The Non-Alignment Stagnation-Point Flow Towards a Permeable Stretching/Shrinking Sheet in a Nanofluid Using Buongiorno’s Model: A Revised Model
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Rohana Abdul Hamid
Abstract
A numerical study on the stagnation-point boundary layer flow of a viscous and incompressible (Newtonian) fluid past a stretching/shrinking sheet with the fluid suction using Buongiorno’s model is considered. The main focus of this article is the effects of the non-alignment of the flow and the surface of the sheet. We have also studied the problem using a new boundary condition that is more physically realistic which assumes that the nanoparticle fraction at the surface is passively controlled. The governing equations of this problem are reduced to the ordinary differential equations using some similarity transformations which are then solved using the bvp4c function in Matlab. From the results obtained, we concluded that the effect of the non-alignment function is the same as in the regular fluid or nanofluid. However, it is found that the fluid suction can reduce the effect of the non-alignment at the surface. Dual solutions have also been discovered in this problem and from the stability analysis it is found that the first solution is stable while the second solution is not stable.
Acknowledgments
This work was supported by research grants AP-2013-009 from the Universiti Kebangsaan Malaysia and FRGS TOP DOWN from the Ministry of Education, Malaysia. The authors wish to express their very sincere thanks to the Reviewers for the valuable comments and suggestions.
References
[1] M. Ja’fari and A. B. Rahimi, Sci. Iran. 20, 152 (2013).Suche in Google Scholar
[2] C. Y. Wang, Int. J. Nonlinear Mech. 43, 377 (2008).10.1016/j.ijnonlinmec.2007.12.021Suche in Google Scholar
[3] T. Fan, H. Xu, and I. Pop, Int. Commun. Heat Mass Transfer 37, 1440 (2010).10.1016/j.icheatmasstransfer.2010.08.002Suche in Google Scholar
[4] S. Ahmad, M. Ashraf, and K. S. Syed, World Appl. Sci. J. 15, 835 (2011).Suche in Google Scholar
[5] Y. Y. Lok, A. Ishak, and I. Pop, Int. J. Numer. Methods Heat Fluid Flow 21, 61 (2011).10.1108/09615531111095076Suche in Google Scholar
[6] T. R. Mahapatra and S. K. Nandy, J. Appl. Fluid Mech. 6, 121 (2013).Suche in Google Scholar
[7] K. Bhattacharyya, Chem. Eng. Res. Bull. 15, 12 (2011).10.3329/cerb.v15i1.6524Suche in Google Scholar
[8] K. Bhattacharyya, M. G. Arif, and W. A. Pramanik, Acta Tech. 57, 1 (2012).Suche in Google Scholar
[9] K. Bhattacharyya, Ain Shams Eng. J. 4, 259 (2013).10.1016/j.asej.2012.07.002Suche in Google Scholar
[10] K. Bhattacharyya and I. Pop, Magnetohydrodynamics 47, 337 (2011).10.22364/mhd.47.4.2Suche in Google Scholar
[11] K. Bhattacharyya and G. C. Layek, Int. J. Heat Mass Transfer 54, 302 (2011).10.1016/j.ijheatmasstransfer.2010.09.043Suche in Google Scholar
[12] K. Bhattacharyya, T. Hayat, and A. Alsaedi, J. Appl. Math. Mech. 94, 522 (2014).10.1002/zamm.201200031Suche in Google Scholar
[13] N. Najib, N. Bachok, N. M. Arifin, and A. Ishak, Sci. Rep. 4, 4178 (2014).10.1038/srep04178Suche in Google Scholar
[14] H. T. Chien, C. I. Tsai, P. H. Chen, and P. Y. Chen, Fifth Int. Conf. on Electronic Packag. Technol. Proceedings, ICEPT2003, 389 (2003).Suche in Google Scholar
