Mohammad Ali TAGHİKHANİ

8019

MAGNETIC FIELD EFFECT ON THE HEAT TRANSFER IN A NANOFLUID FILLED LID DRIVEN CAVITY WITH JOULE HEATING

In this paper, the effects of magnetic field, Joule heating and volumetric heat generation on the heat transfer and fluid flow in a Cu-Water nanofluid filled lid driven cavity using enhanced streamfunction–velocity method are investigated. The cavity is heated by a uniform volumetric heat density and side walls have constant temperature. The top wall moves with constant velocity in +x direction, while no-slip boundary conditions are imposed on the other walls of the cavity. An inclined fixed magnetic field is applied to the left side wall of the cavity. The dimensionless governing equations are solved numerically for the stream function and temperature using finite difference method for various Richardson(Ri), Reynolds(Re), Hartmann (Ha), Eckert(Ec)numbers, magnetic field angle(α) and solid volume fraction of the nanofluid() in MATLAB software. To discretize the streamfunction-velocity formulation, a five point constant coefficient second-order compact finite difference approximation which avoids difficulties inherent in the conventional streamfunction–vorticity and primitive variable formulations is used. The stream function equation is solved using fast Poisson's equation solver on a rectangular grid (POICALC function in MATLAB) and the temperature equation is solved using Jacobi bi-conjugate gradient stabilized (BiCGSTAB) method. The heat transfer within the cavity is characterized by Nusselt number (Nu1). The results show that Nu1 is significantly increased by increasing Ri and  and increasing the Reynolds number enhances convective cooling. The heat transfer within the cavity is decreased by increasing Hartmann number which improves conduction heat transfer and reduces Nu1. Joule heating has a negative effect on the convection within the cavity and convection is decreased by increasing the value of Ec. It can be investigated that Nu1 is decreased by increasing Ec due to the strong distortion effect of Joule heating on convection current of heat transfer.
Keywords:

Magnetic Field, Nano-fluid, Lid Driven Cavity, Stream Function-Velocity, Joule Heating Volumetric Heat Generation,

