Analytical solution of magnetohydrodynamics generalized Burger’s fluid embedded with porosity

Abro, et al.

International Journal of Advanced and Applied Sciences

Int. j. adv. appl. sci.

EISSN: 2313-3724

Print ISSN: 2313-626X

Volume 4, Issue 7 (July 2017), Pages: 80-89

Title: Analytical solution of magnetohydrodynamics generalized Burger’s fluid embedded with porosity

Author(s): Kashif Ali Abro ^1,*, Mukarrum Hussain ², Mirza Mahmood Baig ¹

Affiliation(s):

¹Department of Mathematics, NED University of Engineering Technology, 75270, Karachi, Pakistan
²Institute of Space Technology, 75270, Karachi, Pakistan

https://doi.org/10.21833/ijaas.2017.07.012

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Abstract:

This analysis is devoted to investigate analytical solutions of magnetohydrodynamics (MHD) generalized Burger’s fluid embedded with porous medium as a sum of Newtonian and non-Newtonian forms. The solutions are investigated for velocity field and shear stress and governing partial differential equations have been solved via the integral transforms. The solutions for velocity field and shear stress have been expressed into compact form i-e in terms of series form. The general solutions also satisfy initial and boundary condition and particularized for special cases along with sum of Newtonian and non-Newtonian forms. The impacts of permeability (porosity), magnetism and several rheological parameters have been analyzed for fluid flows by portraying graphical illustrations. The graphs are depicted via latest software namely Mathematica and Mathcad (16) packages.

This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Keywords: Generalized Burger’s model, Porosity, Magnetic field, Analytical solutions and rheological, parameters

Article History: Received 21 February 2017, Received in revised form 7 June 2017, Accepted 8 June 2017

Digital Object Identifier:

https://doi.org/10.21833/ijaas.2017.07.012

Citation:

Abro KA, Hussain M, and Baig MM (2017). Analytical solution of magnetohydrodynamics generalized Burger’s fluid embedded with porosity. International Journal of Advanced and Applied Sciences, 4(7): 80-89

http://www.science-gate.com/IJAAS/V4I7/Abro.html

References:

Abbasbandy S, Hayat T, Alsaedi A, and Rashidi MM (2014). Numerical and analytical solutions for Falkner-Skan flow of MHD Oldroyd-B fluid. International Journal of Numerical Methods for Heat and Fluid Flow, 24(2): 390-401. https://doi.org/10.1108/HFF-05-2012-0096

Abro KA (2016). Porous effects on second grade fluid in oscillating plate. Journal of Applied Environmental and Biological Sciences, 6(5): 17-82.

Abro KA and Shaikh AA (2015). Exact analytical solutions for Maxwell fluid over an oscillating plane. Science International (Lahore) ISSN, 27(2): 923-929.

Ahmad K and Nazar R (2010). Magnetohydrodynamic three-dimensional flow and heat transfer over a stretching surface in a viscoelastic fluid. Journal of Science and Technology, 3(1): 1-14.

Fetecau C, Hayat T, and Fetecau C (2008). Starting solutions for oscillating motions of Oldroyd-B fluids in cylindrical domains. Journal of non-Newtonian Fluid Mechanics, 153(2): 191-201. https://doi.org/10.1016/j.jnnfm.2008.02.005

Freidoonimehr N, Rashidi MM, and Mahmud S (2015). Unsteady MHD free convective flow past a permeable stretching vertical surface in a nano-fluid. International Journal of Thermal Sciences, 87: 136-145. https://doi.org/10.1016/j.ijthermalsci.2014.08.009

Hayat T, Fetecau C, and Sajid M (2008b). Analytic solution for MHD transient rotating flow of a second grade fluid in a porous space. Nonlinear Analysis: Real World Applications, 9(4): 1619-1627. https://doi.org/10.1016/j.nonrwa.2007.04.006

Hayat T, Khan SB, and Khan M (2008a). Exact solution for rotating flows of a generalized Burgers' fluid in a porous space. Applied Mathematical Modelling, 32(5): 749-760. https://doi.org/10.1016/j.apm.2007.02.011

