ANALYTICAL AND NUMERICAL STUDY OF HYDRODYNAMIC NANO FLUID FLOW IN A TWO –DIMENSIONAL SEMI-POROUS CHANNEL WITH TRANSVERSE MAGNETIC FIELD

Nozar Akbarı; Mosayeb Gholınıa; Saber Gholınıa; Shoeil Dabbaghıan; Davood Domiri Ganjı

ANALYTICAL AND NUMERICAL STUDY OF HYDRODYNAMIC NANO FLUID FLOW IN A TWO –DIMENSIONAL SEMI-POROUS CHANNEL WITH TRANSVERSE MAGNETIC FIELD

Abstract

In this research, we used Akbari-Ganji’s Method (AGM) to solve the issue of laminar Nano fluid flow in a semi-porous channel in the presence of latitudinal magnetic field. The effectual viscosity and thermal conductivity of Nano fluid flow are computed by Brinkman and Maxwell–Garnetts (MG) models, respectively. Also, the concept of Akbari-Ganji’s Method is briefly employed and introduced to derive solutions of nonlinear equations. The received outcomes of AGM are compared with those of acquired from Numerical Method (fourth-order Runge–Kutta method), Collocation Method (CM), Homotopy Perturbation Method (HPM) and Flex-PDE software to check the precision of the considered manner. In the present perusal, the impact of the three dimensionless numbers like the Nano fluid volume fraction, Reynolds number and Hartmann number on non-dimensional velocity profiles are examined. Outcomes show when Ha is tiny, the impact of Re number is very sensible on the velocity profiles but in Ha large, Re number is less impact. In addition, this study shows AGM is strong manner to solve nonlinear differential equations.

Keywords

References

[1] M. Hatami, D.D. Ganji, Motion of a spherical particle in a fluid forced vortex by DQM and DTM. Particuology, Volume16, 2014, Pages 206-212.
[2] Seiyed E. Ghasemi, M. Hatami, A. Kalani Sarokolaie and D.D. Ganji, Study on Blood flow containing Nanoparticles trough porous arteries in presence of magnetic field using analytical methods, Physica E: Lowdimensional Systems and Nanostructures, Volume 70, October 2015, Pages 146–156.
[3] A.F. Jameela, A.I.M. Ismaila, F. Mabood, Optimal homotopy asymptotic method for solving nth order linear fuzzy initial value problems, Journal of the Association of Arab Universities for Basic and Applied Sciences Volume 21, 2016, Pages 77–85.
[4] D.D. Ganji, M. Gorji, M. Hatami, A. Hasanpour, N. Khademzadeh, Propulsion and launching analysis of variable-mass rockets by analytical methods, Propulsion and Power Research, Volume 2, Issue3, 2013, Pages 225-233
[5] M. Hatami, S. Vahdani, D.D. Ganji, Deflection prediction of a cantilever beam subjected to static co-planar loading by analytical methods, Housing and Building National Research Center HBRC Journal, Volume 10, 2014, Pages 191-197.
[6] M. Hatami, Dengwei Jing, Dongxing Song, M. Sheikholeslami, D.D. Ganji, Heat transfer and flow analysis of Nano fluid flow between parallel plates in presence of variable magnetic field using HPM, Journal of Magnetism and Magnetic Materials, Volume 396, 2015, Pages 275-282.
[7] M. Sheikholeslami, M. Hatami, D.D. Ganji, Micropolar fluid flow and heat transfer in a permeable channel using analytical method, Journal of Molecular Liquids, Volume 194, 2014, Pages 30-36.
[8] He. Ji-Huan and Wu. Xu-Hong, Exp-function method for nonlinear wave equations, Chaos, Solitons and Fractals 30 (2006) 700–708.

