Evaluation of Micropolar Fluid Transport through Penetrable Medium: Effect of Flow and Thermal Slip

Document Type : Research Article


1 Department of Mechanical Engineering, University of Lagos, Akoka-Yaba, Nigeria.

2 Department of Mechanical Engineering, Igbinedion University, Edo, Nigeria.


In this study, the micropolar fluid flow through penetrable walls under slip flow and thermal jump condition is examined. The Micropolar fluid accounts for the hydrodynamic limit of the classical Navier Stokes model, it takes into consideration the micro-structure of the fluid, local structure, and micro rotation of fluid particles. Here the thermal exchange and mass transport of the micropolar fluid are studied considering transport conditions such as radiation, variable magnetism, and nanoparticle concentration. The micropolar fluid flows into the channel and exits under slip velocity and temperature jump condition. The channel walls are assumed porous, fluid is incompressible, Newtonian, and flowing steadily. The mechanics of the fluid is described by coupled, highly successive, nonlinear system of higher-order partial differential equations transformed using appropriate similarity transform to ordinary differentials. These are analyzed by adopting the Homotopy perturbation method of analysis. Results obtained from the analysis show a quantitative increase of nanoparticle concentration from  enhanced thermal transfer, which effect is significant towards the lower plate. Similarly, radiation increase reveals higher heat transfer while the Reynolds parameter shows reducing heat transfer. Results obtained compared with similar literature are in good agreement. The study finds good application in tribology, ferrofluids, and arterial blood flow amongst other practical, yet relevant applications.