PDF

___

  • [1] Oreper GM, Szekely J. The effect of an externally imposed magnetic field on buoyancy driven flow in a rectangular cavity. J. Cryst. Growth 1983; 64: 505-15. https://doi.org/10.1016/0022-0248(83)90335-4.
  • [2] Mohamad AA, Viskanta R. Transient low Prandtl number fluid convection in a lid-driven cavity. Numer. Heat Transf. A 1991; 19: 187-205. https:// doi.org/10.1080/10407789108944845
  • [3] Garandet JP, Alboussiere JP, Moreau T. Buoyancy driven convection in a rectangular cavity with a transverse magnetic field. Int. J. Heat Mass Transf. 1992; 35: 741-48. https://doi.org/10.1016/0017-9310(92)90242-K
  • [4] Rudraiah N, Barron RM, Venkatachalappa M, Subbaraya CK. Effect of a magnetic field on free convection in a rectangular enclosure. Int. J. Eng. Sci. 1995; 33: 1075-84. https://doi.org/10.1016/0020-7225(94)00120-9
  • [5] Al-Najem NM, Khanafer KM, El-Refaee MM. Numerical study of laminar natural convection in tilted enclosure with transverse magnetic field. Int J Numer Method H 1998; 8: 651–72. https://doi.org/10.1108/09615539810226094
  • [6] Sarris IE, Kakarantzas SC, Grecos AP, Vlachos NS. MHD natural convection in a laterally and volumetrically heated square cavity. Int. J. Heat Mass Transf. 2005; 48: 3443–53. https://doi.org/10.1016/j.ijheatmasstransfer.2005.03.014
  • [7] Kandaswamy P, MalligaSundari S, Nithyadevi N. Magnetoconvection in an enclosure with partially active vertical walls. Int. J. Heat Mass Transf. 2008; 51: 1946–54. https://doi.org/10.1016/j.ijheatmasstransfer.2007.06.025
  • [8] Borghi CA, Cristofolini A, Minak G. Numerical methods for the solution of the electrodynamics in magnetohydrodynamic flows. IEEE T Magn 1996; 32: 1010-13. https://doi.org/10.1109/20.497411
  • [9] Borghi CA, Carraro MR, Cristofolini A. Numerical solution of the nonlinear electrodynamics in MHD regimes with magnetic Reynolds number near one. IEEE T Magn 2004; 40: 593-6. https://doi.org/10.1109/TMAG.2004.825414
  • [10] Verardi SLL., Cardoso JR. A solution of two-dimensional magneto-hydrodynamic flow using the finite element method. IEEE T Magn 1998; 34: 3134-7. https://doi.org/10.1109/20.717734
  • [11] Verardi SLL, Cardoso JR, Costa MC. Three-dimensional finite element analysis of MHD duct flow by the penalty function formulation. IEEE T Magn 2001; 37: 3384-7. https://doi.org/10.1109/20.952619
  • [12] Verardi SLL, Machado JM, Cardoso JR. The element-free Galerkin method applied to the study of fully developed magneto-hydrodynamic duct flows. IEEE T Magn 2002; 38: 941-4. https://doi.org/ 10.1109/20.996242
  • [13] Shadid JN, Pawlowski RP, Banks JW, Chacon L, Lin PT, Tuminaro RS. Towards a scalable fully-implicit fully-coupled resistive MHD formulation with stabilized FE methods. J. Comput. Phys. 2010; 229: 7649–71. https://doi.org/10.1016/j.jcp.2010.06.018
  • [14] Taghikhani MA. Magnetic field effect on natural convection flow with internal heat generation using fast Ψ – Ω method. J Appl Fluid Mech 2015; 8: 189-96. https://doi.org/10.18869/acadpub.jafm.67.221.19377
  • [15] Taghikhani MA. Numerical study of magneto-convection inside an enclosure using enhanced stream function-vorticity formulation. Sci Iran B 2015; 22: 854-64. https://doi.org/ 10.1109/TMAG.2009.2018959
  • [16] Ece MC, Buyuk E. Natural convection flow under magnetic field in an inclined rectangular enclosure heated and cooled on adjacent walls. Fluid Dyn. Res. 2006; 38: 564-90. https://doi.org/10.1016/j.fluiddyn.2006.04.002
  • [17] Ece MC, Büyük E. Natural convection flow under a magnetic field in an inclined square enclosure differentially heated on adjacent walls. Meccanica 2007; 42: 435–49. https://doi.org/ 10.1007/s11012-007-9067-5
  • [18] Rashidi MM, Nasiri M, Khezerloo M, Laraqi N. Numerical investigation of magnetic field effect on mixed convection heat transfer of nanofluid in a channel with sinusoidal walls. J. Magn. Magn. Mater. 2016; 401:159–68. https://doi.org/10.1016/j.jmmm.2015.10.034
  • [19] Bourantas GC, Loukopoulos VC. MHD natural-convection flow in an inclined square enclosure filled with a micropolar-nanofluid. Int. J. Heat Mass Transf. 2014; 79: 930–44. https://doi.org/10.1016/j.ijheatmasstransfer.2014.08.075
  • [20] Heidary H, Hosseini R, Pirmohammadi M, Kermani MJ. Numerical study of magnetic field effect on nano-fluid forced convection in a channel. J. Magn. Magn. Mater. 2015; 374: 11–17. https://doi.org/10.1016/j.jmmm.2014.08.001