[9] Z. Sheng, Exp-function method for solving Maccari’s system, Physics Letters A 371 (2007) 65–71.
[10] A. M. WAZWAZ, A Sine-Cosine Method for Handling Nonlinear Wave Equations, Mathematical and Computer Modelling 40 (2004) 499-508.
[11] A. M. WAZWAZ, The Tanh and the Sine-Cosine Method s for the Complex Modified K dV and the Generalized K dV Equations, Computers and Mathematics with Applications 49 (2005) 1101-1112.
[12] M. Hatami, D. Song, D. Jing, Optimization of a circular-wavy cavity filled by nanofluid under the natural convection heat transfer condition, International Journal of Heat and Mass Transfer, Volume 98, 2016, Pages 758-767.
[13] M. Hatami, Nanoparticles migration around the heated cylinder during the RSM optimization of a wavy-wall enclosure, Advanced Powder Technology, Volume 28, 2017, Pages 890-899.
[14] W. Luwai, A modified tanh–coth method for solving the general Burgers–Fisher and the Kuramoto–Sivashinsky equations, Commun Nonlinear Sci Numer Simulat 14 (2009) 2642–2652.
[15] Ömer Faruk Gözükızıl and ¸Samil Akçagıl, The tanh-coth method for some nonlinear pseudoparabolic equations with exact solutions, Gözükızıl and Akçagıl Advances in Difference Equations 2013, 2013:143.
[16] V. Wernert, O. Schäf, H. Ghobarkar, R. Denoyel, Adsorption properties of zeolites for artiﬁcial kidney applications, Microporous and Mesoporous Materials 83 (1–3) (2005) 101–113.
[17] A. Jafari, P. Zamankhan, S.M. Mousavi, P. Kolari, Numerical investigation of blood ﬂow part II: in capillaries, Communications in Nonlinear Science and Numerical Simulation 14 (2009) 1396–1402.
[18] A.R. Goerke, J. Leung, S.R. Wickramasinghe, Mass and momentum transfer in blood oxygenators, Chemical Engineering Science 57 (2002) 2035–2046.
[19] A. Runstedtler, on the modiﬁed Stefan–Maxwell equation for isothermal multi com- ponent gaseous diffusion, Chemical Engineering Science 61 (2006) 5021–5029.
[20] Y.H. Andoh, B. Lips, Prediction of porous walls thermal protection by effusion or transpiration cooling: an analytical approach, Applied Thermal Engineering 23 (2003) 1947–1958.
[21] S.S. Mneina, G.O. Martens, Linear phase matched ﬁlter design with causal real symmetric impulse response, AEU International Journal of Electronics and Com- munications 63 (2009) 83–91.
[22] A.S. Berman, Journal of Applied Physics 24 (1953) 1232.
[23] M. Fakour, D.D. Ganji, M. Abbasi, Scrutiny of underdeveloped nanofluid MHD flow and heat conduction in a channel with porous walls, Case Studies in Thermal Engineering 4 (2014) 202–214.
[24] M. Sheikholeslami, M. Hatami, D. D. Ganji, Analytical investigation of MHD nanofluid flow in a Semi-Porous Channel, Powder Technology 10 (2013).
[25] M.M. Rashidi, T. Hayatb, E. Erfania, Poura SAMohimanian, Hendi Awatif A. Simultaneous effects of partial slip and thermal-diffusion and diffusion- thermo on steady MHD convective flow due to a rotating disk. Commun Nonlinear Sci Numer Simul 2011; 16(11):4303–17.
[26] P. Chandran, N.C. Sacheti, A.K. Singh, International Communications in Heat and Mass Transfer 23 (1996) 889.
[27] M.A.A. Hamad, I. Pop, A.I. Md Ismail, Magnetic ﬁeld effects on free convection ﬂow of a nanoﬂuid past a vertical semi-inﬁnite ﬂat plate, Nonlinear Analysis: Real World Applications 12 (2011) 1338–1346.
[28] H.R. Ashorynejad, M. Sheikholeslami, I. Pop, D.D. Ganji, Nanoﬂuid ﬂow and heat transfer due to a stretching cylinder in the presence of magnetic ﬁeld, Heat and Mass Transfer 49 (2013) 427–436.
