Magnetohydrodynamic micropolar fluid flow in presence of nanoparticles through porous plate: A numerical study

Magnetohydrodynamic micropolar fluid flow in presence of nanoparticles through porous plate: A numerical study

S.M. Arifuzzaman Md. Farid Uddin Mehedi Abdullah Al-Mamun Pronab Biswas Md. Rafiqul Islam Md. Shakhaoath Khan 

Mathematics Discipline, Khulna University, Khulna 9208, Bangladesh

Department of Thermal Science & Energy Engineering, University of Science & Technology of China, Anhui 230026, China

Physics Discipline, Khulna University, Khulna-9208, Bangladesh

Department of Mathematics, Pabna University of Science & Technology, Pabna 6600, Bangladesh

School of Engineering, RMIT University, GPO Box 2476, Melbourne 3001, VIC, Australia

Corresponding Author Email:
11 December 2017
15 September 2018
30 September 2018
| Citation



This study numerically investigates Magnetohydrodynamic (MHD) convective and chemically reactive unsteady micropolar fluid flow with nanoparticles through the vertical porous plate with mass diffusion, thermal radiation, radiation absorption and heat source. A flow model is established by employing the well-known boundary layer approximations. To obtain the non-similar equation, the boundary layer governing equations including continuity, momentum, energy and concentration balance were nondimensionalised by usual transformation. A non-similar approach is applied to the flow model. To optimize the parametric values, the stability and convergence analysis (SCA) have been analysed for the Prandtl number (Pr) and Lewis number (Le). It is observed that with initial boundary conditions, U =V =T = C= 0 and for Δτ = 0.005, ΔX = 0.20 and ΔY = 0.25, the system converged at Prandtl number, Pr≥ 0.356 and Lewis number, Le ≥ 0.16. The coupled non-linear partial differential equations are solved by explicit finite difference method (EFDM) and the numerical results have been calculated by Compaq Visual FORTRAN 6.6a. Evaluation of the thermal and momentum boundary layer thickness with isotherms and streamlines analysis of boundary layer flows have been shown for the thermal radiation parameter (R). The effects of various parameters entering the problem on velocity, angular velocity, temperature and concentration are shown graphically.


micropolar fluid, nanoparticles, radiation absorption, chemical reaction, thermal radiation, stability and convergence analysis

1. Introduction
2. Mathematical Flow Model
3. Shear Stress, Nusselt Number and Sherwood Number
4. Numerical Solution
5. Results and Discussions
6. Conclusions

[1]   Eringen AC. (1966). Theory of micropolar fluids. Journal of Mathematics and Mechanics 16: 1-18.

[2]   Hudimoto B, Tokuoka T. (1969). Two-dimensional shear flows of linear micropolar fluids. Int. J. Eng. Sci. 7: 515-522.

[3]   Lockwood F, Benchaita F, Friberg S. (1987). Study of lyotropic liquid crystal in viscometric flow and elasto hydrodynamics contact. Tribol. Trans. 30: 539-548.

[4]   Ariman T, Turk MA, Sylvester ND. (1974). On steady and pulsatile flow of blood. J. Appl. Mech. 41: 1-7.

[5]   Eringen AC. (1976) Polar and nonlocal field theories. Academic Press, New York, p. 288. 

[6]   Ariman T, Turk MA, Sylvester ND. (1974), Microcontinuum fluid mechanics - a review. Int. J. Eng. Sci. 12: 273-293.

[7]   Crane LJ. (1970). Flow past a stretching plate. Z. Angew. Math. Phys. 21: 645-647.

[8]   Kelson NA, Desseaux A. (2001). Effect of surface condition on flow of micropolar fluid driven by a porous stretching sheet. Int. J. Eng. Sci. 39: 1881-1897.

[9]   Mohammadein AA, Gorla RSR. (2001). Heat transfer in a micropolar fluid over a stretching sheet with viscous dissipation and internal heat generation. Int. J. Num. Methods Heat Fluid Flow 11: 50-58.

[10]  Hussain ST, Nadeem S, Rizwan ULH. (2014). Model-based analysis of micropolar nanofluid flow over a stretching surface. Eur. Phys. J. Plus 129(8): 1-10.

[11]  Nazar R, Amin N, Filip D, Pop I. (2004). Stagnation point flow of a micropolar fluid towards a stretching sheet. Int. J. Non-Linear Mech. 39(7): 1227–35. 

[12]  Nazar R, Ishak A, Pop I. (2008). Unsteady boundary layer flow over a stretching sheet in a micropolar fluid. Int. J. Math. Phys. Eng. Sci. 2(3): 161–5.

[13]   Bhargava R, Kumar L, Takhar HS. (2003). Finite element solution of mixed convection micropolar fluid driven by a porous stretching sheet. Int. J. Eng. Sci. 41: 2161-2178.

[14]   Bhargava R, Sharma S, Takhar HS, Beg OA, Bhargava P. (2007). Numerical solutions for microplar transport phenomena over a nonlinear stretching sheet. Nonlinear Anal., Model. Control 12: 45-63.

