ANALYTICAL AND NUMERICAL STUDY OF MICROPOLAR FLUID FLOW IN A POROUS PLATE DUE TO LINEAR STRETCHING

Yıl 2018, Cilt: 36 Sayı: 4, 1181 - 1196, 01.12.2018

Nozar Akbarı Mosayeb Gholınıa Saber Gholınıa Soheil Dabbaghıan Hossein Javadı Davood Domairry Ganjı

Öz

In this research, micropolar fluid flow of a porous plate due to Linear stretching is analyzed. The basic partial differential equations are reduced to nonlinear ordinary differential equations which are solved using Homotopy Perturbation Method (HPM). Comparison between results of Flex-PDE software and analytical method of the issue illustrates excellent precision in solving the nonlinear differential equation. Furthermore, impact of injection and suction velocity (∅), coupling parameter between velocity field and micro-rotation field (ε), vortex viscosity parameter (β) on micro-rotation, and fluid velocity profiles are examined. Conclusions indicate that: by increasing the ε parameter, the f'(η) value decreases. Also, the shear stress F''(0) values are gradually reduced with increasing β, while the opposite trend is observed in H' (0) variations.

Anahtar Kelimeler

Micropolar fluid flow, injection and suction, homotopy perturbation method (HPM), porous plate.

Kaynakça

• ⦁ Eringen, A. Cemal. “Theory of micropolar fluids.” Journal of Mathematics and Mechanics (1966): 1-18.
• ⦁ Hassanien, I. A., and R. S. R. Gorla. “Heat transfer to a micropolar fluid from a non-isothermal stretching sheet with suction and blowing.” Acta Mechanica 84, no. 1-4 (1990): 191-199.
• ⦁ Vajravelu, K. “Convection heat transfer at a stretching sheet with suction or blowing.” Journal of mathematical analysis and applications 188, no. 3 (1994): 1002-1011.
• ⦁ Salleh, Mohd Zuki, Azizah Mohd Rohni, and Norsarahaida Amin. “Boundary layer flow due to a moving flat plate in micropolar fluid.” Jurnal Teknologi 43: 67-83.
• ⦁ Zhou, Jiandong, M. Hatami, Dongxing Song, and Dengwei Jing. “Design of microchannel heat sink with wavy channel and its time-efficient optimization with combined RSM and FVM methods.” International Journal of Heat and Mass Transfer 103 (2016): 715-724.
• ⦁ Hatami, M., M. Sheikholeslami, and G. Domairry. “High accuracy analysis for motion of a spherical particle in plane Couette fluid flow by multi-step differential transformation method.” Powder Technology 260 (2014): 59-67.
• ⦁ Dogonchi, A. S., M. Hatami, and G. Domairry. “Motion analysis of a spherical solid particle in plane Couette Newtonian fluid flow.” Powder Technology 274 (2015): 186-192.
• ⦁ Hatami, M., and D. D. Ganji. “Motion of a spherical particle on a rotating parabola using Lagrangian and high accuracy multi-step differential transformation method.” Powder Technology258 (2014): 94-98.
• ⦁ Tang, Wenhui, M. Hatami, Jiandong Zhou, and Dengwei Jing. “Natural convection heat transfer in a nanofluid-filled cavity with double sinusoidal wavy walls of various phase deviations.” International Journal of Heat and Mass Transfer115 (2017): 430-440.
• ⦁ Sheikholeslami, M., M. Hatami, and D. D. Ganji. “Numerical investigation of nanofluid spraying on an inclined rotating disk for cooling process.” Journal of Molecular Liquids 211 (2015): 577-583.
• ⦁ Pourmehran, O., M. Rahimi-Gorji, M. Hatami, S. A. R. Sahebi, and G. Domairry. “Numerical optimization of microchannel heat sink (MCHS) performance cooled by KKL based nanofluids in saturated porous medium.” Journal of the Taiwan Institute of Chemical Engineers 55 (2015): 49-68.
• ⦁ Hatami, M., Dongxing Song, and Dengwei Jing. “Optimization of a circular-wavy cavity filled by nanofluid under the natural convection heat transfer condition.” International Journal of Heat and Mass Transfer 98 (2016): 758-767.
