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Research Papers

Magnetohydrodynamics Mixed Convection in a Lid-Driven Cavity Having a Corrugated Bottom Wall and Filled With a Non-Newtonian Power-Law Fluid Under the Influence of an Inclined Magnetic Field

[+] Author and Article Information
Fatih Selimefendigil

Associate Professor
Department of Mechanical Engineering,
Celal Bayar University,
Manisa 45240, Turkey
e-mail: fatih.selimefendigil@cbu.edu.tr

Ali J. Chamkha

Professor
Department of Mechanical Engineering,
Prince Mohammad Bin Fahd University,
Al-Khobar 31952, Kingdom of Saudi Arabia
e-mail: achamkha@pmu.edu.sa

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF THERMAL SCIENCE AND ENGINEERING APPLICATIONS. Manuscript received March 23, 2015; final manuscript received December 22, 2015; published online March 8, 2016. Assoc. Editor: Giulio Lorenzini.

J. Thermal Sci. Eng. Appl 8(2), 021023 (Mar 08, 2016) (8 pages) Paper No: TSEA-15-1092; doi: 10.1115/1.4032760 History: Received March 23, 2015; Revised December 22, 2015

In this study, the problem of magnetohydrodynamics (MHD) mixed convection of lid-driven cavity with a triangular-wave shaped corrugated bottom wall filled with a non-Newtonian power-law fluid is numerically studied. The bottom corrugated wall of the cavity is heated and the top moving wall is kept at a constant lower temperature while the vertical walls of the enclosure are considered to be adiabatic. The governing equations are solved by the Galerkin weighted residual finite element formulation. The influence of the Richardson number (between 0.01 and 100), Hartmann number (between 0 and 50), inclination angle of the magnetic field (between 0 deg and 90 deg), and the power-law index (between 0.6 and 1.4) on the fluid flow and heat transfer characteristics are numerically investigated. It is observed that the effects of free convection are more pronounced for a shear-thinning fluid and the buoyancy force is weaker for the dilatant fluid flow compared to that of the Newtonian fluid. The averaged heat transfer decreases with increasing values of the Richardson number and enhancement is more effective for a shear-thickening fluid. At the highest value of the Hartmann number, the averaged heat transfer is the lowest for a pseudoplastic fluid. As the inclination angle of the magnetic field increases, the averaged Nusselt number generally enhances.

