MAGNETOHYDRODYNAMIC FLOW AND HEAT TRANSFER OF NON-NEWTONIAN POWER-LAW NANOFLUID OVER A ROTATING DISK WITH HALL CURRENT

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Abe-El Aziz M. SALEM Rania FATHY

Abstract

This work studies the flow and heat transfer of a power-law nanofluid in the presence of an axial uniform magnetic field in the vicinity of a constantly rotating infinite disk. The Hall current effect is taken into consideration. The governing momentum and energy equations are solved numerically by the shooting method. Some of the results obtained for a special case of the problem are compared to the results published in a previous work and are found to be in excellent agreement. The effects of the solid fractionf , the magnetic interaction number M, the Hall current m, and the viscosity index n on the velocity and temperature profiles as well as the local skin friction coefficients and the heat transfer rate are shown graphically.

Article Details

How to Cite
SALEM, Abe-El Aziz M.; FATHY, Rania. MAGNETOHYDRODYNAMIC FLOW AND HEAT TRANSFER OF NON-NEWTONIAN POWER-LAW NANOFLUID OVER A ROTATING DISK WITH HALL CURRENT. Thermal Science, [S.l.], mar. 2017. ISSN 2334-7163. Available at: <http://thermal-science.tech/journal/index.php/thsci/article/view/2219>. Date accessed: 24 nov. 2017. doi: https://doi.org/10.2298/TSCI151009123S.
Section
Articles
Received 2017-03-06
Accepted 2017-03-13
Published 2017-03-13

