Abstract
Motion of a vertically falling nano droplet in incompressible Newtonian media with initial velocity is investigated. The instantaneous velocity and acceleration are carried out by using the variational iteration method (VIM) and homotopy perturbation method (HPM), which are analytical solution techniques. The obtained results are compared with Runge–Kutta method in order to verify the accuracy of the proposed methods. The results show that, the analytical solutions are in good agreement with each other and with the numerical solution. Also, the effects of sphericity (φ) on the velocity and acceleration profiles of the nano droplet are explained. Moreover, the results demonstrate that the VIM-Padé and HPM-Padé are very effective in generating analytical solutions for even highly nonlinear problems.
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ZOLFAGHARIAN A, VALIPOUR P, GHASEMI S E. Fuzzy force learning controller of flexible wiper system [J]. Neural Computing and Application, 2016(27): 483-493
ZOLFAGHARIAN A, NOSHADI A, GHASEMI S E M D, ZAIN M Z. A nonparametric approach using artificial intelligence in vibration and noise reduction of flexible systems, Proceedings of the Institution of Mechanical Engineers, Part C, Journal of Mechanical Engineering Science, 2014, 228(8): 1329-1347.
NOSHADI A, MAILAH M, ZOLFAGHARIAN A. Intelligent active force control of a 3-RRR parallel manipulator incorporating fuzzy resolved acceleration control [J]. Applied Mathematical Modelling, 2012, 36(6): 2370-2383.
ZOLFAGHARIAN A, NOSHADI A, KHOSRAVANI M R M D, ZAIN M Z. Unwanted noise and vibration control using finite element analysis and artificial intelligence in flexible wiper system [J]. Applied Mathematical Modelling, 2014, 38: 2435-2453.
ZOLFAGHARIAN A, GHASEMI S E, IMANI M. A multi-objective, active fuzzy force controller in control of flexible wiper system [J]. Latin Am J Solids Struct, 2014, 11(9): 1490-514.
AHMADI ASOOR A A, VALIPOUR P, GHASEMI S E. Investigation on vibration of single walled carbon nanotubes by variational iteration method [J]. Appl Nanosci, 2016, 6: 243-249.
GHASEMI S E, JALILI PALANDI S, HATAMI M, GANJI D D. Efficient analytical approaches for motion of a spherical solid particle in plane couette fluid flow using nonlinear methods [J]. The Journal of Mathematics and Computer Science 2012, 5(2): 97-104
GHASEMI S E, HATAMI M, GANJI D D. Analytical thermal analysis of air-heating solar collectors [J]. Journal of Mechanical Science and Technology, 2013, 27(11): 3525-3530.
MOHAMMADIAN E, GHASEMI S E, POORGASHTI H, HOSSEINI M, GANJI D D. Thermal investigation of Cu–water nanofluid between two vertical planes [J]. Proc IMechE Part E: J Process Mechanical Engineering 2015, 229(1): 36-43.
GHASEMI S E, HATAMI M, GANJI D D. Thermal analysis of convective fin with temperature-dependent thermal conductivity and heat generation [J]. Case Studies in Thermal Engineering, 2014(4): 1-8.
GHASEMI S E, VALIPOUR P, HATAMI M, GANJI D D. Heat transfer study on solid and porous convective fins with temperaturedependent heat generation using efficient analytical method [J]. Journal of Central South University, 2014, 21: 4592-4598.
AHMADI ASOOR A A, VALIPOUR P, GHASEMI S E, GANJI D D. Mathematical modelling of carbon nanotube with fluid flow using Keller box method: A vibrational study [J]. Int J Appl Comput Math DOI 10.1007/s40819-016-0206-3.
VALIPOUR P, GHASEMI S E. Numerical investigation of MHD water-based nanofluids flow in porous medium caused by shrinking permeable sheet [J]. J Braz Soc Mech Sci Eng, 2016, 38: 859-868.
GHASEMI S E, HATAMI M, JING D, GANJI D D. Nanoparticles effects on MHD fluid flow over a stretching sheet with solar radiation: A numerical study [J]. Journal of Molecular Liquids 2016, 219: 890-896.
GHASEMI S E, ZOLFAGHARIAN A, GANJI D D. Study on motion of rigid rod on a circular surface using MHPM [J]. Propulsion and Power Research, 2014, 3(3): 159-164.
GHASEMI S E, HATAMI M, HATAMI J, SAHEBI S A R, GANJI D D. An efficient approach to study the pulsatile blood flow in femoral and coronary arteries by Differential Quadrature Method [J]. Physica A, 2016, 443: 406-414.
GHASEMI S E, HATAMI M, ARMIA SALARIAN, DOMAIRRY G. Thermal and fluid analysis on effects of a nanofluid outside of a stretching cylinder with magnetic field the using differential quadrature method [J]. Journal of Theoretical and Applied Mechanics 2016, 54(2): 517-528.