  • [21] Sheikholeslami M, Hayat T, Alsaedi A. Numerical study for external magnetic source influence on water based nanofluid convective heat transfer. Int. J. Heat Mass Transf. 2017; 106: 745–55. https://doi.org/10.1016/j.ijheatmasstransfer.2016.09.077
  • [22] Sheikholeslami M, Ganji DD. Ferrohydrodynamic and magnetohydrodynamic effects on ferrofluid flow and convective heat transfer. Energy 2014; 75: 400-10. https://doi.org/10.1016/j.energy.2014.07.089
  • [23] Sheikholeslami M, GorjiBandpy M, Ellahi R, Zeeshan A. Simulation of MHD CuO-water nanofluid flow and convective heat transfer considering Lorentz forces. J. Magn. Magn. Mater. 2014; 369: 69–80. https://doi.org/10.1016/j.jmmm.2014.06.017
  • [24] Selimefendigil F, Oztop HF. Analysis of MHD mixed convection in a flexible walled and nanofluids filled lid-driven cavity with volumetric heat generation. Int. J. Mech. Sci. 2016; 118: 113–24. https://doi.org/10.1016/j.ijmecsci.2016.09.011
  • [25] Selimefendigil F, Oztop HF. Mixed convection in a partially heated triangular cavity filled with nanofluid having a partially flexible wall and internal heat generation. J Taiwan Int Chem E 2017; 70: 168–78. https://doi.org/10.1016/j.jtice.2016.10.038
  • [26] Selimefendigil F, Oztop HF. Natural convection in a flexible sided triangular cavity with internal heat generation under the effect of inclined magnetic field. J. Magn. Magn. Mater. 2016; 417: 327–37. https://doi.org/10.1016/j.jmmm.2016.05.053
  • [27] Selimefendigil F, Oztop HF. Mixed convection of nanofluid filled cavity with oscillating lid under the influence of an inclined magnetic field. J Taiwan Int Chem E 2016; 63: 202–15. https://doi.org/10.1016/j.jtice.2016.03.003
  • [28] Selimefendigil F, Oztop HF, Chamkha AJ. MHD mixed convection and entropy generation of nanofluid filled lid driven cavity under the influence of inclined magnetic fields imposed to its upper and lower diagonal triangular domains. J. Magn. Magn. Mater. 2016; 406: 266–81. https://doi.org/10.1016/j.jmmm.2016.01.039
  • [29] Sheremet MA, Oztop HF, Pop I. MHD natural convection in an inclined wavy cavity with corner heater filled with a nanofluid. J. Magn. Magn. Mater. 2016; 416: 37–47. https://doi.org/10.1016/j.jmmm.2016.04.061
  • [30] Ghaffarpasand O. Numerical Study of MHD Natural Convection Inside a Sinusoidally Heated Lid-Driven Cavity Filled with Fe3O4-water Nanofluid in the Presence of Joule Heating. Appl. Math. Model. 2016; 40: 9165–82. https://doi.org/10.1016/j.apm.2016.05.038
  • [31] Hussain S, Ahmad S, Mehmood K, Sagheer M. Effects of inclination angle on mixed convective nanofluid flow in a double lid-driven cavity with discrete heat sources. Int. J. Heat Mass Transf. 2017; 106: 847–60. https://doi.org/10.1016/j.ijheatmasstransfer.2016.10.016
  • [32] Hussain S, Mehmood K, Sagheer M. MHD mixed convection and entropy generation of water-alumina nanofluid flow in a double lid driven cavity with discrete heating. J. Magn. Magn. Mater. 2016; 419: 140–55. https://doi.org/10.1016/j.jmmm.2016.06.006
  • [33] Job VM, Gunakala SR. Mixed convection nanofluid flows through a grooved channel with internal heat generating solid cylinders in the presence of an applied magnetic field. Int. J. Heat Mass Transf. 2017;107: 133–45. https://doi.org/10.1016/j.ijheatmasstransfer.2016.11.021
  • [34] Karimipour A, Taghipour A, Malvandi A. Developing the laminar MHD forced convection flow of water/FMWNT carbon nanotubes in a microchannel imposed the uniform heat flux. J. Magn. Magn. Mater. 2016; 419: 420–28. https://doi.org/10.1016/j.jmmm.2016.06.063
  • [35] Ismael MA, Mansour MA, Chamkha AJ, Rashad AM. Mixed convection in a nanofluid filled-cavity with partial slip subjected to constant heat flux and inclined magnetic field. J. Magn. Magn. Mater. 2016; 416: 25–36. https://doi.org/10.1016/j.jmmm.2016.05.006
  • [36] Aghaei A, Khorasanizadeh H, Sheikhzadeh GA, Abbaszadeh M. Numerical study of magnetic field on mixed convection and entropy generation of nanofluid in a trapezoidal enclosure. J. Magn. Magn. Mater. 2016; 403: 133–45. https://doi.org/10.1016/j.jmmm.2015.11.067
  • [37] Mehrez Z, El Cafsi A, Belghith A, Le Quéré P. MHD effects on heat transfer and entropygeneration of nanofluid flow in an open cavity. J. Magn. Magn. Mater. 2015; 374: 214–24. https://doi.org/10.1016/j.jmmm.2014.08.010
