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

## Abstract

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 d_{1}, d

_{2}and d

_{3}, heat source parameter l and magnetic parameter M, suction/injection parameter S, Eckert number E

_{c}, Radiation parameter R

_{n}and Prandtl number P

_{r}. The flow speed and microrotation are slowed with incremented inputs of micropolar parameter d

_{1}. The fluid temperature increases with radiation parameter but it diminishes against suction.

## References

A.C. Eringen, â€œTheory of micropolar fluidsâ€, J. Math. Mech., vol. 16, pp. 1â€“18, 1966.

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

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

E.M. Abo-Eldahab and M.A. El-Aziz, â€œFlow and heat transfer in micropolar fluid past a stretching surface embedded in a non-Darcian porous medium with uniform free streamâ€, Appl. Math. Comput.,

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

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

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

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

P. Vimala and P.B. Omega, â€œSolution of micropolar fluid flow through porous channels a differential transform approachâ€, Appl. Math. Sci., vol. 9, no. 66, pp. 3291â€“3302, 2015.

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

B.H. Veena, â€œEffect of velocity slip and permeability on micropolar squeezing flowâ€, Int. J. Comp. Math. Sci., vol. 3, no. 4, pp. 41-50, 2014.

A.C. Eringen, â€œTheory of thermomicropolar fluidsâ€, J. Math. Anal. Appl., vol. 38, pp. 480-496, 1972.

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

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

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

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

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

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

pp. 4297- 4302, 2016.

G.M. Abdel-Rahman, â€œEffect of magnetohydrodynamic on thin film of unsteady micropolar fluid through a porous mediumâ€, J. Mod. Phys., vol. 2, pp. 1290-1304, 2011.

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

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

S. Jena, â€œNumerical solution of boundary layer MHD flow with viscous dissipationâ€, The Experiment, vol. 18, no.2, pp. 1235-1244, 2014.

Y. Ren, â€œFundamentals of Computational Fluid Dynamics (in Chinese)â€, Beijing Qsinghua University Press, 2006.

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

K. Kanagarajan and S. Indrakumar, â€œNumerical solution of Nth-order fuzzy differential equation by Runge-Kutta method of order fiveâ€, Int. J. Math. Anal., vol. 6, pp. 2885-2896, 2012.

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

## Downloads

## Published

## How to Cite

*The Nucleus*, vol. 57, no. 3, pp. 76–80, Feb. 2021.