[29] M. Sheikholeslami, H.R. Ashorynejad, D.D. Ganji, I. Hashim, Investigation of the laminar viscous ﬂow in a semi-porous channel in the presence of uniform magnetic ﬁeld using optimal homotopy asymptotic method, Sains Malaysiana 41 (10) (2012) 1177–1229.
[30] M. Sheikholeslami, M. Gorji-Bandpy, D.D. Ganji, S. Soleimani, Natural convec- tion heat transfer in a cavity with sinusoidal wall ﬁlled with CuO-water nanoﬂuid in presence of magnetic ﬁeld, Journal of the Taiwan Institute of Chemical Engi- neers (2013), http://dx.doi.org/10.1016/j.jtice.2013.04.019.
[31] M. Sheikholeslami, M. Gorji-Bandpy, D.D. Ganji, S. Soleimani, Effect of a mag- netic ﬁeld on natural convection in an inclined half- annulus enclosure ﬁlled with Cu-water nanoﬂuid using CVFEM, Advanced Powder Technology (2013), http: //dx.doi.org/10.1016/j.apt.2013.01.012.
[32] M. Hatami, J. Zhou, J. Geng, D. Song, D. Jing, Optimization of a lid-driven T-shaped porous cavity to improve the nanofluids mixed convection heat transfer, Journal of Molecular Liquids, Volume 231, 2017, Pages 620-631.
[33] M. Hatami, D.D. Ganji, Motion of a spherical particle on a rotating parabola using Lagrangian and high accuracy Multi-step Differential Transformation Method, Powder Technology, Volume 258, 2014, Pages 94-98.
[34] A.S. Dogonchi, M. Hatami, G. Domairry, Motion analysis of a spherical solid particle in plane Couette Newtonian fluid flow, Powder Technology, Volume 274, 2015, Pages 186-192.
[35] M. Hatami, M. Sheikholeslami, G. Domairry, High Accuracy Analysis for Motion of a Spherical Particle in Plane Couette Fluid Flow by Multi-step Differential Transformation Method, Powder Technology, Volume 260, 2014, Pages 59-67.
[36] M. Sheikholeslami, M. Hatami, D.D. Ganji, Analytical investigation of MHD Nano fluid flow in a semi-porous channel, Powder Technology, Volume 246, 2013, Pages 327-336.
[37] A. Desseaux, Influence of a magnetic field over a laminar viscous flow in a semi-porous channel. Int J Eng Sci 37(1999)1781–94.
[38] S. Soleimani, M. Sheikholeslami, D.D. Ganji, M. Gorji-Bandpay, Natural con- vection heat transfer in a nanoﬂuid ﬁlled semi-annulus enclosure, International Communications in Heat and Mass Transfer 39 (2012) 565–574.
[39] H. Brinkman, "The viscosity of concentrated suspensions and solutions", The Journal of Chemical Physics, Vol. 20, (1952), 571.
[40] M. Sheikholeslami, S. Soleimani, M. Gorji-Bandpy, D.D. Ganji and S. Seyyedi, "Natural convection of nanofluids in an enclosure between a circular and a sinusoidal cylinder in the presence of magnetic field", International Communications in Heat and Mass Transfer, (2012).
[41] Ozisk MN (1993) Heat conduction, 2nd edn. Wiley, USA.
[40] M. Hatami, D.D. Ganji, M. Jafaryar, F. Farkhadnia, Transient combustion analysis for iron micro-particles in a gaseous media by weighted residual methods (WRMs), Case Studies in Thermal Engineering, Volume 4, 2014, Pages 24-31.
[42] A.R. Ahmadi, M.R. Akbari, D.D. Ganji, Nonlinear Dynamic in Engineering by Akbari–Ganji's Method, ISBN– 13:9781514401712 (2015).
[43] M. Hatami, D. Jing, Optimization of Wavy Direct Absorber Solar Collector (WDASC) using Al2O3-water Nanofluid and RSM analysis, Applied Thermal Engineering, Volume 121, 2017, Pages 1040-1050.
[44] R. Nouri, D. D. Ganji, M. Hatami, MHD Nanofluid Flow Analysis in a Semi-Porous Channel by a Combined Series Solution Method, Trans. Phenom. Nano Micro Scales, 1(2): 1 24-1 37.

