The application of analytical methods in the investigation effects of Magnetic parameter and Brownian motion on the fluid flow between two equal plates

Document Type : Original Article


1 Department of mechanical Engineering Mazandaran University of science and Technology, Babol, Iran

2 Department of mechanical Engineering Babol Noshirvani University of Technology, Babol, Iran


In the present paper, the heat transfer and fluid velocity between two horizontal plates is examined in existence of magnetic parameter. The parameters such as magnetic fluid flow, viscosity, Brownian motion, and thermo-phoretic have been investigated according to this analysis. The innovation of this paper is using two analytical methods for calculate differential equations and comparison these results together. In this paper, the effects of magnetic field on fluid flow for industrial use are investigated. The effects of magnetic field on fluid flow are surveyed by using the Variation Iteration Method (VIM) and the Adomian Decomposition Method (ADM) and compare these methods with the numerical Runge-Kutta method. According to results, increasing the values of the magnetic parameter, the fluid velocity decreased and the fluid viscosity increased. Also, Brownian motion and thermo-phoretic parameters were directly related to the coefficient of friction. The Brownian motion of nanoparticles results in the thermophoresis phenomenon, and increasing both Brownian motion and thermophoresis causes an increase in temperature.


  1. Adibi, T., Razavi, S.E. and Adibi, O., "A characteristic-based numerical simulation of water-titanium dioxide nano-fluid in closed domains", International Journal of Engineering, Vol. 33, No. 1, (2020), 158-163, doi: 10.5829/IJE.2020.33.01A.18.
  2. Sadripour, S., "Investigation of flow characteristics and heat transfer enhancement in a nanofluid flow in a corrugated duct", Journal of Applied Mechanics and Technical Physics, Vol. 59, No. 6, (2018), 1049-1057, doi: 10.1134/S002189441806010X.
  3. Loganathan, P., Chand, P.N. and Ganesan, P., "Transient natural convective flow of a nanofluid past a vertical plate in the presence of heat generation", Journal of Applied Mechanics and Technical Physics, Vol. 56, No. 3, (2015), 433-442, doi: 10. 1134/ s002189441503013x.
  4. Razmara, N., "Microstructure of the poiseuille flow in a model nanofluid by molecular dynamics simulation", Journal of Applied Mechanics and Technical Physics, Vol. 56, No. 5, (2015), 894-900, doi: 10.1134/S002189441505017X.
  5. Derakhshan, R., Shojaei, A., Hosseinzadeh, K., Nimafar, M. and Ganji, D., "Hydrothermal analysis of magneto hydrodynamic nanofluid flow between two parallel by agm", Case Studies in Thermal Engineering, Vol. 14, (2019), 100439, doi: 10.1016/j.csite.2019.100439.
  6. Humphries, U., Govindaraju, M., Kaewmesri, P., Hammachukiattikul, P., Unyong, B., Rajchakit, G., Vadivel, R. and Gunasekaran, N., "Analytical approach of fe3o4-ethylene glycol radiative magnetohydrodynamic nanofluid on entropy generation in a shrinking wall with porous medium", International Journal of Engineering, Vol. 34, No. 2, (2021), 517-527, doi.
  7. Mobadersani, F. and Bahjat, S., "Magnetohydrodynamic (mhd) flow in a channel including a rotating cylinder", International Journal of Engineering, Vol. 34, No. 1, (2021), 224-233, doi. https://dx.doi:org/10.5829/ije.2021.34.01a.25
  8. Akbarzadeh, P. and Fardi, A., "Natural convection heat transfer in 2d and 3d trapezoidal enclosures filled with nanofluid", Journal of Applied Mechanics and Technical Physics, Vol. 59, No. 2, (2018), 292-302, doi: 10.1134/S0021894418020128.
  9. Shahriari, A., Jahantigh, N. and Rakani, F., "Assessment of particle-size and temperature effect of nanofluid on heat transfer adopting lattice boltzmann model", International Journal of Engineering, Vol. 31, No. 10, (2018), 1749-1759, doi: 10.5829/ije.2018.31.10a.18.
  10. Alagappan, N. and Karunakaran, N., "Performance investigation of 405 stainless steel thermosyphon using cerium (iv) oxide nano fluid", International Journal of Engineering, Vol. 30, No. 4, (2017), 575-581, doi: 10.5829/idosi.ije.2017.30.04a.16.
  11. Akbari, M., Yavari, M., Nemati, N., Babaee Darband, J., Molavi, H. and Asefi, M., "An investigation on stability, electrical and thermal characteristics of transformer insulting oil nanofluids", International Journal of Engineering, Vol. 29, No. 10, (2016), 1332-1340, doi: 10.5829/idosi.ije.2016.29.10a.02.
  12. AJAY, K., "Performance evaluation of nanofluid (al2o3/h2o-c2h6o2) based parabolic solar collector using both experimental and cfd techniques", International Journal of Engineering, Vol. 29, No. 4, (2016), 572-580, doi: 10.5829/idosi.ije.2016.29.04a.17.
  13. Kheiri, M. and Davarnejad, R., "Numerical comparison of turbulent heat transfer and flow characteristics of sio2/water nanofluid within helically corrugated tubes and plain tube", International Journal of Engineering, Vol. 28, No. 10, (2015), 1408-1414, doi: 10.5829/idosi.ije.2015.28.10a.02.