Main Subjects

[1] A.C. Eringen, Theory of Micropolar fluids, Journal of mathematical Mechanics, 16 (1966) 1-18.
[2] M.D. Aurangzaib, S. Uddin, K. Bhattacharyya, S. Shafie, Micropolar fluid flow and heat transfer over an exponentially permeable shrinking sheet, Propulsion and Power Research, 5(4) (2016) 310-317.
[3] R.N. Bank, G.C. Dash, Chemical reaction effect on peristaltic motion of micropolar fluid through a porous medium with heat absorption the presence of magnetic field, Advances in Applied Science Research, 6 (2015) 20-34.
[4] M, Sheikholeslami, M. Hatami, D.D. Ganji, Micropolar fluid flow and heat transfer in a permeable channel using analytical method, Journal of Molecular Liquids, 194 (2014) 30-36.
[5]K.S. Mekheir, S.M. Mohammed, Interaction of pulsatile flow on peristaltic motion of magneto micropolar fluid through porous medium in a flexible channel: Blood flow model, International Journal Pure and Applied Mathematics, 94 (2014) 323-339.
[6] K. Ahmad, A. Ishak, R. Nazar, Micropolar fluid flow and heat transfer over a nonlinear stretching plate with viscous dissipation, Mathematical Problems in Engineering, 13 (2013) Article ID: 257161.
[7] S. Deo, D.K. Maurya, A.N. Filippo, Influence of magnetic field on micropolar fluid flow in a cylindrical tube enclosing an impermeable core coated with porous layer, Colloid Journal , 82 (2020) 649-660.
 [8] M. Trkyilmazoglu, Mixed convection flow of magnetohydramic micropolar due to a porous heater / heated deformable plate: exact solution, International Journal Heat Mass Transfer, 106 (2017) 127-134.
[9] A.T.  Akinshilo, Flow and heat transfer of nanofluid with injection through an expanding or contracting porous channel under magnetic force field, Engineering Science and Technology, an International Journal, 21 (2018) 486-494.
[10] L.I. Lund, Z. Omar, I. Khan, J. Raza, E.M. Sharif, A.H. Seikh, Magneto hydrodynamic (MHD) flow of micropolar fluid with effects of viscous dissipation and joule heating over an exponential shrinking sheet: Triple solution and stability analysis, Symmetry, 12(142) (2015) 1-16.
[11] S. Ahmad, M. Ashraf, K. Ali, K.S. Nisar, Computational analysis of heat transfer and mass transfer in a micropolar fluid flow through a porous medium between permeable walls, International Journal of Nonlinear Sciences and Numerical Simulation, 52 (4) (2020) 101-113.
[12]R.A. Damseh, M.Q. Al-Odat, A.J. Chamkha, B.A. Shannak, Combined effect of heat generation or absorption and first-order chemical reaction on micropolar fluid flows over a uniformly stretched permeable surface: The full analytical solution, International Journal of Thermal Science, 48 (8) (2009) 1658-1663.
[13] M. Alizadeh, A.S. Dogonchi, D.D. Ganji, Micropolar nanofluid flow and heat transfer between penetrable walls by the presence of thermal radiation and magnetic field, Case Studies in Thermal Engineering, 12 (2018) 319-322.
[14]  M.M. Rahman, I.A. Eltayeb, S. Mohammad, M. Rahaman, Thermo-micropolar fluid flow along a vertical permeable plate with uniform surface heat flux in the presence of heat generation, Thermal Science, 13(1) (2009) 23-26.
[15] A.T. Akinshilo, Investigation of nanofluid conveying porous medium through non-parallel plates using the Akbari Ganji method, Physica Scripta 95 (12) (2019) 1-11 .
[16] T. Hayat, T. Nasir, M.I. Khan, A. Alsaedi, Non-Darcy flow of water based single (SWCNTS) and multiple (MWCNTS) walls carbon nanotubes with multiple slip condition due to rotating disk, Results in Physics,  9 (2019) 390-399.
[17]S.R. Yan, R. Kalbasi, Q. Nguyen, A. Karimipour, Sensitivity of adhesive and cohesive intermolecular forces to the incorporation of MWCNTs into liquid paraffin: Experimental study and modelling of surface tension, Journal of Molecular Liquids, 310 (2020) 113235.
[18] Z. Tian, S. Rostamis, T. Taherialekouhi, A. Karimipour, A. Moradikazerouni, H. Yarmand, N.W.B.M. Zulkifli, Prediction of rheological behavior of a new hybrid nanofluid consists of copper oxide and multi walled carbon nanotubes suspended in a mixture of water and ethylene glycol using curve fitting on experimental data, Physica A: Statistical Mechanics and Its Applications, 549 (2020) 124101.
[19] B. Sharifzadeh, R. Kalbasi, M. Jahangiri, D. Toghraie, A. Karimipour, Computer modelling of pulsatie blood flow in  elastic artery using a software program for application in biomedical engineering, Computer Methods and Programs in Biomedicine, 192 (2020) 105442.
[20] M. Farzinpour, D. Toghraie, B. Mehmandoust, F. Aghadavoudi, A. Karimipour, Molecular dynamics study of barrier effects on ferro-nanofluid flow in the presence of constant and time dependent external magnetic field, Journal of Molecular Liquids, 308 (2020) 113152.
[21] S.R. Yan, R. Kalbasi, Q. Nguyen, A. Karimpour, Rheological behavior of hybrid MWCNTs-TiO2/EG nanofluid: A comprehensive modelling and experimental study, 306 (2020) 112937.
[22]A. Zakari, M. Ghalambaz, A.J. Chamkha, D.D. Rossi, Theoretical analysis of natural convection boundary layer heat and mass transfer of nanofluids: effects of size, shape and type of nanoparticles, type of base fluid and working temperature,  Advanced Powder Technology, 26(3) (2015) 935-946.
[23]A.J.  Chamkha, A. Al-Mudhaf,  Unsteady heat and mass transfer from a rotating vertical cone with a magnetic field and heat generation or absorption effects, International Journal of Thermal Science, 44(3) (2005) 267-276.
[24] S.H. Reddy, M.C. Raju, E.K. Reddy, Magneto convective flow of a non-Newtonian fluid through non-homogeneous porous medium past a vertical porous plate with variable suction, Journal of Applied Mathematics and Physics 4 (2016) 233-248.
[25] M. Naravhani, Unsteady free convection flow past a semi-infinite vertical plate with constant heat flux in water based nanofluids, IOP Conference Series: Materials Science and Engineering, 15, (2018) 81-94.
