Numerical Simulations of Unsteady 3D MHD Micropolar Fluid Flow over a Slendering Sheet

Document Type : Research Paper


1 Department of Mathematics, SAS, Vellore Institute of Technology, Vellore-632014, India

2 Department of Mathematics, SAS, Vellore Institute of Technology, Al-Kharj, Saudi Arabia


The purpose of the present analysis is to explore the numerical investigation on the time-dependent 3D magnetohydrodynamic flow of micropolar fluid over a slendering stretchable sheet. The prevailing PDEs are rehabilitated into coupled non-linear ODEs with the aid of appropriate similarity variables and then numerically calculated by applying the 4th RKM incorporate with shooting scheme. The contributions of various interesting variables are shown graphically. Emerging physical parameters on velocity, microrotation, and the surface drag coefficient are portrayed graphically. It is noticed that the microrotation profiles highly influenced by the vortex viscosity parameter and the micro-inertia density parameter. It is also concluded that the microrotation profiles (h2) are promoted by increasing the spin gradient viscosity parameter. Excellent accuracy of the present results is observed with the formerly published as a result of a special case.


[1] Ahmadi, G., Self-similar solution of incompressible micropolar boundary layer flow over a semi-infinite plate, Int. J. Eng. Sci., 14, 1976, 639–646.
[2] Andersson, H.I., MHD flow of a viscoelastic fluid past a stretching surface, Acta Mech., 95, 1992, 227–230.
[3] Reddy, S.R.R., Bala Anki Reddy, P., Bhattacharyya, K., Effect of nonlinear thermal radiation on 3D magneto slip flow of Eyring-Powell nanofluid flow over a slendering sheet with binary chemical reaction and Arrhenius activation energy, Adv. Powder Technol., 2019, 1-11, in press.
[4] Acharya, N., Das, K., Kumar Kundu, P., Ramification of variable thickness on MHD TiO2 and Ag nanofluid flow over a slendering stretching sheet using NDM, Eur. Phys. J. Plus., 131, 2016, 1–16.
[5] Reddy, S.R.R., Bala Anki Reddy, P., Suneetha, S., Magnetohydrodynamic flow of blood in a permeable inclined stretching surface with viscous dissipation, non-uniform heat source/sink and chemical reaction, Front. Heat Mass Transf., 10, 2018, 1–10.
[6] Nayak, M.K., Akbar, N.S., Tripathi, D., Khan, Z.H., Pandey, V.S., MHD 3D free convective flow of nanofluid over an exponentially stretching sheet with chemical reaction, Adv. Powder Technol., 28, 2017, 2159–2166.
[7] Srinivas, S., Reddy, P.B.A., Prasad, B.S.R. V., Effects of Chemical Reaction and Thermal Radiation on Mhd Flow Over an Inclined Permeable Stretching Surface With Non-Uniform Heat Source/Sink: an Application To the Dynamics of Blood Flow, J. Mech. Med. Biol., 14, 2014, 1–24.
[8] Rashad, A.M., Impact of thermal radiation on MHD slip flow of a ferrofluid over a non-isothermal wedge, J. Magn. Magn. Mater., 422, 2017, 25–31.
[9] Reddy, P.B.A., Suneetha, S., Effects of homogeneous-heterogeneous chemical reaction and slip velocity on MHD stagnation flow of a micropolar fluid over a permeable stretching/shrinking surface embedded in a porous medium, Front. Heat Mass Transf., 8, 2017, 1–11.
[10] Reddy, P.B.A., MHD boundary layer slip flow of a Casson fluid over an exponentially stretching surface in the presence of thermal radiation and chemical reaction, J. Nav. Archit. Mar. Eng., 3, 2016, 165–177.
[11] Pal, D., Roy, N., Vajravelu, K., Effects of thermal radiation and Ohmic dissipation on MHD Casson nanofluid flow over a vertical non-linear stretching surface using scaling group transformation, Int. J. Mech. Sci., 114, 2016, 257–267.
[12] Khader, M.M., Megahed, A.M., Numerical solution for boundary layer flow due to a nonlinearly stretching sheet with variable thickness and slip velocity, Eur. Phys. J. Plus., 128, 2013, 1–7.
[13] Soomro, F.A., Haq, R. ul, Khan, Z.H., Zhang, Q., Passive control of nanoparticle due to convective heat transfer of Prandtl fluid model at the stretching surface, Chinese J. Phys., 55, 2017, 1561–1568.
[14] Hosseini, E., Loghmani, G.B., Heydari, M., Rashidi, M.M., Numerical investigation of velocity slip and temperature jump effects on unsteady flow over a stretching permeable surface, Eur. Phys. J. Plus., 132, 2017, 1–16.
