Abstract
This study is carried out on the unsteady flow and heat transfer of a nanofluid in a stretching flat plate. Least square method is implemented for solving the governing equations. It also attempts to demonstrate the accuracy of the aforementioned method compared with a numerical one, Runge-Kutta fourth order. Furthermore, the impact of some physical parameters like unsteadiness parameter (S), Prandtl number (Pr) and the nanoparticles volume fraction (ϕ) on the temperature and velocity profiles is scrutinized carefully. Accordingly, the results obtained from this study reveal that the temperature enhances by means of augmenting the nanoparticles volume fraction. At η ∈ {0, 0.5}, the velocity decreases as a result of a rise in nanoparticles volume fraction and at η ∈ {0.5, 1}, an opposite treatment takes place. Moreover, velocity distribution augments by raising the S value, however an inverse trend is observed in temperature values. Moreover, the local skin friction coefficient indicated a notable rise by increasing the S parameter as well as a steady decrease by rising ϕ. Finally, water-Alumina nanofluid demonstrated better heat transfer enhancement compared to other types of nanofluids.
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S. Kumar, S. K. Prasad and J. Banerjee, Analysis of flow and thermal field in nanofluid using a single phase thermal dispersion model, Appl. Math. Model., 34 (2010) 573–592.
S. U. S. Choi and J. A. Eastman, Enhancing thermal conductivity of fluids with nanoparticles, ASME IMECE, San Francisco, USA (1995) 99–105.
H. Masuda, A. Ebata, K. Teramae and N. Hishinuma, Alteration of thermal conductivity and viscosity of liquid by dispersing ultrafine particles. Dispersion of Al2O3, SiO2 and TiO2 ultrafine particles, Netsu Bussei, 7 (4) (1993) 227–233.
A. Majidian, M. Fakour and A. Vahabzadeh, Analytical investigation of the Laminar viscous flow in a semi-porous channel in the presence of a uniform magnetic field, International Journal of Partial Differential Equations and Applications, 2 (4) (2014) 79–85.
A. Vahabzadeh, M. Fakour, D. D. Ganji and I. Rahimi Petroudi, Analytical accuracy of the one dimensional heat transfer in geometry with logarithmic various surfaces, Cent. Eur. J. Eng., 4 (2014) 341–355.
M. Fakour, A. Vahabzadeh and D. D. Ganji, Scrutiny of mixed convection flow of a nanofluid in a vertical channel, International Journal of Case Studies in Thermal Engineering, 4 (2014) 15–23.
D. D. Ganji, M. Fakour, A. Vahabzadeh and S. H. H. Kachapi, Accuracy of VIM, HPM and ADM in solving nonlinear equations for the steady three-dimensional flow of a Walter’s B fluid in vertical channel, Walailak Journal of Science and Technology, 11 (7) (2014) 593–609.
M. Fakour, D. D. Ganji and M. Abbasi, Scrutiny of underdeveloped nanofluid MHD flow and heat conduction in a channel with porous walls, International Journal of Case Studies in Thermal Engineering, 4 (2014) 202–214.
M. Sheikholeslami, M. Hatami and D. D. Ganji, Nanofluid flow and heat transfer in a rotating system in the presence of a magnetic field, J. Mol. Liq., 190 (2014) 112–120.
M. Hatami and D. D. Ganji, Thermal performance of circular convective-radiative porous fins with different section shapes and materials, Energy Convers. Manag., 76 (2013) 185–193.
A. Vahabzadeh, D. D. Ganji and M. Abbasi, Analytical investigation of porous pin fins with variable section in fully-wet conditions, International Journal of Case Studies in Thermal Engineering, 5 (2015) 1–12.
M. Hatami, M. Sheikholeslami and D. D. Ganji, Laminar flow and heat transfer of nanofluid between contracting and rotating disks by least square method, Powder Technol., 253 (2014) 769–779.
M. Hatami and D. D. Ganji, Heat transfer and nanofluid flow in suction and blowing process between parallel disks in presence of variable magnetic field, J. Mol. Liq., 190 (2014) 159–168.
G. Domairry and M. Hatami, Squeezing Cu-water nanofluid flow analysis between parallel plates by DTM-Padé method, J. Mol. Liq., 193 (2014) 37–44.
N. S. Akbar and S. Nadeem, Mixed convective Magnetohydrodynamic peristaltic flow of a Jeffrey nanofluid with Newtonian heating, Z. Naturforsch A, 68 (2013) 433–441.
N. S. Akbar and S. Nadeem, Peristaltic flow of a Phan-Thien-Tanner nanofluid in a diverging tube, Heat Transf. Asian Res., 41 (2012) 10–22.
