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Advances in Mechanical Engineering Volume 12 ,Issue 2 ,2020-02-01
Flow over a non-uniform sheet with non-uniform stretching (shrinking) and porous velocities
Research Article
Aftab Alam 1 Dil Nawaz Khan Marwat 1 Saleem Asghar 2
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DOI:10.1177/1687814020909000
Received 2019-7-18, accepted for publication 2020-1-31, Published 2020-02-01
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摘要

Viscous flow over a porous and stretching (shrinking) surface of an arbitrary shape is investigated in this article. New dimensions of the modeled problem are explored through the existing mathematical analogies in such a way that it generalizes the classical simulations. The latest principles provide a framework for unification, and the consolidated approach modifies the classical formulations. A realistic model is presented with new features in order to explain variety of previous observations on the said problems. As a result, new and upgraded version of the problem is appeared for all such models. A set of new, unusual, and generalized transformations is formed for the velocity components and similarity variables. The modified transformations are equipped with generalized stretching (shrinking), porous velocities, and surface geometry. The boundary layer governing equations are reduced into a set of ordinary differential equations (ODEs) by using the unification procedure and technique. The set of ODEs has two unknown functions f and g. The modeled equations have five different parameters, which help us to reduce the problem into all previous formulations. The problem is solved analytically and numerically. The current simulation and its solutions are also compared with existing models for specific value of the parameters, and excellent agreement is found between the solutions.

关键词

arbitrary surface;injection/suction;Stretching/shrinking

授权许可

© The Author(s) 2020
This article is distributed under the terms of the Creative Commons Attribution 4.0 License (https://creativecommons.org/licenses/by/4.0/) which permits any use, reproduction and distribution of the work without further permission provided the original work is attributed as specified on the SAGE and Open Access pages (https://us.sagepub.com/en-us/nam/open-access-at-sage).

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通讯作者

Aftab Alam.Department of Mathematics, Faculty of Technologies and Engineering Sciences, Islamia College Peshawar, Peshawar, Pakistan.aftab@icp.edu.pk

推荐引用方式

Aftab Alam,Dil Nawaz Khan Marwat,Saleem Asghar. Flow over a non-uniform sheet with non-uniform stretching (shrinking) and porous velocities. Advances in Mechanical Engineering ,Vol.12, Issue 2(2020)