References

[1] Von Kármán, T., Über Laminare und Turbulente Reibung, ZAMM1 4 (1921), PP. 233- 235.
[2] Cochran, W. G., The Flow due to a Rotatin disk, Proc. Cambridge Phileos. Soc. 30, 3(1934), PP. 365-375
[3] Benton, E. R., On the Flow due to a Rotating Disk, J. Fluid Mech. 24, 4(1966), PP. 781- 800
[4] Hall, P., An Asymptotic Investigation of the Stationary Modes of Instability of the Boundary Layer on a Rotating Disk, Proc Roy. Soc. London Ser. A, 406(1986), PP. 93- 106
[5] Jarre, S. L. G., Chauve, M. P., Experimental Study of Rotating Disk Instability, Phys. Fluids, 8(1996), PP. 496-508
[6] Attia, H. A., Hassan, A., On Hydromagnetic Flow Due to a Rotating Disk, Appl. Math. odel, 28(2004) , PP. 1007-1014
[7] Kelson, N., Desseaux, A., Note on Poroud Rotating Disk, ANZIAM J., 42(2000), PP. 837-855.
[8] Maleque, Kh. A., Sattar, M. A., The Effect of Variable Properties on Steady Laminar Convective Flow due to a Porous Rotating Disk, ASME J. Heat Transfer, 127(2005b), PP. 1406-1409
[9] Sparrow, E. M., and Gregg, J. L., Mass Transfer Flow and Heat Transfer About a Rotating Disk, ASME J. Heat Transfer, (1960), PP. 294-302
[10] Turkyilmazoglu, M., Exact Solution for the Incompressible Viscous Fluid of Porous Rotating Disk, Int. Non-linear Mech., 44( 2009), PP. 352-357
[11] Anjali Devi, S. P., Uma Devi, R., On Hydromagnetic Flow due to Rotating Disk with Radiation Effects, Nonlinear Analysis:Modeling Control, 16(2011), PP. 17-29
[12] Hassan, A. L., Attia, H. A., Flow due to Rotating Disk with Hall Effect, Phys. Letter A, 28(1997), PP. 246-290
[13] Anjali, Devi S. P., Uma, Devi R., Effects of Thermal Radiation on Hydromagnetic Flow due to a Porous Rotating Disk with Hall Effect, J. of Applied Fluid Mechanics, 5(2012), PP. 1-7
[14] Khidir, A. A., Viscous Dissipation, Ohmic Heating and Radiation effects on MHD Flow Past a Rotating Disk Embedded in a Pporous Medium with Variable Properties, Arab. J. Math., 2(2013), PP. 263-277.
[15] Choi, S. U. S., Enhancing Thermal Conductivity of Fluids With Nanoparticles, in: The proceedings of ASME International Mechanical Engineering Congress and Exposition, San Francesco, USA, ASME, FED 231/MD (1995), pp. 99-105.
[16] Wang, X. Q., Mujumdar, A. S., Heat Transfer Characteristics of Nano-Fluids: a Review, Int. J. Ther. Sci., 46(2007), PP. 1-19.
[17] Khanafer, R., Vafai, K., Lightstone, M., Buoyancy-driven Heat Transfer Enhancement in a two-Dimensional Enclosure Utilizing Nanofluids, Int. J. Heat Mass Transfer, 46(2003), PP. 3639-3653.
[18] Masuda, H., Ebata,A., Teramea, K., Hishinuma, N., Altering the Thermal Conductivity and Viscosity of Liquid by Dispersing Ultra-Fine Particles, Netsu Bussei, 4 (1993), PP. 227-233.
[19] Das, S., Temperature Dependence of Thermal Conductivity Enhancement for Nanofluids, J. Heat Transfer, 125 (2003), PP. 567-574).
[20] Pak, B. C., Cho, Y., Hydrodynamic and Heat Transfer Study of Dispersed Fluids with Submicron Metallic Oxide Particles, Exp. Heat transfer, 11 (1998), PP. 151-170.
[21] Xuan, Y., Li, Q., Investigation on Convective Heat Transfer and Flow Features of Nanofluids, J. Heat Transfer, 125 (2003), PP. 151-155.
[22] Eastman, J. A., Choi, S. U. S., Li, S., Yu, W., Thompo, L. J., Anomalously Increased Effective Thermal Conductivity of Ethylene Glycol-Based Nanofluids Containing Copper Nano-Particles, Appl. Phys. Lett., 78 (2001), PP. 718-725.
[23] Minsta, H. A., Roy, G., Nguyen, C. T., Doucet, D., New Temperature Dependent Thermal Conductivity Data for Water-Based Nanofluids, Int. j. Therm. Sci., 48 (2009), PP. 363-371.
[24] Bachok, N., Ishak, A., Pop, I., Flow and Heat Transfer Over a Rotating Porous Disk in a Nanofluid, Physica A, 406(2011), PP. 1767-1772.
[25] Mustafa, T., Nanofluid Flow and Heat Transfer due to a Rotating Disk, Computers &Fluids, 64(2014), PP. 139-146.
[26] Acrivos, A., Shah J., Petersen, E., On the Flow of a Non-Newtonian Liquid on a Rotating Disk, J. of Applied Physics, 31(1960), 6, PP. 963-968.
[27] Mitschka, P., and Ulbricht, J., Nicht-Newtonsche Flüssigkeiten IV. Strömung Nicht- Newtonscher Flüssigkeiten Ostwald-de-Waeleschen Ttyps in der Umgebung Rotierender Drehkegel und Scheiben, NCollect. Czech. Chem. Commun. 30 (1965), PP. 2511-2526
[28] Wichterle, K., and Mitschka, P., Relative Shear Deformation of Non-Newtonian Liquids in Impeller Induced Flow, Collect. Czech. Chem. Commun., 63(1998), PP.2092- 2102
[29] Andersson, H. I., De Korte E., Meland, R., Flow of a Power-Law Fluid Over a Rotating Disk Revisited, Fluid Dynamics Research, 28(2001), PP. 75-88
[30] El-Mistikawy T. M. A., and Attia, H. A., The Rotating Disk Fflow in the Presence of Strong Magnetic Field, Proc. 3rd Int. Cong. Of Fluid Mech., Cairo, Egypt, 3(1990), PP. 1211
[31] Hossian, Md. A., Akter Hossain and Mike Wilson, Unsteady Flow of Viscous Incompressible Fluid with Temperature-Dependent Viscosity due to a Rotating Disk in Presence of Transverse Magnetic Field and Heat Transfer, Int. J. Therm. Sci., 40(2001), PP. 11-20
[32] Takhar, H. S., Singh, A. K., and Nath, G., Unsteady MHD Flow and Heat Transfer on a Rotating Disk in Ambient Fluid, Int. J. Therm. Sci., 41(2002) ,PP. 147-155
[33] Andersson H. I., and Korte, E. De., MHD Flow of a Power-Law Fluid Over a Rotating Disk, European J. of Mechanics B/Fluids, 21(2002), PP. 317-324
[34] Hassan A. L. A., and Attia, H. A., Flow due to a Rotating Disk with Hall Effect, Phys. Lett. A. 228(1997), PP. 246-290
[35] Attia, H. A. and Aboul-Hassan, A. L., On Hydromagnetic Flow due to a Rotating Disk, Applied Mathematical Modelling, 28(2004), PP. 1007-1014
[36] Abdul Maleque, Kh., and Abdus Sttar, Md., The Effects of Variable Properties and Hall Current on Steady MHD Laminar Cconvective Fluid Flow Due to a Porous Rotating Disk, Int. J. of Heat and Mass Transfer, 48(2005), PP. 4963-4972.
[37] Abo-Eldahab, E. M., and Salem, A. M., MHD Flow and Heat Transfer of Non-Newtonian Power-Law Fluid with Diffusion and Chemical Reaction on Moving Cylinder, Heat Mass Transfer, 41(2005), PP. 703-708
[38] Chunying, M., Liancun, Z., and Xinxin, Z., Steady Flow and Heat Transfer of the Power-Law Fluid Over a Rrotating Disk, Int. Comm. In Heat and Mass Transfer, 38(2011), PP. 280-284
[39] Tiwari, I. K. and Das, M. K. Heat Transfer Augmentation in a Two-Sided Lid-Driven Differentially Heated Square Cavity Utilizing Nanofluids, Int. J. Heat Mass Trans., 50(2007), PP. 2002-2018
[40] Zwillinger, D., Handbook of Differential Equations, Second Ed., Academic Press, New York (1992).
[41] G. W. Stton, A. Sherman, Engineering Magnetohydrodynamics, McGraw-Hill, New York (1965).
[42] Zheng, H., Lian-Cun, H., Zhang, H., Xin-Xin, H., Ma, H., Lian-Xi, H., Fully Developed Convective Heat Transfer of Power Law Fluids in Circular Tube, Chinese Physics Letters, 25(2008), PP. 195-197.
[43] Mitschka, P., Nicht-Newtonsche Flüssigkeiten II. Drehströmung Ostwald-de Waelescher Nicht-Newtonscher Flüssigkeiten. Coll. Czech. Chem. Comm. 29,(1964), PP. 2892- 2905