Study of Exponential Thermal Boundary Condition on Unsteady Magnetohydrodynamic Convection in a Square Enclosure Filled with Fe3O4- Water Ferrofluid
DOI:
https://doi.org/10.18034/ei.v6i1.173Keywords:
Ferrofluid, magnetohydrodynamic convection, exponential boundary condition, unsteady flowAbstract
In this paper, magnetohydrodynamic convection is analyzed numerically for a square enclosure filled with Fe3O4–water ferrofluid. A time-dependent exponential thermal boundary condition is applied at the bottom wall of the cavity. The ferrofluid is modeled as a single-phase fluid. Maxwell-Garnet model is used for modeling the effective thermal conductivity and viscosity of the ferrofluid. The Galerkin-weighted residuals method of finite-element analysis is adopted for the numerical solutions. The solid volume fraction, f is varied from 2.5 to 10% and the Hartmann number Ha from 0 to 20. Investigations are carried out for Rayleigh number Ra =104 and 105 over dimensionless times τ=0.01–1.0. The present study indicates that Ra, Ha and f, have a significant effect on heat transfer. At τ =1, if Ra=104, a higher solid volume fraction maximizes heat transfer whereas at Ra=105, a lower solid volume fraction maximizes heat transfer. Moreover, at τ =1, incrementing Ha diminishes heat transfer at Ra=104 whereas an optimum value of Ha=10 maximizes heat transfer for Ra=105. The exponential thermal boundary conditions have a certain importance on heat transfer. The present results provide necessary information for further investigation of heat transfer in its different applications.
Downloads
References
A.A. Bozhko, G.F. Putin, T. Tynjälä, P. Sarkomaa, Experimental and numerical investigation of wave ferrofluid convection, J. Magn. Magn. Mater. 316 (2007) 433–435. doi:10.1016/j.jmmm.2007.03.105.
A.H. Mahmoudi, I. Pop, M. Shahi, F. Talebi, MHD natural convection and entropy generation in a trapezoidal enclosure using Cu–water nanofluid, Comput. Fluids. 72 (2013) 46–62. doi:10.1016/j.compfluid.2012.11.014.
A.H. Mahmoudi, M. Shahi, A.H. Raouf, A. Ghasemian, Numerical study of natural convection cooling of horizontal heat source mounted in a square cavity filled with nanofluid, Int. Commun. Heat Mass Transf. 37 (2010) 1135–1141. doi:10.1016/j.icheatmasstransfer.2010.06.005.
A.H. Mahmoudi, M. Shahi, A.H. Raouf, A. Ghasemian, Numerical study of natural convection cooling of horizontal heat source mounted in a square cavity filled with nanofluid, Int. Commun. Heat Mass Transf. 37 (2010) 1135–1141.
A.K. Santra, S. Sen, N. Chakraborty, Study of heat transfer augmentation in a differentially heated square cavity using copper–water nanofluid, Int. J. Therm. Sci. 47 (2008) 1113–1122. doi:10.1016/j.ijthermalsci.2007.10.005.
A.V. Belyaev, B.L. Smorodin, The stability of ferrofluid flow in a vertical layer subject to lateral heating and horizontal magnetic field, J. Magn. Magn. Mater. 322 (2010) 2596–2606. doi:10.1016/j.jmmm.2010.03.028.
B.J. Gireesha, B. Mahanthesh, I.S. Shivakumara, K.M. Eshwarappa, Melting heat transfer in boundary layer stagnation-point flow of nanofluid toward a stretching sheet with induced magnetic field, Engineering Science and Technology, an International Journal 19 (2016) 313–321
Bouchmel Mliki, Mohamed Ammar Abbassi, Kamel Guedri, Ahmed Omri, Lattice Boltzmann simulation of natural convection in an L-shaped enclosure in the presence of nanofluid, Engineering Science and Technology, an International Journal 18 (2015) 503-511.
C.J. Ho, M.W. Chen, Z.W. Li, Numerical simulation of natural convection of nanofluid in a square enclosure: Effects due to uncertainties of viscosity and thermal conductivity, Int. J. Heat Mass Transf. 51 (2008) 4506–4516. doi:10.1016/j.ijheatmasstransfer.2007.12.019.
E. Abu-Nada, H.F. Oztop, Effects of inclination angle on natural convection in enclosures filled with Cu–water nanofluid, Int. J. Heat Fluid Flow. 30 (2009) 669–678.
E. Abu-Nada, H.F. Oztop, Effects of inclination angle on natural convection in enclosures filled with Cu–water nanofluid, Int. J. Heat Fluid Flow. 30 (2009) 669–678. doi:10.1016/j.ijheatfluidflow.2009.02.001.
F. Selimefendigil, H.F. Öztop, Forced convection of ferrofluids in a vented cavity with a rotating cylinder, Int. J. Therm. Sci. 86 (2014) 258–275. doi:10.1016/j.ijthermalsci.2014.07.007.