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参考文献
[1] SJ. Liao A new branch of solutions of boundary-layer flows over a permeable stretching plate. Int J Non Lin Mech 2007; 42: 819–830.
[2] HS Takhar, AJ Chamkha, G. Nath Unsteady flow and heat transfer on a semi-infinite flat plate with an aligned magnetic field. Int J Eng Sci 1999; 37: 1723–1736.
[3] T Altan, S Oh, H. Gegel Metal forming fundamentals and applications. Cleveland, OH: ASM International, 1983.
[4] HS Takhar, AJ Chamkha, G. Nath Unsteady three-dimensional MHD-boundary-layer flow due to the impulsive motion of a stretching surface. Acta Mech 2001; 146: 59–71.
[5] RSR Gorla, AJ Chamkha. Natural convective boundary layer flow over a nonisothermal vertical plate embedded in a porous medium saturated with a nanofluid. Nanoscale Microscale Thermophys Eng 2011; 15: 81–94.
[6] C RamReddy, PVSN Murthy, AJ Chamkha, AM. Rashad et al. Soret effect on mixed convection flow in a nanofluid under convective boundary condition. International Journal of Heat and Mass Transfer 2013; 64: 384–392.
[7] AJ Chamkha, RA Mohamed, SE. Ahmed Unsteady MHD natural convection from a heated vertical porous plate in a micropolar fluid with Joule heating, chemical reaction and radiation effects. Meccanica 2011; 46: 399–411.
[8] HS Takhar, AJ Chamkha, G. Nath Flow and mass transfer on a stretching sheet with a magnetic field and chemically reactive species. Int J Eng Sci 2000; 38: 1303–1314.
[9] S Ghosh, S Mukhopadhyay, K. Vajravelu Dual solutions of slip flow past a nonlinearly shrinking permeable sheet. Alex Eng J 2016; 55: 1835–1840.
[10] T Fang, J Zhang, Y. Zhong Boundary layer flow over a stretching sheet with variable thickness. Appl Math Comput 2012; 218: 7241–7252.
[11] JB McLeod, KR. Rajagopal On the uniqueness of flow of a Navier-Stokes fluid due to a stretching boundary. Arch Rational Mech An 1987; 98: 385–393.
[12] AJ Chamkha, M Jaradat, I. Pop Three-dimensional micropolar flow due to a stretching flat surface. Int J Fluid Mech Res 2003; 30: 357–366.
[13] WHH Banks, MB Zaturska. Eigensolutions in boundary-layer flow adjacent to a stretching wall. IMA J Appl Math 1986; 36: 263–273.
[14] WHH Banks. Similarity solutions of the boundary-layer equations for a stretching wall. J De Mecanique Theorique Appliquee 1983; 2: 375–392.
[15] EG. Fisher Extrusion of plastics. New York: John Wiley & Sons, 1976.
[16] AJ Chamkha, S Abbasbandy, AM. Rashad Non-Darcy natural convection flow for non-Newtonian nanofluid over cone saturated in porous medium with uniform heat and volume fraction fluxes. Int J Numer Method Heat Fluid Flow 2015; 25: 422–437.
[17] S Asghar, A Ahmad, A. Alsaedi Flow of a viscous fluid over an impermeable shrinking sheet. Appl Math Lett 2013; 26: 1165–1168.
[18] RA Damseh, MQ Al-Odat, AJ Chamkha, et al. Combined effect of heat generation or absorption and first-order chemical reaction on micropolar fluid flows over a uniformly stretched permeable surface. Int J Therm Sci 2009; 48: 1658–1663.
[19] LJ Grubka, KM. Bobba Heat transfer characteristics of a continuous stretching surface with variable temperature. J Heat Trans 1985; 107: 248–250.
[20] LJ. Crane Flow past a stretching plate. Zeitschrift Für Angewandte Mathematik Und Physik (ZAMP) 1970; 21: 645–647.
[21] Z Tadmor, I. Klein Engineering principles of plasticating extrusion. New York: Van Nostrand Reinhold, 1970.
[22] WD Chang, ND Kazarinoff, C. Lu A new family of explicit solutions for the similarity equations modelling flow of a non-Newtonian fluid over a stretching sheet. Arch Rational Mech An 1991; 113: 191–195.
[23] MA Chaudhary, JH Merkin, I. Pop Similarity solutions in the free convection boundary-layer flows adjacent to vertical permeable surfaces in porous media. Europ J Mech B: Fluid 1995; 14: 217–237.
[24] BC. Sakiadis Boundary-Layer behavior on continuous solid surfaces: (II). The boundary layer on a continuous flat surface. Aiche J 1961; 7: 26–28.
[25] PS Lawrence, BN. Rao The nonuniqueness of the MHD flow of a viscoelastic fluid past a stretching sheet. Acta Mech 1995; 112: 223–228.
[26] M Sheikholeslami, AJ. Chamkha Influence of Lorentz forces on nanofluid forced convection considering Marangoni convection. J Mol Liquid 2017; 225: 750–757.
[27] QM Al-Mdallal, MI Syam, PD. Ariel A reliable method for boundary layer due to an exponentially stretching continuous surface. Am J Fluid Dynam 2012; 2: 5–13.
[28] MEM Khedr, AJ Chamkha, M. Bayomi MHD flow of a micropolar fluid past a stretched permeable surface with heat generation or absorption. Nonlin Anal 2009; 14: 27–40.
[29] T. Fang Boundary layer flow over a shrinking sheet with power-law velocity. Int J Heat Mass Tran 2008; 51: 5838–5843.
[30] M Ghalambaz, E Izadpanahi, A Noghrehabadi, et al. Study of the boundary layer heat transfer of nanofluids over a stretching sheet: passive control of nanoparticles on the surface. Canad J Phys 2015; 93: 725–733.
[31] E Magyari, AJ. Chamkha Exact analytical results for the thermosolutal MHD Marangoni boundary layers. Int J Thermal Sci 2008; 47: 848–857.
[32] AJ Chamkha, S Abbasbandy, AM Rashad, et al. Radiation effects on mixed convection about a cone embedded in a porous medium filled with a nanofluid. Meccanica 2013; 48: 275–285.
[33] AJ Chamkha, AF Al-Mudhaf, I. Pop Effect of heat generation or absorption on thermophoretic free convection boundary layer from a vertical flat plate embedded in a porous medium. Int Commun Heat Mass Tran 2006; 33: 1096–1102.
[34] HS Takhar, AJ Chamkha, G. Nath MHD flow over a moving plate in a rotating fluid with magnetic field Hall currents and free stream velocity. Int J Eng Sci 2002; 40: 1511–1527.
[35] M Madhu, N Kishan, AJ. Chamkha Boundary layer flow and heat transfer of a non-Newtonian nanofluid over a non-linearly stretching sheet. Int J Numer Method Heat Fluid Flow 2016; 26: 2198–2217.
[36] M Sajjid, T. Hayat Influence of thermal radiation on the boundary layer flow due to an exponentially stretching sheet. Int Commun Heat Mass Tran 2008; 35: 347–356.
[37] A Ali, DNK Marwat, S. Asghar New approach to the exact solution of viscous flow due to stretching (shrinking) and porous sheet. Result Phys 2017; 7: 1122–1127.
[38] KV Prasad, K Vajravelu, I. Pop Flow and heat transfer at a nonlinearly shrinking porous sheet: the case of asymptotically large powerlaw shrinking rates. Int J Appl Mech Eng 2013; 18: 779–791.
[39] E Magyari, B. Keller Exact solutions for self-similar boundary-layer flows induced by permeable stretching walls. Europ J Mech B: Fluid 2000; 19: 109–122.
[40] T Fang, J. Zhang Flow between two stretchable disks an exact solution of the Navier-Stokes equations. Int Commun Heat Mass Transfer 2008; 35: 892–905.
[41] V. Kármán Über laminare und turbulente reibung. ZAMM 1921; 1: 233–252.
[42] AJ Chamkha, ARA Khaled. Similarity solutions for hydromagnetic mixed convection heat and mass transfer for Hiemenz flow through porous media. Int J Numer Method Heat Fluid Flow 2000; 10: 94–115.
[43] M Miklavcic, CY. Wang Viscous flow due to a shrinking sheet. Quart Appl Math 2006; 64: 283–290.
[44] E Magyari, I Pop, B. Keller The “missing” similarity boundary-layer flow over a moving plane surface. Zeitschrift Für Angewandte Mathematik Und Physik (ZAMP) 2002; 53: 782–793.
[45] HS Takhar, AJ Chamkha, G. Nath Unsteady mixed convection flow from a rotating vertical cone with a magnetic field. Heat Mass Tran 2003; 39: 297–304.
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