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References

Nkurikiyimfura, I. , Wang, Y. , and Pan, Z. , 2013, “ Heat Transfer Enhancement by Magnetic Nanofluids—A Review,” Renewable Sustainable Energy Rev., 21, pp. 548–561. [CrossRef]
Hasanuzzaman, M. , Oztop, H. F. , Rahman, M. , Rahim, N. , Saidur, R. , and Varol, Y. , 2012, “ Magnetohydrodynamic Natural Convection in Trapezoidal Cavities,” Int. Commun. Heat Mass Transfer, 39(9), pp. 1384–1394. [CrossRef]
Hossain, M. S. , and Alim, M. A. , 2014. “ MHD Free Convection Within Trapezoidal Cavity With Non-Uniformly Heated Bottom Wall,” Int. J. Heat Mass Transfer, 69, pp. 327–336. [CrossRef]
Selimefendigil, F. , and Oztop, H. F. , 2014, “ Effect of a Rotating Cylinder in Forced Convection of Ferrofluid Over a Backward Facing Step,” Int. J. Heat Mass Transfer, 71, pp. 142–148. [CrossRef]
Bednarz, T. , Patterson, J. C. , Lei, C. , and Ozoe, H. , 2009, “ Enhancing Natural Convection in a Cube Using a Strong Magnetic Field—Experimental Heat Transfer Rate Measurements and Flow Visualization,” Int. Commun. Heat Mass Transfer, 36(8), pp. 781–786. [CrossRef]
Grosan, T. , Revnic, C. , Pop, I. , and Ingham, D. , 2009, “ Magnetic Field and Internal Heat Generation Effects on the Free Convection in a Rectangular Cavity Filled With a Porous Medium,” Int. J. Heat Mass Transfer, 52(5–6), pp. 1525–1533. [CrossRef]
Yu, P. , Qiu, J. , Qin, Q. , and Tian, Z. F. , 2013, “ Numerical Investigation of Natural Convection in a Rectangular Cavity Under Different Directions of Uniform Magnetic Field,” Int. J. Heat Mass Transfer, 67, pp. 1131–1144. [CrossRef]
Sheikholeslami, M. , Gorji-Bandpy, M. , Ganji, D. , Soleimani, S. , and Seyyedi, S. , 2012, “ Natural Convection of Nanofluids in an Enclosure Between a Circular and a Sinusoidal Cylinder in the Presence of Magnetic Field,” Int. Commun. Heat Mass Transfer, 39(9), pp. 1435–1443. [CrossRef]
Azimi, M. , Azimi, A. , and Mirzaei, M. , 2015, “ Analytical Investigation of MHD Jeffery Hamel Problem With Graphene Oxide Nanoparticles Using Goham,” J. Comput. Theoritical Nanosci., 12(6), pp. 991–995. [CrossRef]
Selimefendigil, F. , and Oztop, H. F. , 2014, “ Numerical Study of MHD Mixed Convection in a Nanofluid Filled Lid Driven Square Enclosure With a Rotating Cylinder,” Int. J. Heat Mass Transfer, 78, pp. 741–754. [CrossRef]
Selimefendigil, F. , and Oztop, H. F. , 2014, “ MHD Mixed Convection of Nanofluid Filled Partially Heated Triangular Enclosure With a Rotating Adiabatic Cylinder,” J. Taiwan Inst. Chem. Eng., 45(5), pp. 2150–2162. [CrossRef]
Selimefendigil, F. , Oztop, H. F. , and Al-Salem, K. , 2014, “ Natural Convection of Ferrofluids in Partially Heated Square Enclosures,” J. Magn. Magn. Mater., 372, pp. 122–133. [CrossRef]
Oztop, H. F. , Al-Salem, K. , and Pop, I. , 2011, “ MHD Mixed Convection in a Lid-Driven Cavity With Corner Heater,” Int. J. Heat Mass Transfer, 54, pp. 494–3504.
Sheikholeslami, M. , and Ganji, D. D. , 2014, “ Ferrohydrodynamic and Magnetohydrodynamic Effects on Ferrofluid Flow and Convective Heat Transfer,” Energy, 75, pp. 400–410. [CrossRef]
Ahmed, M. , Shuaib, N. , Yusoff, M. , and Al-Falahi, A. , 2011, “ Numerical Investigations of Flow and Heat Transfer Enhancement in a Corrugated Channel Using Nanofluid,” Int. Commun. Heat Mass Transfer, 38(10), pp. 1368–1375. [CrossRef]
Hasan, M. N. , Saha, S. C. , and Gu, Y. , 2012, “ Unsteady Natural Convection Within a Differentially Heated Enclosure of Sinusoidal Corrugated Side Walls,” Int. J. Heat Mass Transfer, 55, pp. 5696–5708. [CrossRef]
Hussain, S. H. , Hussein, A. K. , and Mohammed, R. N. , 2012, “ Studying the Effects of a Longitudinal Magnetic Field and Discrete Isoflux Heat Source Size on Natural Convection Inside a Tilted Sinusoidal Corrugated Enclosure,” Comput. Math. Appl., 64(4), pp. 476–488. [CrossRef]
Mendu, S. S. , and Das, P. , 2012, “ Flow of Power-Law Fluids in a Cavity Driven by the Motion of Two Facing Lids—A Simulation by Lattice Boltzmann Method,” J. Non-Newtonian Fluid Mech., 175, pp. 10–24. [CrossRef]
Haque, S. , Lashgari, I. , Giannetti, F. , and Brandt, L. , 2012, “ Stability of Fluids With Shear-Dependent Viscosity in the Lid-Driven Cavity,” J. Non-Newtonian Fluid Mech., 173, pp. 49–61. [CrossRef]
Kefayati, G. , 2014, “ Simulation of Magnetic Field Effect on Natural Convection of Non-Newtonian Power-Law Fluids in a Sinusoidal Heated Cavity Using FDLBM,” Int. Commun. Heat Mass Transfer, 53, pp. 139–153. [CrossRef]
Kefayati, G. , 2014, “ FDLBM Simulation of Magnetic Field Effect on Non-Newtonian Blood Flow in a Cavity Driven by the Motion of Two Facing Lids,” Powder Technol., 253, pp. 325–337. [CrossRef]
Kefayati, G. , 2014, “ FDLBM Simulation of Magnetic Field Effect on Natural Convection of Non-Newtonian Power-Law Fluids in a Linearly Heated Cavity,” Powder Technol., 256, pp. 87–99. [CrossRef]
Pirmohammadi, M. , and Ghassemi, M. , 2009, “ Effect of Magnetic Field on Convection Heat Transfer Inside a Tilted Square Enclosure,” Int. Commun. Heat Mass Transfer, 36(7), pp. 776–780. [CrossRef]
Sarris, I. , Zikos, G. , Grecos, A. , and Vlachos, N. , 2006, “ On the Limits of Validity of the Low Magnetic Reynolds Number Approximation in MHD Natural-Convection Heat Transfer,” Numer. Heat Transfer Part B, 50, pp. 158–180. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Schematic diagram of the physical model with boundary conditions and grid distribution

