# MHD EFFECTS ON NANOFLUID WITH ENERGY AND HYDROTHERMAL BEHAVIOR BETWEEN TWO COLLATERAL PLATES: APPLICATON OF NEW SEMI ANALYTICAL TECHNIQUE

## Main Article Content

## Abstract

In this study, heat and mass transfer characteristic of unsteady nanofluid flow between parallel plates is investigated. The important effect of Brownian motion and thermophoresis has been included in the model of nanofluid. The governing equations are solved via Differential Transformation Method. The validity of this method was verified by comparison previous work which is done for viscous fluid. The analytical investigation is carried out for different governing parameters namely; the squeeze number, Hartmann number, Schmidt number, Brownian motion parameter, thermophoretic parameter and Eckert number. The results indicate that skin friction coefficient has direct relationship with Hartmann number and squeeze number. Also it can be found that Nusselt number increases with increase of Hartmann number, Eckert number and Schmidt number but it is decreases with augment of squeeze number.

## Article Details

**Thermal Science**, [S.l.], mar. 2017. ISSN 2334-7163. Available at: <http://thermal-science.tech/journal/index.php/thsci/article/view/2121>. Date accessed: 23 june 2017. doi: https://doi.org/10.2298/TSCI150228095S.

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Accepted 2017-03-13

Published 2017-03-13

## References

[2] R.Y. Jou, S.C. Tzeng, Numerical research of nature convective heat transfer enhancement filled with nanofluids in rectangular enclosures, International Communications in Heat and Mass Transfer 33 (2006), pp. 727–36.

[3] M.M. Rashidi, S.Abelman, N. Freidooni Mehr, Entropy generation in steady MHD flow due to a rotating porous disk in a nanofluid, International Journal of Heat and Mass Transfer 62 (2013), pp. 515– 525.

[4] Mohsen Sheikholeslami, Mohammad Mehdi Rashidi, Effect of space dependent magnetic field on free convection of Fe3O4-water nanofluid, Journal of the Taiwan Institute of Chemical Engineers, (2015) DOI: 10.1016/j.jtice.2015.03.035.

[5] Mohsen Sheikholeslami, Mofid Gorji Bandpy, Hamid Reza Ashorynejad, 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.

[6] R. Ellahi, The effects of MHD and temperature dependent viscosity on the flow of non-Newtonian nanofluid in a pipe: Analytical solutions, Applied Mathematical Modelling 37 (2013), pp. 1451-1467.

[7] S. Nadeem, R.U. Haq, N.S. Akbar, MHD Three-Dimensional Boundary Layer Flow of Casson Nanofluid Past a Linearly Stretching Sheet With Convective Boundary Condition, IEEE Transactions on Nanotechnology 13(2014),pp.109-115.

[8] N.S Akbar, Metallic Nanoparticles Analysis for the Peristaltic Flow in an Asymmetric Channel With MHD, IEEE Transactions on Nanotechnology 13(2014), pp. 357 - 361.

[9] Mohsen Sheikholeslami, Mofid Gorji-Bandpy, Davood Domiri Ganji, Review of heat transfer enhancement methods: Focus on passive methods using swirl flow devices Renewable and Sustainable Energy Reviews 49 (2015),pp. 444–469.

[10] M. Sheikholeslami and R. Ellahi, Simulation of ferrofluid flow for magnetic drug targeting using Lattice Boltzmann method, Journal of Zeitschrift Fur Naturforschung A, Verlag der Zeitschrift für Naturforschung ,70 (2015),pp. 115–124.

[11] Mohsen Sheikholeslami, M. Hatami, M. Jafaryar, F. Farkhadni, Davood Domiri Ganji, Mofid Gorji-Bandpy, Thermal management of double-pipe air to water heat exchanger, Energy and Buildings 88 (2015), pp. 361–366.

[12] Mohsen Sheikholeslami, M. Jafaryar, F. Farkhadnia, Mofid Gorji-Bandpy, Davood Domiri Ganji, Investigation of turbulent flow and heat transfer in an air to water double-pipe heat exchanger , Neural Computer & Application, 26 (2015),pp. 941-947.

[13] M. Sheikholeslami , R. Ellahi , Mohsan Hassan , Soheil Soleimani, A study of natural convection heat transfer in a nanofluid filled enclosure with elliptic inner cylinder, International Journal of Numerical Methods for Heat & Fluid Flow, 24 (2014),pp. 1906 – 1927.