F. Selimefendigil, H.F. Öztop, K. Al-Salem, Natural convection of ferrofluids in partially heated square enclosures, J. Magn. Magn. Mater. 372 (2014) 122–133. doi:10.1016/j.jmmm.2014.07.058.
F. Wu, W. Zhou, X. Ma, Natural convection in a porous rectangular enclosure with sinusoidal temperature distributions on both side walls using a thermal non-equilibrium model, Int. J. Heat Mass Transf. 85 (2015) 756–771. doi:10.1016/j.ijheatmasstransfer.2015.02.039.
G.H.R. Kefayati, Natural convection of ferrofluid in a linearly heated cavity utilizing LBM, J. Mol. Liq. 191 (2014) 1–9. doi:10.1016/j.molliq.2013.11.021.
G.R. Kefayati, Simulation of Ferrofluid Heat Dissipation Effect on Natural Convection at an Inclined Cavity Filled with Kerosene/Cobalt Utilizing the Lattice Boltzmann Method, Numer. Heat Transf. Part Appl. 65 (2014) 509–530. doi:10.1080/10407782.2013.836022.
H. Aminfar, M. Mohammadpourfard, S. Ahangar Zonouzi, Numerical study of the ferrofluid flow and heat transfer through a rectangular duct in the presence of a non-uniform transverse magnetic field, J. Magn. Magn. Mater. 327 (2013) 31–42. doi:10.1016/j.jmmm.2012.09.011.
H.C. Brinkman, The Viscosity of Concentrated Suspensions and Solutions, J. Chem. Phys. 20 (1952) 571–571. doi:10.1063/1.1700493.
I. Mejri, A. Mahmoudi, M.A. Abbassi, A. Omri, Magnetic field effect on entropy generation in a nanofluid-filled enclosure with sinusoidal heating on both side walls, Powder Technol. 266 (2014) 340–353. doi:10.1016/j.powtec.2014.06.054.
I. Mejri, A. Mahmoudi, MHD natural convection in a nanofluid-filled open enclosure with a sinusoidal boundary condition, Chem. Eng. Res. Des. 98 (2015) 1–16. doi:10.1016/j.cherd.2015.03.028.
J.C. Maxwell, A treatise on electricity and magnetism, in: 2nd ed., Cambridge: Oxford University Press, 1904.
K.M. Rabbi, S. Saha, S. Mojumder, M.M. Rahman, R. Saidur, T.A. Ibrahim, Numerical investigation of pure mixed convection in a ferrofluid-filled lid-driven cavity for different heater configurations, Alex. Eng. Journ. (2016). doi:10.1016/j.aej.2015.12.021.
M. Ashouri, B. Ebrahimi, M.B. Shafii, M.H. Saidi, M.S. Saidi, Correlation for Nusselt number in pure magnetic convection ferrofluid flow in a square cavity by a numerical investigation, J. Magn. Magn. Mater. 322 (2010) 3607–3613. doi:10.1016/j.jmmm.2010.05.041.
M. Ghasemian, Z. Najafian Ashrafi, M. Goharkhah, M. Ashjaee, Heat transfer characteristics of Fe3O4 ferrofluid flowing in a mini channel under constant and alternating magnetic fields, J. Magn. Magn. Mater. 381 (2015) 158–167. doi:10.1016/j.jmmm.2014.12.078.
M. Jahanshahi, S.F. Hosseinizadeh, M. Alipanah, A. Dehghani, G.R. Vakilinejad, Numerical simulation of free convection based on experimental measured conductivity in a square cavity using Water/SiO2 nanofluid, Int. Commun. Heat Mass Transf. 37 (2010) 687–694. doi:10.1016/j.icheatmasstransfer.2010.03.010.
M. Sheikholeslami, D.D. Ganji, M.M. Rashidi, Ferrofluid flow and heat transfer in a semi annulus enclosure in the presence of magnetic source considering thermal radiation, J. Taiwan Inst. Chem. Eng. 47 (2015) 6–17. doi:10.1016/j.jtice.2014.09.026.
M. Sheikholeslami, M. Gorji-Bandpy, D.D. Ganji, Lattice Boltzmann method for MHD natural convection heat transfer using nanofluid, Powder Technol. 254 (2014) 82–93. doi:10.1016/j.powtec.2013.12.054.
M. Sheikholeslami, M. Gorji-Bandpy, Free convection of ferrofluid in a cavity heated from below in the presence of an external magnetic field, Powder Technol. 256 (2014) 490–498. doi:10.1016/j.powtec.2014.01.079.
M.A. Mansour, Sameh E. Ahmed, A numerical study on natural convection in porous media-filled an inclined triangular enclosure with heat sources using nanofluid in the presence of heat generation effect, Engineering Science and Technology, an International Journal 18 (2015) 485-495.
M.A.Y. Bakier, Flow in open C-shaped cavities: How far does the change in boundaries affect nanofluid?, Engineering Science and Technology, an International Journal 17 (2014) 116-130.
M.M. Rahman, H.F. Öztop, M. Steele, A.G. Naim, K. Al-Salem, T.A. Ibrahim, Unsteady natural convection and statistical analysis in a CNT–water filled cavity with non-isothermal heating, Int. Commun. Heat Mass Transf. (n.d.). doi:10.1016/j.icheatmasstransfer.2015.02.012.