S. Nadeem, R. Mehmood and N. S. Akbar, Nonorthogonal stagnation point flow of a nano non-Newtonian fluid towards a stretching surface with heat transfer, Int. J. Heat Mass Transf., 57 (2013) 679–689.
N. S. Akbar, M. T. Mustafa and Z. H. Khan, Stagnation point flow study with water based nanoparticles aggregation over a stretching sheet: Numerical solution, Journal of Computational and Theoretical Nanoscience, 13 (11) (2016) 8615–8619.
N. S. Akbar, D. Tripathi, Z. H. Khan and O. A. Beg, A numerical study of magnetohydrodynamic transport of nanofluids over a vertical stretching sheet with exponential temperature-dependent viscosity and buoyancy effects, Chemical Physics Letters, 661 (2016) 20–30.
N. S. Akbar and Z. H. Khan, Effect of variable thermal conductivity and thermal radiation on the flow of CNTS over a stretching sheet with convective slip boundary conditions: Numerical study, Journal of Molecular Liquid, 222 (2016) 279–286.
N. S. Akbar, Z. H. Khan, S. Nadeem and W. khan, Double-diffusive natural convective boundary-layer flow of a nanofluid over a stretching sheet with magnetic field, International Journal of Numerical Methods for Heat and Fluid Flow, 26 (1) (2016) 108–121.
N. S. Akbar and A. W. Butt, Magnetic field analysis in a suspension of gyrotactic microorganisms and nanoparticles over a stretching surface, Journal of Magnetism and Magnetic Materials, 378 (2016) 320–326.
M. N. Ozisik, Heat conduction, Second edition, John Wiley and Sons Inc, USA (1993).
R. H. Stern and H. Rasmussen, Left ventricular ejection: Model solution by collocation, an approximate analytical method, Comput. Biol. Med., 26 (1996) 255–261.
B. Vaferi, V. Salimi, D. Dehghan Baniani, A. Jahanmiri and S. Khedri, Prediction of transient pressure response in the petroleum reservoirs using orthogonal collocation, J. Pet. Sci. Eng., 98–99 (2012) 156–163.
M. Hatami, A. Hasanpour and D. D. Ganji, Heat transfer study through porous fins also the problem of laminar nanofluid flow in a semi-porous channel in the presence of transverse magnetic field, Energy Convers. Manag., 74 (2013) 9–16.
M. Hatami and D. D. Ganji, Thermal performance of circular convective-radiative porous fins with different section shapes and materials, Energy Convers. Manag, 76 (2013) 185–193.
H. Schlichting and K. Gersten, Boundary-layer theory, 8th Ed., Springer, New York (2000).
H. Görtler, Eineneue Reihenent wickling für laminare Grenzschichten, Z. Angew. Math. Mech., 32 (1952) 270–271.
R. K. Tiwari and M. K. Das, Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluids, Int. J. Heat Mass Transfer, 50 (2007) 2002–2018.
C. Y. Wang, Liquid film on an unsteady stretching surface, Quart. Appl. Math., 48 (1990) 601–610.
M. Sheikholeslami, M. Hatami and D. D. Ganji, Analytical investigation of MHD nanofluid flow in a semi-porous channel, Powder Technol., 246 (2013) 327–336.
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M. Fakour received his M.Sc. degree in Mechanical Engineering at Azad University in 2014. His major research interests are engineering mathematics, heat transfer, solar thermal science and analytical methods. He has published several papers in the mentioned subjects.
A. Rahbari received his Ph.D. degree from Mechanical engineering at Iran University of Science and Technology in 2011. He has been an Assistant Professor at Shahid Rajaee Teacher Training University (SRTTU). His research interests include heat transfer enhancement using nanofluids, permeability analysis in porous media, exergy analysis and supercritical water gasification.
E. Khodabandeh received his B.S. and M.S. degrees from Mechanical Engineering at Isfahan University of Technology in 2012 and Amirkabir University of Technology in 2014, respectively. He is currently a Technical Manager in a private company. His research interests are in the area of fluid engineering, CFD in applications and optimization.
D. D. Ganji received his Ph.D. degree in Mechanical Engineering from Tarbiat Modarres University in 2004. He is a Professor in Department of Mechanical Engineering at Babol University of Technology. His core research interest is the development of new analytical techniques for solving ordinary and partial differential equations in a wide range of subjects including heat conduction, mechanics of fluid and engineering control.
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Fakour, M., Rahbari, A., Khodabandeh, E. et al. Nanofluid thin film flow and heat transfer over an unsteady stretching elastic sheet by LSM. J Mech Sci Technol 32, 177–183 (2018). https://doi.org/10.1007/s12206-017-1219-5
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DOI: https://doi.org/10.1007/s12206-017-1219-5