[14] Mohsen Sheikholeslami Kandelousi, Effect of spatially variable magnetic field on ferrofluid flow and heat transfer considering constant heat flux boundary condition, The European Physical Journal Plus 129 (2014),pp.241 - 248.

[15] Noreen Sher Akbar, Z.H. Khan, Influence of magnetic field for metachoronical beating of cilia for nanofluid with Newtonian heating, Journal of Magnetism and Magnetic Materials, 381( 2015), pp. 235- 242.

[16] S. Nadeem, Rashid Mehmood, Noreen Sher Akbar, Optimized analytical solution for oblique flow of a Casson-nano fluid with convective boundary conditions, International Journal of Thermal Sciences, 78, ( 2014), pp. 90-100.

[17] Noreen Sher Akbar, S. Nadeem, Changhoon Lee, Zafar Hayat Khan, Rizwan Ul Haq, Numerical study of Williamson nano fluid flow in an asymmetric channel, Results in Physics, 3(2013), pp.161-166.

[18] Mohsen Sheikholeslami, Davood Domiri Ganji, Mohammad Mehdi Rashidi, Ferrofluid flow and heat transfer in a semi annulus enclosure in the presence of magnetic source considering thermal radiation, Journal of the Taiwan Institute of Chemical Engineers, 47 (2015),pp. 6–17.

[19] M. Sheikholeslami, M. Hatami, G. Domairry, Numerical simulation of two phase unsteady nanofluid flow and heat transfer between parallel plates in presence of time dependent magnetic field, J Taiwan Inst Chem Eng , 46 (2015),pp. 43–50.

[20] Mohsen Sheikholeslami Kandelousi, KKL correlation for simulation of nanofluid flow and heat transfer in a permeable channel, Physics Letters A, 378 (2014), pp. 3331-3339.

[21] Mohsen Sheikholeslami, Davood Domiri Ganji, Entropy generation of nanofluid in presence of magnetic field using Lattice Boltzmann Method, Physica A, 417 (2015), pp. 273–286.

[22] Mohsen Sheikholeslami, Mofid Gorji-Bandpy and Kuppalapalle Vajravelu, Lattice Boltzmann Simulation of Magnetohydrodynamic Natural Convection Heat Transfer of Al2O3-water Nanofluid in a Horizontal Cylindrical Enclosure with an Inner Triangular Cylinder, International Journal of Heat and Mass Transfer, 80 (2015), pp. 16–25.

[23] M. Sheikholeslami, Effect of uniform suction on nanofluid flow and heat transfer over a cylinder, J Braz. Soc. Mech. Sci. Eng. 2(2014), pp. 212-214

[24] Mohsen Sheikholeslami, Davood Domiri Ganji, M. Younus Javed, R. Ellahi, Effect of thermal radiation on magnetohydrodynamics nanofluid flow and heat transfer by means of two phase model, Journal of Magnetism and Magnetic Materials, 374 (2015), pp. 36–43.

[25] Mohsen Sheikholeslami, Shirley Abelman, Davood Domiri Ganji, Numerical simulation of MHD nanofluid flow and heat transfer considering viscous dissipation, International Journal of Heat and Mass Transfer, 79 (2014),pp. 212–222.

[26] Mohsen Sheikholeslami, Davood Domiri Ganji, Ferrohydrodynamic and Magnetohydrodynamic effects on ferrofluid flow and convective heat transfer, Energy, 75 (2014), pp. 400-410.

[27] Mohsen Sheikholeslami, Mofid Gorji Bandpy, R. Ellahi, A. Zeeshan, Simulation of MHD CuO– water nanofluid flow and convective heat transfer considering Lorentz forces, Journal of Magnetism and Magnetic Materials, 369 (2014), pp. 69–80.

[28] Noreen Sher Akbar, M. Raza, R. Ellahi, Influence of induced magnetic field and heat flux with the suspension of carbon nanotubes for the peristaltic flow in a permeable channel, Journal of Magnetism and Magnetic Materials, 381( 2015), pp. 405-415

[29] Noreen Sher Akbar, S.U. Rahman, R. Ellahi, S. Nadeem, Nano fluid flow in tapering stenosed arteries with permeable walls, International Journal of Thermal Sciences, 85( 2014), pp. 54-61.

[30] R. Ellahi, S.U. Rahman, S. Nadeem, Blood flow of Jeffrey fluid in a catherized tapered artery with the suspension of nanoparticles, Physics Letters A, 378( 2014), pp. 2973-2980.