Details

Primary Language

English

Subjects

Engineering

Journal Section

Research Article

Authors

Nozar Akbarı This is me
0000-0003-0924-8363
Iran

Mosayeb Gholınıa This is me
0000-0001-8291-8824
Iran

Saber Gholınıa This is me
0000-0003-4597-2279
Iran

Shoeil Dabbaghıan This is me
0000-0002-4774-8054
Iran

Davood Domiri Ganjı This is me
0000-0002-4293-5993
Iran

Publication Date

September 1, 2018

Submission Date

April 18, 2018

Acceptance Date

June 27, 2018

Published in Issue

Year 2018 Volume: 36 Number: 3

IZ

https://izlik.org/JA32HG96DG

Cite

RIS / Bibtex

APA

Akbarı, N., Gholınıa, M., Gholınıa, S., Dabbaghıan, S., & Ganjı, D. D. (2018). ANALYTICAL AND NUMERICAL STUDY OF HYDRODYNAMIC NANO FLUID FLOW IN A TWO –DIMENSIONAL SEMI-POROUS CHANNEL WITH TRANSVERSE MAGNETIC FIELD. Sigma Journal of Engineering and Natural Sciences, 36(3), 587-608. https://izlik.org/JA32HG96DG

AMA

1.Akbarı N, Gholınıa M, Gholınıa S, Dabbaghıan S, Ganjı DD. ANALYTICAL AND NUMERICAL STUDY OF HYDRODYNAMIC NANO FLUID FLOW IN A TWO –DIMENSIONAL SEMI-POROUS CHANNEL WITH TRANSVERSE MAGNETIC FIELD. SIGMA. 2018;36(3):587-608. https://izlik.org/JA32HG96DG

Chicago

Akbarı, Nozar, Mosayeb Gholınıa, Saber Gholınıa, Shoeil Dabbaghıan, and Davood Domiri Ganjı. 2018. “ANALYTICAL AND NUMERICAL STUDY OF HYDRODYNAMIC NANO FLUID FLOW IN A TWO –DIMENSIONAL SEMI-POROUS CHANNEL WITH TRANSVERSE MAGNETIC FIELD”. Sigma Journal of Engineering and Natural Sciences 36 (3): 587-608. https://izlik.org/JA32HG96DG.

EndNote

Akbarı N, Gholınıa M, Gholınıa S, Dabbaghıan S, Ganjı DD (September 1, 2018) ANALYTICAL AND NUMERICAL STUDY OF HYDRODYNAMIC NANO FLUID FLOW IN A TWO –DIMENSIONAL SEMI-POROUS CHANNEL WITH TRANSVERSE MAGNETIC FIELD. Sigma Journal of Engineering and Natural Sciences 36 3 587–608.

IEEE

[1]N. Akbarı, M. Gholınıa, S. Gholınıa, S. Dabbaghıan, and D. D. Ganjı, “ANALYTICAL AND NUMERICAL STUDY OF HYDRODYNAMIC NANO FLUID FLOW IN A TWO –DIMENSIONAL SEMI-POROUS CHANNEL WITH TRANSVERSE MAGNETIC FIELD”, SIGMA, vol. 36, no. 3, pp. 587–608, Sept. 2018, [Online]. Available: https://izlik.org/JA32HG96DG

ISNAD

Akbarı, Nozar - Gholınıa, Mosayeb - Gholınıa, Saber - Dabbaghıan, Shoeil - Ganjı, Davood Domiri. “ANALYTICAL AND NUMERICAL STUDY OF HYDRODYNAMIC NANO FLUID FLOW IN A TWO –DIMENSIONAL SEMI-POROUS CHANNEL WITH TRANSVERSE MAGNETIC FIELD”. Sigma Journal of Engineering and Natural Sciences 36/3 (September 1, 2018): 587-608. https://izlik.org/JA32HG96DG.

JAMA

1.Akbarı N, Gholınıa M, Gholınıa S, Dabbaghıan S, Ganjı DD. ANALYTICAL AND NUMERICAL STUDY OF HYDRODYNAMIC NANO FLUID FLOW IN A TWO –DIMENSIONAL SEMI-POROUS CHANNEL WITH TRANSVERSE MAGNETIC FIELD. SIGMA. 2018;36:587–608.

MLA

Akbarı, Nozar, et al. “ANALYTICAL AND NUMERICAL STUDY OF HYDRODYNAMIC NANO FLUID FLOW IN A TWO –DIMENSIONAL SEMI-POROUS CHANNEL WITH TRANSVERSE MAGNETIC FIELD”. Sigma Journal of Engineering and Natural Sciences, vol. 36, no. 3, Sept. 2018, pp. 587-08, https://izlik.org/JA32HG96DG.

Vancouver

1.Nozar Akbarı, Mosayeb Gholınıa, Saber Gholınıa, Shoeil Dabbaghıan, Davood Domiri Ganjı. ANALYTICAL AND NUMERICAL STUDY OF HYDRODYNAMIC NANO FLUID FLOW IN A TWO –DIMENSIONAL SEMI-POROUS CHANNEL WITH TRANSVERSE MAGNETIC FIELD. SIGMA [Internet]. 2018 Sep. 1;36(3):587-608. Available from: https://izlik.org/JA32HG96DG