MHD Boundary Layer Flow of Micropolar Fluids due to Porous Shrinking Surface with Viscous dissipation and Radiation

H. Waqas, S. Hussain, S. Khalid


The mathematical analysis and numerical solution for the flow of micropolar fluids owing to shrinking boundary is considered in the presence of magnetic field and thermal radiation. The parametric study of the problem demonstrates the effects of magnetic field, suction, micropolar material parameter and thermal radiation on velocity, microrotation and temperature. The mathematical model of the problem is transformed to non-dimensional form to obtain numerical solution. The results have been obtained for several representative values of the material parameters d1, d2 and d3, heat source parameter l and magnetic parameter M, suction/injection parameter S, Eckert number Ec, Radiation parameter Rn and Prandtl number Pr . The flow speed and microrotation are slowed with incremented inputs of micropolar parameter d1. The fluid temperature increases with radiation parameter but it diminishes against suction.

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A.C. Eringen, “Theory of micropolar fluids”, J. Math. Mech., vol. 16, pp. 1–18, 1966.

S. Baag, S.R. Mishra, G.C. Dash and M.R. Acharya, “Numerical investigation on MHD micropolar fluid flow toward a stagnation point on a vertical surface with heat source and chemical reaction”, J. King Saud Uni – Engg. Sci., vol. 29, pp. 75–83, 2017.

H.S. Takhar, R. Bhargava, R.S. Agrawal and A.V.S. Balaji, “Finite element solution of micropolar fluid flow and heat transfer between two porous discs”, Int. J. Engg. Sci., vol. 38, pp. 1907-1922, 2000.

E.M. Abo-Eldahab and M.A. El-Aziz, “Flow and heat transfer in micropolar fluid past a stretching surface embedded in a non-Darcian porous medium with uniform free stream”, Appl. Math. Comput.,

vol. 162, pp. 881-899, 2005.

H. Sajjad, A.K. Muhammad and S. Muhammad, “Hydromagnetic flow of micropolar fluid between two horizontal plates, both the plates being stretching sheets”, World Appl. Sci. J., vol. 28, pp. 1888-1895, 2013.

R.N. Barik and G.C. Dash. “Chemical reaction effect on peristaltic motion of micropolar fluid through a porous medium with heat absorption in the presence of magnetic field”, Adv. Appl. Sci. Res.

vol. 6, no. 3, pp. 20-34, 2015.

P. Vimala and P.B. Omega, “Solution of micropolar fluid flow through porous channels a differential transform approach”, Appl. Math. Sci., vol. 9, no. 66, pp. 3291–3302, 2015.

M. Shafique, “Numerical solution of MHD viscous flow of micropolar fluid over a shrinking sheet using SOR iterative procedure”, Intl. J. Innov. Sci. Res., vol. 14, no. 2, pp. 259-267, 2015.

B.H. Veena, “Effect of velocity slip and permeability on micropolar squeezing flow”, Int. J. Comp. Math. Sci., vol. 3, no. 4, pp. 41-50, 2014.

A.C. Eringen, “Theory of thermomicropolar fluids”, J. Math. Anal. Appl., vol. 38, pp. 480-496, 1972.

F. Ahmad, S. Hussain and A. Ansari, “Unsteady MHD blood flow with micropolar fluid characteristics and heat source through parallel plate channel”, J. Appl. Environ. Biol. Sci., vol. 5, no.4. pp. 80-86, 2015.

S. Khilap and K. Manoj, “Effect of thermal radiation on melting heat transfer in stagnation point flow of MHD micropolar fluid towards a stretching surface”, Int. J. Adv. Eng. Res. Tech., vol. 15, pp. 22-28, 2014.

H. Waqas, S. Hussain, A. Saboor and S. Khalid, “Micropolar fluids flow over a shrinking porous surface in the presence of magnetic field and thermal radiation”, Sci. Int. (Lahore), vol. 28, no.1, pp. 53-57, 2016.

H. Waqas, M.A. Kamal, A Farooq, S. Khalid and S. Hussain, “The radiation effect on MHD stagnation point flow of micropolar fluids due to a porous shrinking sheet with heat generation”, Sci. Int. (Lahore),

vol. 28, no.5, pp. 4271-4275, 2016.

S. Khalid, S. Hussain and H. Waqas. “Numerical solution of MHD flow and heat transfer in porous medium over a porous shrinking surface with radiation and viscous dissipation”, Sci. Int. (Lahore), vol. 28, no.4,

pp. 4297- 4302, 2016.

G.M. Abdel-Rahman, “Effect of magnetohydrodynamic on thin film of unsteady micropolar fluid through a porous medium”, J. Mod. Phys., vol. 2, pp. 1290-1304, 2011.

S. Asghar, M.R. Mohyuddin and T. Hayat, “Effects of Hall current and heat transfer on flow due to a pull of eccentric rotating disks”, Int. J. Heat Mass Transfer, vol. 48, pp. 599-607, 2005.

M.R. Mohyuddin and T. Goetz, “Resonance behavior of viscoelastic fluid in Poiseuille flow in the presence of a transversal magnetic field”, Int. J. Num. Meth. Fluids, vol. 49, no. 8, pp. 837–847, 2005.

S. Jena, “Numerical solution of boundary layer MHD flow with viscous dissipation”, The Experiment, vol. 18, no.2, pp. 1235-1244, 2014.

Y. Ren, “Fundamentals of Computational Fluid Dynamics (in Chinese)”, Beijing Qsinghua University Press, 2006.

E.O. Fatunmbi and A. Adeniyan, “MHD stagnation point-flow of micropolar fluids past a permeable stretching plate in porous media with thermal radiation, chemical reaction and viscous dissipation”, J. Adv. Math. Comp. Sci., vol. 26, no. 1, pp. 11-19, 2018.

K. Kanagarajan and S. Indrakumar, “Numerical solution of Nth-order fuzzy differential equation by Runge-Kutta method of order five”, Int. J. Math. Anal., vol. 6, pp. 2885-2896, 2012.

B. Mohanty, S.R. Mishra and H.B. Pattanayak, “Numerical investigation on heat and mass transfer effect of micropolar fluid over a stretching sheet through porous media”, Alexandria Engg. J., vol. 54, pp. 223–232, 2015.


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