[31] R. Ellahi, M. Raza, K. Vafai, Series solutions of non-Newtonian nanofluids with Reynolds’ model and Vogel’s model by means of the homotopy analysis method, Mathematical and Computer Modelling, 55( 2012), pp. 1876-1891.

[32] M. Sheikholeslami, M. Gorji-Bandpy, D.D. Ganji, MHD free convection in an eccentric semi- annulus filled with nanofluid, Journal of the Taiwan Institute of Chemical Engineers, 45 (2014),pp. 1204–1216.

[33] M. Sheikholeslami, M. Hatami, D.D. Ganji, Nanofluid flow and heat transfer in a rotating system in the presence of a magnetic field, Journal of Molecular Liquids, 190 (2014), pp. 112–120.

[34] M. Sheikholeslami, M. Gorji Bandpy, R. Ellahi, Mohsan Hassan , Soheil Soleimani, Effects of MHD on Cu-water nanofluid flow and heat transfer by means of CVFEM, Journal of Magnetism and Magnetic Materials, 349 (2014), pp. 188–200.

[35] M. Sheikholeslami, F. Bani Sheykholeslami, S. Khoshhal, H. Mola-Abasi, D. D. Ganji, Houman B. Rokni, Effect of magnetic field on Cu–water nanofluid heat transfer using GMDH-type neural network, Neural Computing & Application,5(2014), pp.171–178.

[36] M. Sheikholeslami, M. Gorji-Bandpay, D.D. Ganji, Magnetic field effects on natural convection around a horizontal circular cylinder inside a square enclosure filled with nanofluid, International Communications in Heat and Mass Transfer, 39 (2012), pp. 978–986.

[37] D.A. Nield, A.V. Kuznetsov, Thermal instability in a porous medium layer saturated by a nanofluid, International Journal of Heat and Mass Transfer, 52 (2009), pp. 5796–5801.

[38] W.A. Khan, I. Pop, Boundary-layer flow of a nanofluid past a stretching sheet, International Journal of Heat and Mass Transfer, 53 (2010), pp. 2477-2483.

[39] Mohsen Sheikholeslami, Shirley Abelman, Two phase simulation of nanofluid flow and heat transfer in an annulus in the presence of an axial magnetic field, IEEE Transactions on Nanotechnology, 2015, DOI: 10.1109/TNANO.2015.2416318

[40] M. Sheikholeslami, D.D. Ganji, Three dimensional heat and mass transfer in a rotating system using nanofluid, Powder Technology, 253 (2014), pp. 789–796.

[41] M. Sheikholeslami, D.D. Ganji, M. Gorji-Bandpy, Soheil Soleimani, Magnetic field effect on nanofluid flow and heat transfer using KKL model, Journal of the Taiwan Institute of Chemical Engineers, 45 (2014), pp. 795–807.

[42] M. Sheikholeslami, M. Gorji-Bandpy, Soheil Soleimani, Two phase simulation of nanofluid flow and heat transfer using heatline analysis, International Communications in Heat and Mass Transfer, 47 (2013), pp. 73–81.

[43] M. Sheikholeslami, M. Gorji-Bandpy, D.D. Ganji, Natural convection in a nanofluid filled concentric annulus between an outer square cylinder and an inner elliptic cylinder, Scientia Iranica, Transaction B: Mechanical Engineering, 20 (2013), pp. 1241-1253.

[44] M.J. Stefan, Versuch Über die scheinbare adhesion, Akad Wissensch Wien Math Nature, 69 (1874), pp. 713–721.

[45] M. Mahmood, S. Asghar, MA. Hossain, Squeezed flow and heat transfer over a porous surface for viscous fluid. Heat Mass Transf 44(2007), pp.165–173.

[46] K. Zhou, Differential transformation and its applications for electrical circuits, Huazhong Univ. Press,Wuhan,China, (1986).

[47] M.J. Jang, C.L. Chen, YC. Liu, Two-dimensional differential transform for partial differential equations, Applied Math. Comput. 121(2001) 261-270.

[48] M. Mustafa, T. Hayat, S. Obaidat, On heat and mass transfer in the unsteady squeezing flow between parallel plates, Meccanica, DOI 10.1007/s11012-012-9536-3.

[49] Noreen Sher Akbar, S. Nadeem, T. Hayat and Awatif A. Hendi, Influence of mixed convection on blood flow of Jeffrey fluid through a tapered stenosed artery, Journal of thermal sciences, 17(2013), pp.533-546