[15] Fang, T., Zhang, J., Zhong, Y., Boundary layer flow over a stretching sheet with variable thickness, Appl. Math. Comput., 218, 2012, 7241–7252.
[16] Bala Anki Reddy, P., Magnetohydrodynamic flow of a Casson fluid over an exponentially inclined permeable stretching surface with thermal radiation and chemical reaction, Ain Shams Eng. J., 7, 2016, 593–602.
[17] Eringen, A.C., Theory of Micropolar Fluids, J. Math. Mech., 16, 1966, 1–18.
[18] Eringen, A.C., Theory of thermomicrofluids, J. Math. Anal. Appl., 38, 480–496.1972,
[19] Rahman, M.M., Al-Lawatia, M., Effects of higher-order chemical reaction on micropolar fluid flow on a power-law permeable stretched sheet with variable concentration in a porous medium, Can. J. Chem. Eng., 88, 2010, 23–32.
[20] Srinivas, S., Reddy, P.B.A., Prasad, B.S.R.V., Non-Darcian unsteady flow of a micropolar fluid over a porous stretching sheet with thermal radiation and chemical reaction, Heat Transf. Res., 44, 2015, 172–187.
[21] Gupta, D., Kumar, L., Anwar Bég, O., Singh, B., Finite Element Analysis of MHD Flow of Micropolar Fluid over a Shrinking Sheet with a Convective Surface Boundary Condition, J. Eng. Thermophys., 27, 2018, 202–220.
[22] Ayano, M.S., Sikwila, S.T., Shateyi, S., MHD Mixed Convection Micropolar Fluid Flow through a Rectangular Duct, Math. Probl. Eng., 2018, 2018, 1–8.
[23] Ibrahim, S.M., Kumar, V., Raju, C.S.K., Possessions of viscous dissipation on radiative MHD heat and mass transfer flow of a micropolar fluid over a porous stretching sheet with chemical reaction, Transp. Phenom. Nano Macro Scales., 6, 2018, 60–71.
[24] Shamshuddin, M.D., Satya Narayana, P.V., Primary and secondary flows on unsteady MHD free convective micropolar fluid flow past an inclined plate in a rotating system: A finite element analysis, Fluid Dyn. Mater. Process., 14, 2018, 57–86.
[25] Pal, D., Mandal, G., Thermal radiation and MHD effects on boundary layer flow of micropolar nanofluid past a stretching sheet with non-uniform heat source/sink, Int. J. Mech. Sci., 126, 2017, 308–318.
[26] Reddy, P.B.A., Sekhar, D.V., Effects of radiation on MHD mixed convection flow of a micropolar fluid over a heated stretching surface with heat generation/absorption, Int. J. Eng. Res. Appl., 3, 2013, 572–581.
[27] Gnaneswara Reddy, M., Reddy, G.R.S., Micropolar fluid flow over a nonlinear stretching convectively heated vertical surface in the presence of Cattaneo-Christov heat flux and viscous dissipation, Front. Heat Mass Transf., 8, 2017, 1–9.
[28] Ramzan, M., Chung, J.D., Ullah, N., Partial slip effect in the flow of MHD micropolar nanofluid flow due to a rotating disk – A numerical approach, Results Phys., 7, 2017, 3557–3566.
[29] Chamkha, A.J., Jaradat, M., Pop, I., Three-Dimensional Micropolar Flow due to a Stretching Flat Surface, Int. J. Fluid Mech. Res., 30, 2003, 357–366.
[30] Ahmad, K., Nazar, R., Ishak, A., Pop, I., Unsteady three-dimensional boundary layer flow due to a stretching surface in amicropolar fluid, Int. J. Numer. Methods Fluids, 68, 2012, 1561–1573.
[31] Subhani, M., Nadeem, S., Numerical analysis of 3D micropolar nanofluid flow induced by an exponentially stretching surface embedded in a porous medium, Eur. Phys. J. Plus., 132, 2017, 1–12.
[32] Mabood, F., Ibrahim, S.M., Rashidi, M.M., Shadloo, M.S., Lorenzini, G., Non-uniform heat source/sink and Soret effects on MHD non-Darcian convective flow past a stretching sheet in a micropolar fluid with radiation, Int. J. Heat Mass Transf.,93, 2016, 674–682.
[33] Kumari, M., Takhar, H.S., Nath, G., MHD flow and heat transfer over a stretching surface with prescribed wall temperature or heat flux, Heat & Mass Transfer, 25, 1990, 331–336.
[34] Attia, H.A., Unsteady MHD flow near a rotating porous disk with uniform suction or injection, Fluid Dyn. Res., 23, 1998, 283–290.
[35] Khan, M., Malik, M.Y., Salahuddin, T., Hussian, A., Heat and mass transfer of Williamson nanofluid flow yield by an inclined Lorentz force over a nonlinear stretching sheet, Results Phys., 8, 2018, 862–868.