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Fig. 2

Code verification with the results of Refs. [23,24]. Comparison of streamlines and isotherms.

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Fig. 3

Code verification with the results of Ref. [15]

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Fig. 4

Effects of varying Richardson number on the streamlines for various power-law fluid indices (Ha=30, a=0.25H,b=0.1H, γ=45 deg)

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Fig. 5

Effects of varying Richardson number on the isotherms for various power-law fluid indices (Ha=30, a=0.25H,b=0.1H, γ=45 deg)

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Fig. 6

Local Nusselt number along corrugated wall for various Richardson numbers and power-law fluid indices (Ha=30,a=0.25H,b=0.1H, γ=45 deg)

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Fig. 7

v-velocity along the mid of the cavity and averaged Nusselt number along the corrugated wall for various Richardson numbers and power-law fluid indices (Ha=30, a=0.25H,b=0.1H, γ=45 deg)

Grahic Jump Location
Fig. 8

Comparison of streamlines for various values of Hartmann number and power-law fluid indices (Ri=0.5, a=0.25H,b=0.1H, γ=45 deg)

Grahic Jump Location
Fig. 9

Comparison of isotherms for various values of Hartmann number and power-law fluid indices (Ri=0.5, a=0.25H,b=0.1H, γ=45 deg)

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Fig. 10

Local Nusselt number along the corrugated wall for different Hartmann numbers and power-law fluid indices (Ri=0.5,a=0.25H, b=0.1H, γ=45 deg)

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Fig. 11

v-velocity along the mid of the cavity and averaged Nusselt number along the corrugated wall for various Hartmann numbers and power-law fluid indices (Ri=0.5, a=0.25H,b=0.1H, γ=45 deg)

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Fig. 12

Influence of varying orientation angles of magnetic field on the streamlines for various power-law fluid indices (Ri=0.5, Ha=20 a=0.25H, b=0.1H)

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Fig. 13

Influence of varying orientation angles of magnetic field on the isotherms for various power-law fluid indices (Ri=0.5, Ha=20 a=0.25H, b=0.1H)

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Fig. 14

Local Nusselt number along the corrugated wall for various orientation angles and power-law fluid indices (Ri=0.5, Ha=20, a=0.25H, b=0.1H)

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Fig. 15

Averaged Nusselt number along the corrugated wall for various orientation angles and power-law indices (Ri=0.5, a=0.25H, b=0.1H)

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