[15]   Erickson LE, Fan LT, Fox VG. (1966). Heat and mass transfer on moving continuous flat plate with suction or injection. Ind. Eng. Chem. Fundam. 5: 19-25.

[16]   Fox VG, Erickson LE, Fan LT. (1968). Methods for solving the boundary layer equations for moving continuous flat surfaces with suction and injection. AIChE J. 14: 726-736.

[17]   Dutta BK, Roy P, Gupta AS. (1985). Temperature field in the flow over a stretching sheet with uniform heat flux. Int. Commun. Heat Mass Transf. 12: 89-94.

[18]   Hayat T, Javed T, Abbas Z. (2009). MHD flow of a micropolar fluid near a stagnation point towards a non-linear stretching surface. Nonlinear Anal., Real World Appl. 10(3):1514-1526.

[19]   Ishak A. (2010). Thermal boundary layer flow over a stretching sheet in a micropolar fluid with radiation effect. Meccanica 45: 367-373.

[20]   Latiff NAA, Uddin MJ, Bég OA, Ismail AI. (2015). Unsteady forced bioconvection slip flow of a micropolar nanofluid from a stretching/shrinking sheet. Proceedings of the Institution of Mechanical Engineers Part N Journal of Nanoengineering 230(4): 177-187.

[21]    Abel MS, Siddheshwar PG, Mahesha N. (2011). Numerical solution of the momentum and heat transfer equations for a hydromagnetic flow due to a stretching sheet of a non-uniform property micropolar liquid. Appl. Math. Comput. 217: 5895-5909.

[22]   Abbas Z, Naveed M, Sajid M. (2013). Heat transfer analysis for stretching flow over a curved surface with magnetic field. Journal of Engineering Thermophysics 22(4): 37–345. 10.1134/S1810232813040061

[23]   Naveed M, Abbas Z, Sajid M. (2016). Hydromagnetic flow over an unsteady curved stretching surface. Eng. Sci. Technol. Int. J. 19(2): 841–5.

[24]   Naveed M, Abbas Z, Sajid M. (2016). MHD flow of a micropolar fluid due to a curved stretching sheet with thermal radiation. J Appl Fluid Mech. 9(1): 131–138.

[25]   Bilal M, Hussain S, Sagheer M. (2017). Boundary layer flow of magneto-micropolar nanofluid flow with Hall and ion-slip effects using variable thermal diffusivity. Bulletin of the Polish Academy of Sciences Technical Sciences 65(3): 383-390.

[26]   Arifuzzaman SM, Rana BMJ, Ahmed R, Ahmmed SF. (2017). Cross diffusion and MHD effect on a high order chemically reactive micropolar fluid of naturally convective heat and mass transfer past through an infinite vertical porous medium with a constant heat sink. AIP Conference Proceedings, 1851, 020006.

[27]   Arifuzzaman SM, Khan MS, Hossain KE, Islam MS, Akter S, Roy R. (2017). Chemically reactive viscoelastic fluid flow in presence of nano particle through porous stretching sheet. Frontiers in Heat and Mass Transfer 9(5): 1-11.

[28]   Khan MS, Rahman MM, Arifuzzaman SM, Biswas P, Karim I. (2017), Williamson fluid flow behaviour of MHD convective and radiative Cattaneo-Christov heat flux type over a linearly stretched surface with heat generation, viscous dissipation and thermal-diffusion. Frontiers in Heat and Mass Transfer 9(15): 1-11.

[29]   Biswas P, Arifuzzaman SM, Karim I, Khan MS. (2017). Impacts of magnetic field and radiation absorption on mixed convective Jeffrey Nano fluid flow over a vertical stretching sheet with stability and convergence analysis. Journal of nanofluids 6(6): 1082-1095.

[30]  Arifuzzaman SM, Khan MS, Islam MS, Islam MM, Rana BMJ, Biswas P, Ahmmed SF. (2017). MHD Maxwell fluid flow in presence of nano-particle through a vertical porous–plate with heat- generation, radiation absorption and chemical reaction. Frontiers in Heat and Mass Transfer 9 (25): 1-14. 

[31]  Arifuzzaman SM, Khan MS, Mehedi MFU, Rana BMJ, Ahmmed SF. (2018). Chemically reactive and naturally convective high-speed MHD fluid flow through an oscillatory vertical porous-plate with heat and radiation absorption effect. Engineering Science and Technology, an International Journal 21(2): 215-228.

[32]  Vedavathi N, Ramakrishna K, Reddy KJ. (2015). Radiation and mass transfer effects on unsteady MHD convective flow past an infinite vertical plate with Dufour and Soret effects. Ain Shams Engineering Journal 6: 363–3.

[33]  Wernik J, Grabowski M, Wołosz KJ. (2018). Thermal analysis of radiator under natural and forced convection conditions using numerical simulation and thermography. Chemical Engineering Transactions 70: 1501-1506.

[34]  Oravec J, Bakošová M, Vasičkaninová A, Mészáros A. (2018). Robust model predictive control of a plate heat exchanger. Chemical Engineering Transactions 70: 25-30.