  • [38] Chamkha AJ, Ismael M, Kasaeipoor A, Armaghani T. Entropy generation and natural convection of CuO-water nanofluid in C-shaped cavity under magnetic field. Entropy 2016; 18: 1-18. https://doi.org/10.3390/e18020050
  • [39] Chamkha AJ, Rashad AM, Mansour MA, 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 2017; 29: 052001. https://doi.org/10.1063/1.4981911
  • [40] Rashad AM, Armaghani T, Chamkha AJ, Mansour MA. 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. Chin. J. Phys. 2018; 56: 193-211. https://doi.org/10.1016/j.cjph.2017.11.026
  • [41] Chamkha AJ, Rashad AM, Armaghani T, Mansour MA. 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. 2018; 132: 1291-306. https://doi.org/10.1007/s10973-017-6918-8
  • [42] Armaghani T, Esmaeili H, Mohammadpoor YA, Pop I. MHD mixed convection flow and heat transfer in an open C-shaped enclosure using water-copper oxide nanofluid. Heat Mass Transfer 2018; 54: 1791-801. https://doi.org/10.1007/s00231-017-2265-3
  • [43] Abedini A, Armaghani T, Chamkha AJ. MHD free convection heat transfer of a water–Fe3O4nanofluid in a baffled C-shaped enclosure. J. Therm. Anal. Calorim., https://doi.org/10.1007/s10973-018-7225-8.
  • [44] Koo J, Kleinstreuer C. Laminar nanofluid flow in microheat-sinks. Int. J. Heat Mass Transf. 2005; 48: 2652–61. https://doi.org/10.1016/j.ijheatmasstransfer.2005.01.029
  • [45] Tian ZF, Yu PX. An efficient compact difference scheme for solving the streamfunction formulation of the incompressible Navier–Stokes equations. J. Comput. Phys. 2011; 230: 6404–19. https://doi.org/10.1016/j.jcp.2010.12.031
  • [46] Dixit HN, Babu V. Simulation of high Rayleigh number natural convection in a square cavity using the lattice Boltzmann method. Int. J. Heat Mass Transf. 2006; 49: 727-39. https://doi.org/10.1016/j.ijheatmasstransfer.2005.07.046
  • [47] Kuznik F, Vareilles J, Rusaouen G, Krauss G. A double-population lattice Boltzmann method with non-uniform mesh for the simulation of natural convection in a square cavity. Int J Heat Fluid Fl 2007; 28: 862–70. https://doi.org/10.1016/j.ijheatfluidflow.2006.10.002
  • [48] Moumni H, Welhezi H, Djebali R, Sediki E. Accurate finite volume investigation of nanofluid mixed convection in two sided lid driven cavity including discrete heat sources. Appl. Math. Model. 2015; 39: 4164-79. https://doi.org/10.1016/j.apm.2014.12.035
  • [49] Djebali R, El Ganaoui M, Sammouda H, Bennacer R. Some benchmarks of a side wall heated cavity using lattice Boltzmann approach. Fluid Dyn. Mater. Process. 2009; 5: 261-82. https://doi.org/10.3970/fdmp.2009.005.261
  • [50] Tian Z, Ge Y. A fourth-order compact finite difference scheme for the steady stream function–vorticity formulation of the Navier–Stokes/Boussinesq equations. Int J Numer Meth Fl 2003; 41: 495–518. https://doi.org/10.1002/fld.444
  • [51] Nonino C, Croce G. An equal-order velocity-pressure algorithm for incompressible thermal flows, part 2: validation. Numer. Heat Transf. B 1997; 32: 17-35. https://doi.org /10.1080/10407799708914997
  • [52] Kalita JC, Dalal DC, Dass AK. Fully compact higher-order computation of steady-state natural convection in a square cavity. Phys Rev E 2001; 64: 066703. https://doi.org/10.1103/PhysRevE.64.066703
  • [53] Arpino F, Massarotti N, Mauro A. High Rayleigh number laminar-free convection in cavities: new benchmark solutions. Numer. Heat Transf. B 2010; 58: 73-97. https://doi.org/10.1080/10407790.2010.508438
  • [54] Sarris IE, Zikos GK, Grecos AP, Vlachos NS. On the limits of validity of the low magnetic Reynolds number approximation in MHD natural-convection heat transfer. Numer. Heat Transf. B 2006; 50: 157–80. https://doi.org/10.1080/10407790500459403
  • [55] Pirmohammadi M, Ghassemi M. Effect of magnetic field on convection heat transfer inside a tilted square enclosure. Int Commun Heat Mass 2009; 36: 776–80. https://doi.org/10.1016/j.icheatmasstransfer.2009.03.023
  • [56] Piazza ID, Ciofalo M. MHD free convection in a liquid-metal filled cubic enclosure. II. internal heating. Int. J. Heat Mass Transf. 2002; 45: 1493–511. https://doi.org/10.1016/S0017-9310(01)00253-8
Journal of Thermal Engineering-Cover
  • Başlangıç: 2015
  • Yayıncı: YILDIZ TEKNİK ÜNİVERSİTESİ
Arşiv
Sayıdaki Diğer Makaleler