[15] C. Y. Tsai, H. T. Chien, P. P. Ding, B. Chan, T. Y. Luh, et al., Mater. Lett. 58, 1461 (2004).10.1016/j.matlet.2003.10.009Suche in Google Scholar
[16] M. N. Labib, J. Nine, H. Afrianto, H. Chung, and H. Jeong, Int. J. Therm. Sci. 71, 163 (2013).10.1016/j.ijthermalsci.2013.04.003Suche in Google Scholar
[17] A. M. Hussein, R. A. Bakar and K. Kadirgama, Case Stud. Therm. Eng. 2, 50 (2014).10.1016/j.csite.2013.12.001Suche in Google Scholar
[18] M. M. Derakhshan, M. A. Akhavan-Behabadi, and S. G. Mohseni, Exp. Therm. Fluid Sci. 61, 241 (2015).10.1016/j.expthermflusci.2014.11.005Suche in Google Scholar
[19] J. Buongiorno, J. Heat Mass Transfer 128, 240 (2006).10.1115/1.2150834Suche in Google Scholar
[20] M. Corcione, M. Cianfrini, and A. Quintino, Int. J. Therm. Sci. 71, 182 (2013).10.1016/j.ijthermalsci.2013.04.005Suche in Google Scholar
[21] K. Bhattacharyya and G. C. Layek, Phys. Res. Int. 2014, 1 (2014).10.1155/2014/592536Suche in Google Scholar
[22] N. C. Roşca and I. Pop, Comput. Fluids 95, 49 (2014).10.1016/j.compfluid.2014.02.011Suche in Google Scholar
[23] F. Garoosi, S. Garoosi, and K. Hooman, Powder Technol. 268, 279 (2014).10.1016/j.powtec.2014.08.006Suche in Google Scholar
[24] L. Tham, R. Nazar, and I. Pop, Int. J. Therm. Sci. 84, 21 (2014).10.1016/j.ijthermalsci.2014.04.020Suche in Google Scholar
[25] A. V. Kuznetsov and D. A. Nield, Int. J. Heat Mass Transfer 65, 682 (2013).10.1016/j.ijheatmasstransfer.2013.06.054Suche in Google Scholar
[26] A. V. Kuznetsov and D. A. Nield, Int. J. Therm. Sci. 77, 126 (2014).10.1016/j.ijthermalsci.2013.10.007Suche in Google Scholar
[27] D. A. Nield and A. V. Kuznetsov, Int. J. Heat Mass Transfer 77, 915 (2014).10.1016/j.ijheatmasstransfer.2014.06.020Suche in Google Scholar
[28] K. Zaimi, A. Ishak, and I. Pop, PLoS ONE 9, e111743 (2014).10.1371/journal.pone.0111743Suche in Google Scholar PubMed PubMed Central
[29] M. M. Rahman, A. V. Roşca, and I. Pop, Int. J. Heat Mass Transfer 77, 1133 (2014).10.1016/j.ijheatmasstransfer.2014.06.013Suche in Google Scholar
[30] S. Jinjing, L. Yangwei, L. Lipeng, and W. Qiuhui, Procedia Eng. 80, 380 (2014).Suche in Google Scholar
[31] A. Sohankar, M. Khodadadi, and E. Rangraz, Comput. Fluids 109, 155 (2015).10.1016/j.compfluid.2014.12.020Suche in Google Scholar
[32] M. Turkyilmazoglu, Int. J. Mech. Sci. 52, 1735 (2010).10.1016/j.ijmecsci.2010.09.007Suche in Google Scholar
[33] M. M. T. Hossain, B. Mandal, M. A. Hoossain, Procedia Eng. 56, 134 (2013).10.1016/j.proeng.2013.03.099Suche in Google Scholar
[34] J. H. Merkin, J. Eng. Math. 20, 171 (1985).10.1007/BF00042775Suche in Google Scholar
[35] P. D. Weidman, D. G. Kubitschek, and A. M. J. Davis, Int. J. Eng. Sci. 44, 730 (2006).10.1016/j.ijengsci.2006.04.005Suche in Google Scholar
[36] K. Merrill, M. Beauchesne, J. Previte, J. Paullet, and P. Weidman, Int. J. Heat Mass Transfer 49, 4681 (2006).10.1016/j.ijheatmasstransfer.2006.02.056Suche in Google Scholar
[37] S. D. Harris, D. B. Ingham, and I. Pop, Transp. Porous Media 77, 267 (2009).10.1007/s11242-008-9309-6Suche in Google Scholar
[38] R. Nazar, A. Noor, K. Jafar, and I. Pop, Int. J. Math. Comput. Phys. Quantum Eng. 8, 776 (2014).Suche in Google Scholar
[39] R. A. Hamid, R. Nazar, and I. Pop, Sci. Rep. 5, 14640 (2015).10.1038/srep14640Suche in Google Scholar