• ⦁ Hatami, M., J. Zhou, J. Geng, D. Song, and D. Jing. “Optimization of a lid-driven T-shaped porous cavity to improve the nanofluids mixed convection heat transfer.” Journal of Molecular Liquids 231 (2017): 620-631.
• ⦁ Hatami, M., and D. Jing. “Optimization of wavy direct absorber solar collector (WDASC) using Al2O3-water nanofluid and RSM analysis.” Applied Thermal Engineering 121 (2017): 1040-1050.
• ⦁ Rahman, M. M., and M. A. Sattar. “Magnetohydrodynamic convective flow of a micropolar fluid past a continuously moving vertical porous plate in the presence of heat generation/absorption.” Journal of Heat Transfer 128, no. 2 (2006): 142-152.
• ⦁ Rahman, M. M., and Tamanna Sultana. “Radiative heat transfer flow of micropolar fluid with variable heat flux in a porous medium.” Nonlinear Anal. Model. Control 13, no. 1 (2008): 71-87.
• ⦁ Sheikholeslami, M., D. D. Ganji, and R. Moradi. “Heat transfer of Fe3O4–water nanofluid in a permeable medium with thermal radiation in existence of constant heat flux.” Chemical Engineering Science 174 (2017): 326-336.
• ⦁ Rahman, M. M., M. J. Uddin, and A. Aziz. “Effects of variable electric conductivity and non-uniform heat source (or sink) on convective micropolar fluid flow along an inclined flat plate with surfaceheat flux.” International Journal of Thermal Sciences 48, no. 12 (2009): 2331-2340.
• ⦁ Alomari, A. K., Mohd Salmi Md Noorani, and R. Nazar. “Homotopy solution for flow of a micropolar fluid on a continuous moving surface.” International Journal for Numerical Methods in Fluids 66, no. 5 (2011): 608-621.
• ⦁ Sheikholeslami, M., and D. D. Ganji. “Analytical investigation for Lorentz forces effect on nanofluid Marangoni boundary layer hydrothermal behavior using HAM.” Indian Journal of Physics 91, no. 12 (2017): 1581-1587.
• ⦁ Sheikholeslami, M., R. Ellahi, H. R. Ashorynejad, G. Domairry, and T. Hayat. “Effects of heat transfer in flow of nanofluids over a permeable stretching wall in a porous medium.” Journal of Computational and Theoretical Nanoscience 11, no. 2 (2014): 486-496.
• ⦁ Hatami, M. “Nanoparticles migration around the heated cylinder during the RSM optimization of a wavy-wall enclosure.” Advanced Powder Technology 28, no. 3 (2017): 890-899.
• ⦁ Kazem, S., and M. Shaban. “Tau-homotopy analysis method for solving micropolar flow due to a linearly stretching of porous sheet.” Commun Numer Anal 2012 (2012): cna-00114.
• ⦁ Ahmad, Kartini, Anuar Ishak, and Roslinda Nazar. “Micropolar fluid flow and heat transfer over a nonlinearly stretching plate with viscous dissipation.” Mathematical Problems in Engineering 2013 (2013).
• ⦁ Sheikholeslami, M., M. Nimafar, and D. Domiri Ganji. “Analytical approach for the effect of melting heat transfer on nanofluid heat transfer.” The European Physical Journal Plus132, no. 9 (2017): 385.
• ⦁ Mirgolbabaee, H., S. T. Ledari, and D. D. Ganji. “Semi-analytical investigation on micropolar fluid flow and heat transfer in a permeable channel using AGM.” Journal of the Association of Arab Universities for Basic and Applied Sciences 24, no. 1 (2017): 213-222.
• ⦁ Hatami, M., and D. D. Ganji. “Motion of a spherical particle in a fluid forced vortex by DQM and DTM.” Particuology 16 (2014): 206-212.
• ⦁ Sui, Jize, Peng Zhao, Zhengdong Cheng, and Masao Doi. “Influence of particulate thermophoresis on convection heat and mass transfer in a slip flow of a viscoelasticity-based micropolar fluid.” International Journal of Heat and Mass Transfer 119 (2018): 40-51.
• ⦁ Kataria, Hari R., Harshad R. Patel, and Rajiv Singh. “Effect of magnetic field on unsteady natural convective flow of a micropolar fluid between two vertical walls.” Ain Shams Engineering Journal 8, no. 1 (2017): 87-102.