GHASEMI S E, HATAMI M, MEHDIZADEH AHANGAR G H R, GANJI D D. Electrohydrodynamic flow analysis in a circular cylindrical conduit using Least Square Method [J]. Journal of Electrostatics, 2014, 72: 47-52.
GHASEMI S E, VATANI M, GANJI D D. Efficient approaches of determining the motion of a spherical particle in a swirling fluid flow using weighted residual methods [J]. Particuology, 2015, 23: 68-74.
DARZI M, VATANI M, GHASEMI S E, GANJI D D. Effect of thermal radiation on velocity and temperature fields of a thin liquid film over a stretching sheet in a porous medium [J]. Eur Phys J Plus, 2015, 130: 100.
GHASEMI S E, VATANI M, HATAMI M, GANJI D D. Analytical and numerical investigation of nanoparticle effect on peristaltic fluid flow in drug delivery systems [J]. Journal of Molecular Liquids, 2016, 215: 88-97.
ATOUEI S A, HOSSEINZADEH K H, HATAMI M, GHASEMI S E, SAHEBI S A R, GANJI D D. Heat transfer study on convective-radiative semi-spherical fins with temperature-dependent properties and heat generation using efficient computational methods [J]. Applied Thermal Engineering, 2015, 89: 299-305.
GHASEMI S E, HATAMI M, KALANI SAROKOLAIE A, GANJI D D. Study on blood flow containing nanoparticles through porous arteries in presence of magnetic field using analytical methods [J]. Physica, 2015, E70: 146-156.
VALIPOUR P, GHASEMI S E, MOHAMMAD REZA KHOSRAVANI, GANJI D D. Theoretical analysis on nonlinear vibration of fluid flow in single-walled carbon nanotube [J]. J Theor Appl Phys, 2016, 10: 211-218.
VATANI M, GHASEMI S E, GANJI D D. Investigation of micropolar fluid flow between a porous disk and a nonporous disk using efficient computational technique [J]. Proc IMechE Part E: J Process Mechanical Engineering, 2016, 230(6): 413-424.
VALIPOUR P, GHASEMI S E, VATANI M. Theoretical investigation of micropolar fluid flow between two porous disks [J]. Journal of Central South University, 2015, 22: 2825-2832.
TALARPOSHTI R A, GHASEMI S E, RAHMANI Y, GANJI D D. Application of exp-function method to wave solutions of the sine-Gordon and Ostrovsky equations [J]. Acta Mathematicae Applicatae Sinica, English Series 2016, 32(3): 571-578.
CLIFT R, GRACE J, WEBER M E. Bubbles, drops and particles [M]. New York: Academic Press, 1978.
KHAN A R, RICHARDSON J F. The resistance to motion of a solid sphere in a fluid [J]. Chemical Engineering Communications, 1987, 62: 135-150.
CHIEN S F. Settling velocity of irregularly shaped particles [J]. SPE Drilling and Completion, 1994, 9: 281-289.
FERNÁNDEZ F M. On the homotopy perturbation method for Boussinesq-like equations [J]. Applied Mathematics and Computation, 2014, 230(3): 208-210.
AKHAVAN BEHABADI M A, SADOUGHI M K, DARZI M, FAKOOR PAKDAMAN M. Experimental study on heat transfer characteristics of R600a/POE/CuO nano-refrigerant flow condensation [J]. Experimental Thermal and Fluid Science, 2015, 66: 46-52.
DARZI M, AKHAVAN BEHABADI M A, SADOUGHI M K, RAZI P. Experimental study of horizontal flattened tubes performance on condensation of R600a vapor [J]. International Communications in Heat and Mass Transfer, 2015, 62: 18-25.
SAZHIN Sergei, CRUA Cyril, KENNAIRD David, HEIKAL Morgan. The initial stage of fuel spray penetration [J]. Fuel, 2003, 82(8): 875-885.
SAZHIN Sergei, SHAKKED Tal, SOBOLEV Vladimir, KATOSHEVSKI David. Particle grouping in oscillating flows [J]. European Journal of Mechanics B/Fluids, 2008, 27: 131-149.
NOOR M A, MOHYUD-DIN S T. Variational iteration method for unsteady flow of gas through a porous medium using He’s polynomials and Pade approximants [J]. Computers and Mathematics with Applications, 2009, 58: 2182-2189.
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Zolfagharian, A., Darzi, M. & Ghasemi, S.E. Analysis of nano droplet dynamics with various sphericities using efficient computational techniques. J. Cent. South Univ. 24, 2353–2359 (2017). https://doi.org/10.1007/s11771-017-3647-x
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DOI: https://doi.org/10.1007/s11771-017-3647-x