  14. Khan, D., Hakim, M.A. and Alam, M., "Analysis of magneto-hydrodynamics jeffery-hamel flow with nanoparticles by hermite-padé approximation", International Journal of Engineering, Vol. 28, No. 4, (2015), 599-607, doi: 10.5829/idosi.ije.2015.28.04a.15.
  15. Goshtasbi Rad, E., "Experimental investigation of mixed convection heat transfer in vertical tubes by nanofluid: Effects of reynolds number and fluid temperature", International Journal of Engineering, Vol. 27, No. 8, (2014), 1251-1258, doi: 10.5829/idosi.ije.2014.27.08b.11.
  16. Mohammadi Ardehali, R., "Modeling of tio2-water nanofluid effect on heat transfer and pressure drop", International Journal of Engineering, Vol. 27, No. 2, (2014), 195-202, doi: 10.5829/idosi.ije.2014.27.02b.04.
  17. Rostami, M., Hassani Joshaghani, A., Mazaheri, H. and Shokri, A., "Photo-degradation of p-nitro toluene using modified bentonite based nano-tio2 photocatalyst in aqueous solution", International Journal of Engineering, Vol. 34, No. 4, (2021), 756-762, doi.
  18. Siavashy, O.S., Nabian, N. and Rabiee, S., "Titanium dioxide nanotubes incorporated bioactive glass nanocomposites: Synthesis, characterization, bioactivity evaluation and drug loading", International Journal of Engineering, Vol. 34, No. 1, (2021), 1-9, doi.
  19. Taheri, A.A. and Taghilou, M., "Towards a uncertainty analysis in thermal protection using phase-change micro/nano particles during hyperthermia", International Journal of Engineering, Vol. 34, No. 1, (2021), 263-271, doi: 10.5829/ije.2021.34.01a.29.
  20. Peiravi, M.M., Alinejad, J., Ganji, D. and Maddah, S., "Numerical study of fins arrangement and nanofluids effects on three-dimensional natural convection in the cubical enclosure", Challenges in Nano and Micro Scale Science and Technology, Vol. 7, No. 2, (2019), 97-112, doi: 10.22111/tpnms.2019.27933.1164.
  21. Gupta, U., Ahuja, J. and Wanchoo, R., "Magneto convection in a nanofluid layer", International Journal of Heat and Mass Transfer, Vol. 64, (2013), 1163-1171, doi: 10.1016/j.ijheatmasstransfer.2013.05.035.
  22. Peiravi, M.M., Alinejad, J., Ganji, D.D. and Maddah, S., "3d optimization of baffle arrangement in a multi-phase nanofluid natural convection based on numerical simulation", International Journal of Numerical Methods for Heat & Fluid Flow, (2019), doi: 10.1108/HFF-01-2019-001.
  23. Peiravi, M.M. and Alinejad, J., "Nano particles distribution characteristics in multi-phase heat transfer between 3d cubical enclosures mounted obstacles", Alexandria Engineering Journal, Vol. 60, No. 6, (2021), 5025-5038, doi: 10.1016/j.aej.2021.04.013.
  24. Pourmehran, O., Rahimi-Gorji, M., Gorji-Bandpy, M. and Ganji, D., Retracted: Analytical investigation of squeezing unsteady nanofluid flow between parallel plates by lsm and cm. 2015, Elsevier.
  25. Azimi, A. and Mirzaei, M., "Analytical investigation of squeezing flow of graphene oxide water nanofluid between parallel plates using rvim", Journal of Computational and Theoretical Nanoscience, Vol. 12, No. 2, (2015), 175-179, doi: 10.1166/jctn.2015.3711.
  26. Domari, G.D., Peiravi, M. and Abbasi, M., "Evaluation of the heat transfer rate increases in retention pools nuclear waste", International Journal of Nano Dimension, Vol. 6, No. 4, (2015), 385-398.
  27. Hatami, M. and Ganji, D., "Motion of a spherical particle in a fluid forced vortex by dqm and dtm", Particuology, Vol. 16, (2014), 206-212, doi: 10.1016/j.partic.2014.01.001.
  28. Rashidi, M.M., Reza, M. and Gupta, S., "Mhd stagnation point flow of micropolar nanofluid between parallel porous plates with uniform blowing", Powder Technology, Vol. 301, (2016), 876-885, doi: 10.1016/j.powtec.2016.07.019.
  29. Peiravi, M.M. and Alinejad, J., "Hybrid conduction, convection and radiation heat transfer simulation in a channel with rectangular cylinder", Journal of Thermal Analysis and Calorimetry, Vol. 140, No. 6, (2020), 2733-2747, doi: 10.1007/s10973-019-09010-0.
  30. Jalilpour, B., Jafarmadar, S., Ganji, D., Shotorban, A. and Taghavifar, H., "Heat generation/absorption on mhd stagnation flow of nanofluid towards a porous stretching sheet with prescribed surface heat flux", Journal of Molecular Liquids, Vol. 195, (2014), 194-204, doi: 10.1016/j.molliq.2014.02.021.
  31. Ganji, D. and HashemiKachapi, S., "Analysis of nonlinear equations in fluids, progress in nonlinear science", Sian Academic, , (2011), 1-294.
  32. Aminoroayaie Yamini, O., Mousavi, S.H., Kavianpour, M. and Safari Ghaleh, R., "Hydrodynamic performance and cavitation analysis in bottom outlets of dam using cfd modelling", Advances in Civil Engineering, Vol. 2021, (2021), doi: 10.1155/2021/5529792.
  33. Mousavimehr, S., Yamini, O.A. and Kavianpour, M., "Performance assessment of shockwaves of chute spillways in large dams", Shock and Vibration, Vol. 2021, (2021), doi: 10.1155/2021/6634086.
  34. Kostikov, Y.A. and Romanenkov, A.M., "Approximation of the multidimensional optimal control problem for the heat equation (applicable to computational fluid dynamics (CFD))", Civil Engineering Journal, Vol. 6, No. 4, (2020), 743-768, doi: 10.28991/cej-2020-03091506.