[40] M. Miklavčič and C. Y. Wang, Quart. Appl. Math. 64, 283 (2006).10.1090/S0033-569X-06-01002-5Suche in Google Scholar
[41] A. V. Kuznetsov and D. A. Nield, Int. J. Therm. Sci. 49, 243 (2010).10.1016/j.ijthermalsci.2009.07.015Suche in Google Scholar
[42] M. Mustafa, T. Hayat, I. Pop, S. Asghar, and S. Obaidat, Int. J. Heat Mass Transfer 54, 5588 (2011).10.1016/j.ijheatmasstransfer.2011.07.021Suche in Google Scholar
©2016 by De Gruyter
Artikel in diesem Heft
- Frontmatter
- Theoretical Investigations on the Elastic and Thermodynamic Properties of Rhenium Phosphide
- Lax Pair, Conservation Laws, Solitons, and Rogue Waves for a Generalised Nonlinear Schrödinger–Maxwell–Bloch System under the Nonlinear Tunneling Effect for an Inhomogeneous Erbium-Doped Silica Fibre
- Effect of Trace Fe3+ on Luminescent Properties of CaWO4: Pr3+ Phosphors
- Rogue-Wave Interaction of a Nonlinear Schrödinger Model for the Alpha Helical Protein
- Multi-Scale Long-Range Magnitude and Sign Correlations in Vertical Upward Oil–Gas–Water Three-Phase Flow
- Theoretical Study of Geometries, Stabilities, and Electronic Properties of Cationic (FeS)n+ (n = 1–5) Clusters
- Explanation of the Quantum-Mechanical Particle-Wave Duality through the Emission of Watt-Less Gravitational Waves by the Dirac Equation
- Closed Analytical Solutions of the D-Dimensional Schrödinger Equation with Deformed Woods–Saxon Potential Plus Double Ring-Shaped Potential
- Solitons, Bäcklund Transformation, Lax Pair, and Infinitely Many Conservation Law for a (2+1)-Dimensional Generalised Variable-Coefficient Shallow Water Wave Equation
- The Non-Alignment Stagnation-Point Flow Towards a Permeable Stretching/Shrinking Sheet in a Nanofluid Using Buongiorno’s Model: A Revised Model
- Rapid Communication
- Extrinsic and Intrinsic Contributions to Plasmon Peaks in Solids
Artikel in diesem Heft
- Frontmatter
- Theoretical Investigations on the Elastic and Thermodynamic Properties of Rhenium Phosphide
- Lax Pair, Conservation Laws, Solitons, and Rogue Waves for a Generalised Nonlinear Schrödinger–Maxwell–Bloch System under the Nonlinear Tunneling Effect for an Inhomogeneous Erbium-Doped Silica Fibre
- Effect of Trace Fe3+ on Luminescent Properties of CaWO4: Pr3+ Phosphors
- Rogue-Wave Interaction of a Nonlinear Schrödinger Model for the Alpha Helical Protein
- Multi-Scale Long-Range Magnitude and Sign Correlations in Vertical Upward Oil–Gas–Water Three-Phase Flow
- Theoretical Study of Geometries, Stabilities, and Electronic Properties of Cationic (FeS)n+ (n = 1–5) Clusters
- Explanation of the Quantum-Mechanical Particle-Wave Duality through the Emission of Watt-Less Gravitational Waves by the Dirac Equation
- Closed Analytical Solutions of the D-Dimensional Schrödinger Equation with Deformed Woods–Saxon Potential Plus Double Ring-Shaped Potential
- Solitons, Bäcklund Transformation, Lax Pair, and Infinitely Many Conservation Law for a (2+1)-Dimensional Generalised Variable-Coefficient Shallow Water Wave Equation
- The Non-Alignment Stagnation-Point Flow Towards a Permeable Stretching/Shrinking Sheet in a Nanofluid Using Buongiorno’s Model: A Revised Model
- Rapid Communication
- Extrinsic and Intrinsic Contributions to Plasmon Peaks in Solids