M.M. Rahman, S. Mojumder, S. Saha, S. Mekhilef, R. Saidur, Augmentation of natural convection heat transfer in triangular shape solar collector by utilizing water based nanofluids having a corrugated bottom wall, Int. Commun. Heat Mass Transf. 50 (2014) 117–127.
M.M. Rahman, S. Mojumder, S. Saha, S. Mekhilef, R. Saidur, Effect of solid volume fraction and tilt angle in a quarter circular solar thermal collectors filled with CNT–water nanofluid, Int. Commun. Heat Mass Transf. 57 (2014) 79–90.
M.M. Rahman, S. Saha, S. Mojumder, A.G. Naim, R. Saidur, T.A. Ibrahim, Effect of sine-squared thermal boundary condition on augmentation of heat transfer in a triangular solar collector filled with different nanofluids, Numer. Heat Transf. Part B Fundam. 68 (2015) 53–74.
M.R. Krishnamurthy, B.C. Prasannakumara, B.J. Gireesha, Rama Subba Reddy Gorla, Effect of chemical reaction on MHD boundary layer flow and melting heat transfer of Williamson nanofluid in porous medium, Engineering Science and Technology, an International Journal 19 (2016) 53–61.
N. Sandeep, C. Sulochana, B. Rushi Kumar, Unsteady MHD radiative flow and heat transfer of a dusty nanofluid over an exponentially stretching surface, Engineering Science and Technology, an International Journal 19 (2016) 227–240.
P. Valinataj-Bahnemiri, A. Ramiar, S.A. Manavi, A. Mozaffari, Heat transfer optimization of two phase modeling of nanofluid in a sinusoidal wavy channel using Artificial Bee Colony technique, Engineering Science and Technology, an International Journal 18 (2015) 727-737.
S. Das, R.N. Jana, O.D. Makinde, Mixed convective magnetohydrodynamic flow in a vertical channel filled with nanofluids, Engineering Science and Technology, an International Journal 18 (2015) 244-255.
S. Eiamsa-ard, K. Kiatkittipong, W. Jedsadaratanachai, Heat transfer enhancement of TiO2/water nanofluid in a heat exchanger tube equipped with overlapped dual twisted-tapes, Engineering Science and Technology, an International Journal 18 (2015) 336-350.
S. Sivasankaran, K.L. Pan, Natural convection of nanofluids in a cavity with Nonuniform Temperature Distributions on Side Walls, Numer. Heat Transf. Part Appl. 65 (2014) 247–268.
S. Sivasankaran, K.L. Pan, Natural Convection of Nanofluids in a Cavity with Nonuniform Temperature Distributions on Side Walls, Numer. Heat Transf. Part Appl. 65 (2014) 247–268. doi:10.1080/10407782.2013.825510.
S.-K. Choi, S.-O. Kim, T.-H. Lee, Dohee-Hahn, Computation of the Natural Convection of Nanofluid in a Square Cavity with Homogeneous and Nonhomogeneous Models, Numer. Heat Transf. Part Appl. 65 (2014) 287–301. doi:10.1080/10407782.2013.831695.
S.M. Aminossadati, B. Ghasemi, Natural convection cooling of a localised heat source at the bottom of a nanofluid-filled enclosure, Eur. J. Mech. - BFluids. 28 (2009) 630–640.
S.M. Aminossadati, B. Ghasemi, Natural convection cooling of a localised heat source at the bottom of a nanofluid-filled enclosure, Eur. J. Mech. - BFluids. 28 (2009) 630–640. doi:10.1016/j.euromechflu.2009.05.006.
S.M. Snyder, T. Cader, B.A. Finlayson, Finite element model of magnetoconvection of a ferrofluid, J. Magn. Magn. Mater. 262 (2003) 269–279. doi:10.1016/S0304-8853(02)01502-0.
Sameh E. Ahmed, M.A. Mansour, Ahmed Kadhim Hussein, S. Sivasankaran, Mixed convection from a discrete heat source in enclosures with two adjacent moving walls and filled with micropolar nanofluids, Engineering Science and Technology, an International Journal 19 (2016) 364–376.
T-C. Jue, Analysis of combined thermal and magnetic convection ferrofluid flow in a cavity, Int. Commun. Heat Mass Transf. 33 (2006) 846–852. doi:10.1016/j.icheatmasstransfer.2006.02.001.
W.N. Zhou, Y.Y. Yan, Numerical Investigation of the Effects of a Magnetic Field on Nanofluid Flow and Heat Transfer by the Lattice Boltzmann Method, Numer. Heat Transf. Part Appl. 68 (2015) 1–16. doi:10.1080/10407782.2014.965017.
--0--
Published
Issue
Section
License
Engineering International is an Open Access journal. Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal the right of first publication with the work simultaneously licensed under a CC BY-NC 4.0 International License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of their work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal. We require authors to inform us of any instances of re-publication.