Hayat T, Najam S, Sajid M, Ayub M, and Mesloub S (2010). On exact solutions for oscillatory flows in a generalized Burgers fluid with slip condition. Zeitschrift für Naturforschung A, 65(5): 381-391. https://doi.org/10.1515/zna-2010-0503

Hsiao KL (2011). MHD mixed convection for viscoelastic fluid past a porous wedge. International Journal of Non-Linear Mechanics, 46(1): 1-8. https://doi.org/10.1016/j.ijnonlinmec.2010.06.005

Hussain M, Hayat T, Asghar S, and Fetecau C (2010). Oscillatory flows of second grade fluid in a porous space. Nonlinear Analysis: Real World Applications, 11(4): 2403-2414. https://doi.org/10.1016/j.nonrwa.2009.07.016

Jamil M (2012). First problem of Stokes' for generalized Burgers' fluids. International Scholarly Research Network Mathematical Physics, 2012: Article ID 831063, 17 pages. https://doi.org/10.5402/2012/831063

Jamil M and Fetecau C (2010). Some exact solutions for rotating flows of a generalized Burgers' fluid in cylindrical domains. Journal of Non-Newtonian Fluid Mechanics, 165(23): 1700-1712. https://doi.org/10.1016/j.jnnfm.2010.08.004

Khan I, Ali F, and Shafie S (2012). MHD free convection flow in a porous medium with thermal diffusion and ramped wall temperature. Journal of the Physical Society of Japan, 81(4): 044401. https://doi.org/10.1143/JPSJ.81.044401

Khan M, Hayat T, and Asghar S (2006). Exact solution for MHD flow of a generalized Oldroyd-B fluid with modified Darcy's law. International Journal of Engineering Science, 44(5): 333-339. https://doi.org/10.1016/j.ijengsci.2005.12.004

Khan M, Iqbal K, and Azram M (2011). Closed-form solutions for MHD flow of a second-grade fluid through porous space. Special Topics and Reviews in Porous Media: An International Journal, 2(2): 125–132. https://doi.org/10.1615/SpecialTopicsRevPorousMedia.v2.i2.60

Murali Krishnan J and Rajagopal KR (2004). Thermodynamic framework for the constitutive modeling of asphalt concrete: Theory and applications. Journal of Materials in Civil Engineering, 16(2): 155-166. https://doi.org/10.1061/(ASCE)0899-1561(2004)16:2(155)

Rajagopal KR (1982). A note on unsteady unidirectional flows of a non-Newtonian fluid. International Journal of Non-Linear Mechanics, 17(5-6): 369-373. https://doi.org/10.1016/0020-7462(82)90006-3

Rashidi MM, Ali M, Freidoonimehr N, Rostami B, and Hossain MA (2014). Mixed convective heat transfer for MHD viscoelastic fluid flow over a porous wedge with thermal radiation. Advances in Mechanical Engineering, 6. https://doi.org/10.1155/2014/735939

Rashidi MM, and Erfani E (2012). Analytical method for solving steady MHD convective and slip flow due to a rotating disk with viscous dissipation and Ohmic heating. Engineering Computations, 29(6): 562-579. https://doi.org/10.1108/02644401211246283

Tan W and Masuoka T (2007). Stability analysis of a Maxwell fluid in a porous medium heated from below. Physics Letters A, 360(3): 454-460. https://doi.org/10.1016/j.physleta.2006.08.054

Tong D (2010). Starting solutions for oscillating motions of a generalized Burgers' fluid in cylindrical domains. Acta Mechanica, 214(3): 395-407. https://doi.org/10.1007/s00707-010-0288-7

Zhang Z, Fu C, Tan W, and Wang CY (2007). Onset of oscillatory convection in a porous cylinder saturated with a viscoelastic fluid. Physics of Fluids, 19(9): 098104. https://doi.org/10.1063/1.2773739

Zhaosheng Y and Jianzhong L (1998). Numerical research on the coherent structure in the viscoelastic second order mixing layers. Applied Mathematics and Mechanics, 19(8): 717-723. https://doi.org/10.1007/BF02457746

Zheng L, Liu Y, and Zhang X (2012). Slip effects on MHD flow of a generalized Oldroyd-B fluid with fractional derivative. Nonlinear Analysis: Real World Applications, 13(2): 513-523. https://doi.org/10.1016/j.nonrwa.2011.02.016