosure in the presence of the magnetic field. Int. J. Eng. Adv. Tech. (IJEAT), 4(4), ISSN: 2249–8958 (2015)
H.C. Brinkman, The viscosity of concentrated suspensions and solution. J. Chem. Phys. 20(4), 571–581 (1952)
J.C. Maxwell, M.A.A Treatise on Electricity and Magnatism, 2nd Edition, Oxford University Press, Cambridge (1904)
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Yasmin, A., Ali, K. & Ashraf, M. MHD Casson nanofluid flow in a square enclosure with non-uniform heating using the Brinkman model. Eur. Phys. J. Plus 136, 151 (2021). https://doi.org/10.1140/epjp/s13360-021-01093-9
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DOI: https://doi.org/10.1140/epjp/s13360-021-01093-9