# EFFECT OF JOULE HEATING AND HALL CURRENT ON MHD FLOW OF A NANOFLUID DUE TO A ROTATING DISK WITH VISCOUS DISSIPATION

## Main Article Content

## Abstract

The present work provides an analysis of the hydro-magnetic Nanofluid boundary layer flow over a rotating disk in a porous medium with a constant velocity in the presence of hall current and thermal radiation. The governing partial differential equations system that describes the problem is converted to a system of ordinary differential equations by the similarity transformation method, which solved analytically using Optimal Homotopy Asymptotic Method (OHAM). The velocity profiles and temperature profiles of the boundary layer are plotted and investigated in details. Moreover, the surface skin friction, rate of heat transfer are deduced and explained in details.

## Article Details

**Thermal Science**, [S.l.], mar. 2017. ISSN 2334-7163. Available at: <http://thermal-science.tech/journal/index.php/thsci/article/view/2300>. Date accessed: 20 feb. 2018. doi: https://doi.org/10.2298/TSCI160312218A.

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Authors retain copyright of the published article and have the right to use the article in the ways permitted to third parties under the - Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International (CC BY-NC-ND) licence. Full bibliographic information (authors, article title, journal title, volume, issue, pages) about the original publication must be provided and a link must be made to the article's DOI.

The authors and third parties who wish use the article in a way not covered by the the -Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International (CC BY-NC-ND) licence must obtain a written consent of the publisher. This license allows others to download the paper and share it with others as long as they credit the journal, but they cannot change it in any way or use it commercially.

Authors grant to the publisher the right to publish the article, to be cited as its original publisher in case of reuse, and to distribute it in all forms and media.

Accepted 2017-03-14

Published 2017-03-14

## References

[2] W. G. Cochran, The flow due to a rotating disk. Proc. Camb. Philos. Soc. 30 (1934), pp. 365-375

[3] E. R. Benton, on the flow due to a rotating disk. J. Fluid Mech. 24 (1966), pp.781-800

[4] M.G. Rogers and G.N. Lance, The rotationally symmetric flow of a viscous fluid in presence of infinite rotating disk. J. Fluid Mech. 7 (1960), pp.617-631

[5] M. E. Erdogan, Unsteady flow of a viscous fluid due to non-coaxial rotations of a disk and a fluid at infinity, International Journal of Non-Linear Mechanics 32(1997), pp. 285–290

[6] M. Sheikholeslami, M. Hatami, and D. D. Ganji, Nanofluid flow and heat transfer due to rotating disk, Journal of Molecular liquids 190 (2014), pp.112–120

[7] M. Turkyilmazoglu, Nanofluid flow and heat transfer in a rotating system in the presence of a magnetic field, Computers & Fluids 94 (2014), pp.139–146

[8] E.M.A. Elbashbeshy and T.G. Emam, Effects of thermal radiation and heat transfer over an unsteady stretching surface embedded in a porous medium in the presence of heat source or sink, Thermal science, 15(2013), pp. 477-485

[9] T. Hayat, Mahiha Rashid, Maria Imtiaz, and A. Alsaedi, Magneto hydrodynamic (MHD) flow of Cu-Water Nanofluid due to a rotating disk with partial slip, AIP Advances 5 (2015), 067169

[10] S. U. S. Choi, and J. A. Eastman, Enhancing thermal conductivity of fluids with nanoparticles, ASME International Mechanical Engineering Congress and Exposition 66 (1995), pp. 99–105

[11] N. Liron, and H.E. Wilhelm, Integration of the magneto-hydrodynamic boundary layer equations by Meksyn’s method, J. Appl. Math. Mech. (ZAMM) 54 (1974), pp.27–37

[12] E.M.A. Elbashbeshy, T.G. Emam, and Abdel-wahed M. S. The effect of thermal radiation and heat generation on the mechanical properties of unsteady continuous moving cylinder in a Nanofluid in the presence of suction or injection. Thermal science, 19(2015), pp. 1591-1601

[13] E.M.A. Elbashbeshy, T.G. Emam, and M.S. Abdel-wahed. Flow and heat transfer over a moving surface with non-linear velocity and variable thickness in a Nanofluid in the presence of thermal radiation. Can. J. Phys. 91(2013), pp. 699-708

[14] O.D. Makinde, F. Mabood, W.A. Khan, M.S. Tshehla. MHD flow of a variable viscosity Nanofluid over a radially stretching convective surface with radiative heat. Journal of Molecular Liquids, 219(2016), pp. 624-630

[15] S. Khamis, O. D. Makinde, Y. Nkansah-Gyekye: Unsteady flow of variable viscosity Cu- water and Al2O3-water nanofluids in a porous pipe with buoyancy force. International Journal of Numerical Methods in Heat and Fluid Flow, 25(2015), pp.1638 –1657

[16] O. D. Makinde: Effects of viscous dissipation and Newtonian heating on boundary layer flow of nanofluids over a flat plate. International Journal of Numerical Methods for Heat and Fluid flow, 23(2013), pp. 1291-1303

[17] T. G. Motsumi, O. D. Makinde: Effects of thermal radiation and viscous dissipation on boundary layer flow of nanofluids over a permeable moving flat plate. Physical Scripta, 86(2012), 045003(8pp)

[18] M. M. Rashidi, S. Abelman, and N. Freidoonimehr, Entropy generation in steady MHD flow due to a rotating porous disk in a Nanofluid, Int. J. Heat Mass Transfer. 62 (2013), pp. 515- 525

[19] D. S. Chauhan and P. Rastogi, Heat Transfer Effects on Rotating MHD Couette Flow in a Channel Partially Filled by a Porous Medium with Hall Current. Journal of Applied Science and Engineering, 15, 3(2012), pp. 281-290

[20] M. Babaelahi, G. Domairry and A.A. Joneidi, Viscoelastic MHD flow boundary layer over a stretching surface with viscous and ohmic dissipations, Meccanica, 45(2010) , pp. 817–827

[21] M. Sheikholeslami, S. abelman, and D. domiri, Numerical simulation of MHD Nanofluid flow and heat transfer considering viscous dissipation, international journal of heat and mass transfer,79 (2014), pp. 212-222

[22] M.S. Abdel-wahed, E.M.A. Elbashbeshy, T.G. Emam, Flow and heat transfer over a moving surface with non-linear velocity and variable thickness in a Nanofluid in the presence of Brownian motion. Applied Mathematics and computation, 254 (2015), pp. 49-62

[23] S. Liao, An optimal homotopy-analysis approaches for strongly nonlinear differential equations, Commun Nonlinear Sci Numer Simulat, 15(2010), pp. 2003–2016