[26] R. Subba, R., Gorla, A.J. Chamkha, Natural convective boundary layer flow over a nonisothermal vertical plate embedded in a porous medium saturated with a nanofluid, Nanoscale and Microscale Thermophysical Engineering, 15 (2) (2010) 81-94.
[27] A.W.  Xiao, H.J.  Lee, I. Capone, A. Robertson, T. Wi,  J. Fawdon, S. Wheeler, H.W. Lee, N. Grobert, M. Pasta, Understanding the conversion mechanism and performance of monodisperse FeF2 nanocrystal cathode, Nature Materials , 19 (2020) 644-654.
[28] D.J. Lewis, L.Z. Zomberg, D.J.D. Carter, R.J. Macfarlane, Single crystal winter bottom constructions of nanoparticles super lattices , Nature Material,  19 (7) (2020) 719-724.
[29] H. Dessie, N. Kishan, MHD effects on heat transfer over stretching sheet embedded in porous medium with variable viscosity, viscous dissipation and heat source/sink, Ain Shams Engineering Journal , 5 (3) (2014) 967-977.
[30] S.M. Ibrahim, Radiation effects on mass transfer flow through a highly porous medium with heat generation and chemical reaction, International Scholarly Research Notices,13 (2013) Article ID 765408.
[31] B. Souyeh, M.G. Reddy, P. Sreenivasulu, T. Poornima, M. Rahimi-Gorji, I.M. Alarifi, Comparative analysis on non-linear radiative heat transfer on MHD Casson nanofluid past a thin needle, Journal of Molecular Liquids, 284 (2019) 163-174.
[32] A.T. Akinshilo, A.G. Davodi, A. Ilegbusi, M.G. Sobamowo, Thermal analysis of radiating film flow of sodium alginate using MWCNT nanoparticles, Journal of Applied and Computational Mechanics 8 (1) (2020) 219-231.
[33] A. Pantokratoras, T. Fang, Sakiadis flow with nonlinear Rosseland thermal radiation, Physica Scripta, 87 (1) (2013) 015703.
[34] H. Khan, M. Haneef, Z. Shah, S. Muhammad, S. Islam, W. Khan, The combined magneto hydrodynamic and electric field effect on unsteady Maxwell nanofluid flow over a stretching surface under the influence of variable heat and thermal radiation, Applied Science, 8 (2) (2018) 160
[35] B. Mahanthesh, B.J. Gireesha, I.L. Animasaun, Exploration of non-linear thermal radiation and suspended nanoparticles effects on mixed convection boundary layer flow on nano liquids on a melting vertical surface , Journal of Nanofluids 7 (5) (2018) 833-843.
[36] M. Mustafa, A. Mushtaq, T. Hayat, B. Ahmad, Nonlinear radiation heat transfer effects in the natural convective boundary layer flow of nanofluid past a vertical plate: a numerical study, PlosOne, 9(9) (2014) e103946.
[37] L. Dianchen, M. Ramzan, N.U. Huda, J.D. Chung, U. Farooq, Nonlinear radiation effect on MHD Carreau nanofluid over a radially stretching surface , Science Reports, 8 (2018) 3709.
[38] J.V. Ramana Reddy, V. Sugunamma, N. Sandeep, Thermophoresis and Brownian motion effects on unsteady MHD nanofluid flow over a slandering surface with slip effects, Alexandria Engineering Journal, 57 (4) (2017) 2465-2473.
[39] M.K. Nayak, F. Mabood, O.D. Makinde, Heat transfer and buoyancy‐driven convective MHD flow of nanofluids impinging over a thin needle moving in a parallel stream influenced by Prandtl number, Heat Transfer—Asian Research,49 (2) (2019) 1–18.
[40] S.N.A. Salleh, N. Bachok, N. Md. Arifin, F. Md. Ali, I. Pop, Stability analysis of mixed convection flow towards moving a thin needle in nanofluid, Applied Science, 8(6) (2018) 842.
[41] P. Mohan Khrishna, R. Prakash Sharma, N. Sandeep, Boundary layer analysis of persistent moving horizontal needle in Blasius and Sakiadis magnetohydrodynamic radiative nanofluid flow, Nuclear Engineering Technology, 49 (8) (2017) 1654-1659.
[42] C. Sulochana, G.P. Ashwinkumar, N. Sandeep, Joule heating effect on a continuously moving thin needle in MHD Sakiadis flow with thermophoresis and Brownian moment , The European Physical Journal Plus, 132 (2017) 387.
[43] O. Pourmehran, M.M. Sarafraz, M. Rahimi-Gorji, D.D. Ganji, Rheological behaviour of various metal-based nano-fluids between rotating discs: a new insight
Journal of the Taiwan Institute of Chemical Engineers, 18 (2018) Article ID:644800.
[44] H. Mirgolbabaee, S.T. Ledari, M. Sheikholeslami, D.D. Ganji, Semi-analytical investigation of momentum and heat transfer of a non-Newtonian fluid flow for specific turbine cooling application using AGM, International Applied Computational Mathematics, 3 (2017) S1463-S1475.
[45] A.T Akinshilo, A.O. Ilegbusi, H. Ali, A. Surajo. Heat transfer analysis of nanofluid flow with porous medium through Jeffery Hamel diverging/converging channel, Journal of Applied and Computational Mechanics, 6(3) (2020) 433-444.
[46] A.T. Akinshilo, Thermal performance evaluation of MHD nanofluid transport through a rotating system undergoing uniform injection/suction with heat generation, Bionanoscience, 9 (3) (2019) 740-748.
[47] F. Mabood, A.T. Akinshilo, Stability analysis and heat transfer of hybrid Cu-Al2O3/H2O nanofluids transport over a stretching surface, International Communications in Heat and Mass Transfer, 123 (2021) 105215.
[48] S. Shen, Application of He’s variational iteration method to the fifth order boundary value problems, Journal of Physics Conference Series, 96 (2008) 012185.
[49] G. Domairry, Z. Ziabakhsh, H. Doumiri, G. Modil Habib, Approximate solution of non-Newtonian  viscoelastic fluid flow on a turbine disc for cooling purpose by using Adomian decomposition method, Meccanica,  98 (2013) 4889-4909.
[50] A.S. Dogonchi, M. Alizadeh, D.D. Ganji, Investigation of MHD GO-water nanofluid flow and heat transfer in a porous channel in the presence of thermal radiation effect, Advanced Powder Technology, 28 (7) (2017) 1815-1825 .
[51] A.S. Dogonchi, D.D. Ganji, Investigation of MHD nanofluid flow and heat transfer in a stretching /shrinking convergent/divergent channel considering thermal radiation, Journal of Molecular Liquid, 220 (2016) 592-603.