Mohamed M. AWAD, Pranab Kumar MONDA, Omid MAHİAN, , Ho Seon AHN, Ahmet Selim DALKİLİÇ, Ioan Pop, Dieter MEWES, Adrian BEJAN, Bahri ŞAHİN

Ambati SANDEEP, K. ARCHANA, Sivakumar ELLAPPAN, Dandu MALLESHAM

Kondru Gnana SUNDARİ, Lazarus Godson ASIRVATHAM, Joseph John MARSHAL, Emerald NİNOLİN, Surekha

Mohammad Ali TAGHİKHANİ

Vikram A. KOLHE, Asmita D. DESHPANDE, Ravindra L. EDLABADKAR

AN INTEGRATED MODEL TO STUDY THE EFFECTS OF OPERATIONAL PARAMETERS ON THE PERFORMANCE AND POLLUTANT EMISSIONS IN A UTILITY BOILE

Hamid ABROSHAN

SH. NAKHJAVANİ, M. A. Abdolhossein ZADEH

Amir OMİDVAR, Amirhossein MAHDAV, Reza MEHRYAR

AN INTEGRATED MODEL TO STUDY THE EFFECTS OF OPERATIONAL PARAMETERS ON THE PERFORMANCE AND POLLUTANT EMISSIONS IN A UTILITY BOILER

Hamid ABROSHAN

Gholam Reza Nabi BİDHENDİ, Iran GHAZI, Shahin BAZARCHİ, Alibakhsh KASAEİAN