• ⦁ Sheikholeslami, M., M. Jafaryar, Davood Domairry Ganji, and Zhixiong Li. “Exergy loss analysis for nanofluid forced convection heat transfer in a pipe with modified turbulators.” Journal of Molecular Liquids 262 (2018): 104-110.
• ⦁ Sheikholeslami, M., Davood Domairry Ganji, and R. Moradi. “Forced convection in existence of Lorentz forces in a porous cavity with hot circular obstacle using nanofluid via Lattice Boltzmann method.” Journal of Molecular Liquids 246 (2017): 103-111.
• ⦁ Sheikholeslami, M., and D. D. Ganji. “Influence of electric field on Fe3O4-water nanofluid radiative and convective heat transfer in a permeable enclosure.” Journal of Molecular Liquids 250 (2018): 404-412.
• ⦁ Hosseini, S. R., M. Sheikholeslami, M. Ghasemian, and D. D. Ganji. “Nanofluid heat transfer analysis in a microchannel heat sink (MCHS) under the effect of magnetic field by means of KKL model.” Powder Technology 324 (2018): 36-47.
• ⦁ Sheikholeslami, M., and D. D. Ganji. “Numerical analysis of nanofluid transportation in porous media under the influence of external magnetic source.” Journal of Molecular Liquids 233 (2017): 499-507.
• ⦁ Sheikholeslami, M., and D. D. Ganji. “Numerical approach for magnetic nanofluid flow in a porous cavity using CuO nanoparticles.” Materials & Design 120 (2017): 382-393.
• ⦁ Sheikholeslami, M., Z. Ziabakhsh, and D. D. Ganji. “Transport of Magnetohydrodynamic nanofluid in a porous media.” Colloids and Surfaces A: Physicochemical and Engineering Aspects 520 (2017): 201-212.
• ⦁ Sheikholeslami, M., M. Jafaryar, K. Bateni, and D. D. Ganji. “Two phase modeling of nanofluid flow in existence of melting heat transfer by means of HAM.” Indian Journal of Physics 92, no. 2 (2018): 205-214.
• ⦁ Sheikholeslami, M., D. D. Ganji, H. R. Ashorynejad, and Houman B. Rokni. “Analytical investigation of Jeffery-Hamel flow with high magnetic field and nanoparticle by Adomian decomposition method.” Applied Mathematics and Mechanics33, no. 1 (2012): 25-36.
• ⦁ Sheikholeslami, M., D. D. Ganji, and H. R. Ashorynejad. “Investigation of squeezing unsteady nanofluid flow using ADM.” Powder Technology 239 (2013): 259-265.
• ⦁ Sheikholeslami, M., D. D. Ganji, and M. M. Rashidi. “Magnetic field effect on unsteady nanofluid flow and heat transfer using Buongiorno model.” Journal of Magnetism and Magnetic Materials 416 (2016): 164-173.
• ⦁ Sheikholeslami, Mohsen, and Davood Domiri Ganji. “Nanofluid flow and heat transfer between parallel plates considering Brownian motion using DTM.” Computer Methods in Applied Mechanics and Engineering 283 (2015): 651-663.
• ⦁ Sheikholeslami, M., and D. D. Ganji. “Nanofluid hydrothermal behavior in existence of Lorentz forces considering Joule heating effect.” Journal of Molecular Liquids 224 (2016): 526-537.
• ⦁ Sheikholeslami, Mohsen, Hamid Reza Ashorynejad, Davood Domairry, and Ishak Hashim. “Investigation of the laminar viscous flow in a semi-porous channel in the presence of uniform magnetic field using optimal homotopy asymptotic method.” Sains Malaysiana 41, no. 10 (2012): 1177-1229.
• ⦁ Sheikholeslami, M., and D. D. Ganji. “Magnetohydrodynamic flow in a permeable channel filled with nanofluid.” Scientia Iranica. Transaction B, Mechanical Engineering 21, no. 1 (2014): 203.
• ⦁ Sheikholeslami, M., and D. D. Ganji. “Heat transfer of Cu-water nanofluid flow between parallel plates.” Powder Technology 235 (2013): 873-879.
• ⦁ Sheikholeslami, M., H. R. Ashorynejad, D. D. Ganji, and A. Yıldırım. “Homotopy perturbation method for three-dimensional problem of condensation film on inclined rotating disk.” Scientia Iranica 19, no. 3 (2012): 437-442.
• ⦁ H. Bararnia, E. Ghasemi, G. Domairry, S. Soleimani. “Behavior of micro-polar flow due to linear stretching of porous sheet with injection and suction” Advances in Engineering Software 41 (2010) 893–897.