# FLOW AND HEAT TRANSFER OF MHD GRAPHENE OXIDE-WATER NANOFLUID BETWEEN TWO NON-PARALLEL WALLS

## Main Article Content

## Abstract

The steady two-dimensional heat transfer and flow between two non- parallel walls of a graphene-oxide nanofluid in presence of uniform magnetic field are investigated in this paper. The analytical solution of the nonlinear problem is obtained by Galerkin Optimal Homotopy Asymptotic Method (GOHAM). At first a similarity transformation is used to reduce the partial differential equations modeling the flow and heat transfer to ordinary nonlinear differential equation systems containing the semi angle between the plates parameter, Reynolds number, the magnetic field strength, nanoparticle volume fraction, Eckert and Prandtl numbers. Finally the obtained analytical results have been compared with results achieved from previous works in some cases.

## Article Details

**Thermal Science**, [S.l.], mar. 2017. ISSN 2334-7163. Available at: <http://thermal-science.tech/journal/index.php/thsci/article/view/2133>. Date accessed: 18 oct. 2017. doi: https://doi.org/10.2298/TSCI150513100A.

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 2017-03-13

Published 2017-03-13

## References

[2] Cimpean, D. S., Pop, I., Fully developed mixed convection flow of a nanofluid through an inclined channel filled with a porous medium, Int. J. Heat Mass Transfer, 55 (2012), pp.907–914.

[3] Alfvén, H., Existence of electromagnetic-hydrodynamic waves, Nature, 150 (1942), pp.405-406.

[4] Hartmann, J., Hg-Dynamics I.: Theory of the laminar flow of an electrically conducting liquid in a homogeneous magnetic field, Levin & Munksgaard, Ejnar Munksgaard, 1937.

[5] Saito, K., et al., Ballistic thermal conductance of a graphene sheet, Phys. Rev. B: Condens Matter, 76 (2007), ARTICLE ID: 115409.

[6] Rashidi, M. M., et al., 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.

[7] Ellahi, R., The effects of MHD and temperature dependent viscosity on the flow of non- Newtonian nanofluid in a pipe: Analytical solutions, Appl. Math. Model., 37 (2013), 3, pp.1451-1467.

[8] Sheikholeslami, M., Abelman, S., Two phase simulation of nanofluid flow and heat transfer in an annulus in the presence of an axial magnetic field, IEEE Transactions on Nanotechnology, 14 (2015), 3, pp.561-568, DOI:10.1109/TNANO.2015.2416318.

[9] Sheikholeslami, M., Rashidi, M. M., Effect of space dependent magnetic field on free convection of Fe3O4-water nanofluid, J. Taiwan. Inst. Chem. E, (2015), DOI: 10.1016/j.jtice.2015.03.035.

[10] Sheikholeslami, M., et al., Lattice Boltzmann Method for simulation of magnetic field effect on hydrothermal behavior of nanofluid in a cubic cavity, Physica A: Statistical Mechanics and its Applications, 432 (2015), pp.58-70.

[11] Sheikholeslami Kandelousi, M., Effect of spatially variable magnetic field on ferrofluid flow and heat transfer considering constant heat flux boundary condition, Eur. Phys. J. Plus., 129 (2014), pp.248-260.

[12] Sheikholeslami, M., et al., Investigation of Nanofluid Flow and Heat Transfer in Presence of Magnetic Field Using KKL Model, Arab. J. Sci. Eng., 39 (2014), pp.5007-5016.

[13] Raftari, B., Yildirim, A., The application of homotopy perturbation method for MHD flows of UCM fluids above porous stretching sheets, Comp. Math. Appl., 59 (2010), pp.3328_3337.

[14] Ganji, D. D., Azimi, M., Application of DTM on MHD Jeffery Hamel Problem with Nanoparticles, U.P.B. Scientific Bulletin: D, 75 (2013), 1, pp. 223-230.

[15] Ganji, D. D., et al., Determination of Temperature Distribution for Annular Fins with Temperature Dependent Thermal Conductivity by HPM, Thermal Science, 15 (2011), 1, pp. 111-115.

[16] Azimi, A., Azimi, M., Analytical Investigation on 2-D unsteady MHD Viscoelastic flow between Moving Parallel Plates Using RVIM and HPM, Walailak J. Sci. & Tech. 11 (2014), 11, pp.955-963.

[17] Azimi, M., et al., Investigation of the Unsteady Graphene Oxide Nanoﬂuid Flow Between Two Moving Plates, J. Comput. Theor. NanoScie. 11 (2014), pp.2104-2108.

[18] Ganji, D. D., Azimi, M., Application of Max min Approach and Amplitude Frequency Formulation to the nonlinear oscillation systems, U.P.B. Scientific Bulletin: A 74 (2012), 3, pp.131- 140.

[19] Ganji, D. D., et al., Energy Balance Method and amplitude frequency formulation based of strongly nonlinear oscillator, Indian J. Pure Ap. Mat. 50 ( 2012), pp.670-675.

[20] Sheikholeslami, M., et al., Analytical Investigation of Jeffery Hamel flow with High Magnetic Field and nanoparticle by Adomian Decomposition Method, App. Math Mech. –Engl. Ed, 33 (2012), 1, pp.25-36.