FINITE ELEMENT SOLUTION OF HYDROMAGNETIC AXISYMMETRIC FLOW AND HEAT TRANSFER OVER A NONLINEARLY SHRINKING SHEET

Article Sidebar

pdf
Published: May 11, 2013

Main Article Content

Chandaneswar Midya
Ghatal R S Mahavidyalaya

Abstract

In this paper, an axisymmetric flow and heat transfer of electrically conducting fluid over a nonlinearly shrinking surface in the presence of magnetic field and suction at the surface is investigated numerically. The shrinking velocity as well as suction at the sheet are assumed to follow the power law of radial distance. A magnetic field is applied normal to the sheet. The governing boundary layer PDEs in cylindrical polar coordinates are reduced into highly nonlinear ordinary differential equations by a similarity transformation. The reduced ODEs are then solved numerically by finite element method for power-law temperature boundary conditions. It is found that radial velocity is decreased with the increase in magnetic field strength and suction at the surface. It is also observed that the thermal boundary layer thickness decreases with the increase in magnetic field strength, suction parameter, power-law index for shrinking velocity and Prandtl number. On the other hand, the thermal boundary layer thickness is increased for increasing values of power-law index for temperature.  

Downloads

Download data is not yet available.

Article Details

How to Cite
Midya, C. (2013). FINITE ELEMENT SOLUTION OF HYDROMAGNETIC AXISYMMETRIC FLOW AND HEAT TRANSFER OVER A NONLINEARLY SHRINKING SHEET. Journal of Global Research in Mathematical Archives(JGRMA), 1(4), 21–30. Retrieved from https://www.jgrma.com/index.php/jgrma/article/view/48
Issue
Vol. 1 No. 4 (2013): April-2013
Section
Research Paper

Open Access: This is an open-access journal. All articles published in the Journal of Global Research in Mathematical Archives(JGRMA) are made immediately and permanently available under the Creative Commons Attribution 4.0 International (CC BY 4.0) License. Authors retain the copyright of their work and grant Journal of Global Research in Mathematical Archives(JGRMA)  the right of first publication. This license permits unrestricted use, distribution, adaptation, and reproduction in any medium or format, including commercial use, provided the original author(s), source, and license are properly acknowledged.

Google Scholar Indexed | DOI Enabled | OAI-PMH Compliant | Open Access Journal

Author Biography

Chandaneswar Midya, Ghatal R S Mahavidyalaya

Dr. Midya obtained his M. Sc. from Jadavpur University, Kolkata in 1997 and is awarded Ph D from Burdwan University in 2008 on numerical study of viscous flows with separation. He joined in the department of Mathematics, Sripat Singh College, Jiaganj, Murshidabad, West Bengal as an Assistant Professor in the year 2002. Presently, He is working in the Department of Mathematics, Ghatal Rabindra Satabarsiki Mahavidyalaya, Paschim Medinipur as an Assistant Professor. His present research includes boundary Layer flow, heat and mass transfer, channel flows. 

References

REFERENCES

B. D. Sakiadis : Boundary-layer behavior on continuous solid surface:I.The Boundary-Layer equations for two-dimensional and asymmetric flow, AIChE J, 7 (1961) 26-28.

B. C. Sakiadis: Boundary-layer behavior on continuous solid surface:II.The Boundary-Layer on a continuous flat surface, AIChE J, 7 (1961) 221-225.

Tsou, F. K., Sparrow, E. M. and Goldstain, R. J. Flow and heat transfer in the boundary layer on a continuous moving surface. Int J Heat Mass Transfer, 10(1967), 219-235.

Wang, C. Y. Liquid film on an unsteady stretching sheet. Quart. Appl. Math., 48(1990), 601-610.

M. Miklavcic, C. Y. Wang : Viscous flow due to a shrinking sheet. Quart Appl. Math. 64(2) (2006) 283-290.

Hayat, T., Abbas, Z. and Sajid, M. On the analytic solution of magnetohydrodynamic flow of a second grade fluid over a shrinking sheet. J Appl Mech Trans ASME, 74(6) (2007), 1165-1171.

Wang, C. Y. Stagnation flow towards a shrinking sheet. Int. J. Nonlinear Mech. 43, 377-382 (2008)

Nadeem, S. and Awais, M. Thin film flow on an unsteady shrinking sheet through porous medium with variable viscosity. Physics Letters A, 372, 4965-4972 (2008)

T. Fang, J. Zhang : Viscous flow over an unsteady shrinking sheet with mass transfer, Chin. Phys. Lett., 26(1) (2009) 014703-1-4.

T. Fang, J. Zhang : Closed form exact solutions of MHD viscous flow over a shrinking sheet. Communications in Nonlinear Science and Numerical Simulation. 14(7) (2009) 2853-2857.

S. Nadeem, and A. Hussain : MHD flow of a viscous fluid on a nonlinear porous shrinking sheet with homotopy analysis method. Appl. Math. Mech. (Engl. Ed.) 30(12) (2009) 1569-1578.

T. Fang, J. Zhang : Thermal boundary layer over a shrinking sheet : an analytical solution. Acta Mech. 209 (2010) 325-343.

N. F. M. Noor, S. A. Kechilb, I. Hashim : Simple non-perturbative solution for MHD viscous flow due to a shrinking sheet. Communications in Nonlinear Science and Numerical Simulation. 15(2) (2010) 144-148.

C. Midya : Hydromagnetic boundary layer flow and heat transfer over a linearly shrinking permeable surface. Int. J. Appl. Math. Mech. 8(3) (2012) 57-68.

C. Midya “Heat transfer in MHD boundary layer flow over a shrinking sheet with radiation and heat sink†Journal of Global Research in Mathematical Archives, 2013, Vol. 1, No. 2, pp. 63-70.

M. Sajid, T. Hayat : The application of homotopy analysis method for MHD viscous flow due to a shrinking sheet. Chaos, Solitons and Fractals. 39(3) (2009) 1317-1323.

Muhaimin, Kandasamy R, and Khamis, A. B. Effects of heat and mass transfer on nonlinear MHD boundary layer flow over a shrinking sheet in the presence of suction. Appl. Math. Mech. (Engl. Ed.), 29(10), 1309-1317 (2008)

Muhaimin, R. Kandasamy, I. Hashim : Effect of chemical reaction, heat and mass transfer on nonlinear boundary layer past a porous shrinking sheet in the presence of suction. Nuclear Engg. and Design. 240(5) (2010) 933-939.

Ali, F. M., Nazar, R. and Arifin, N. M. MHD viscous flow and heat transfer induced by a permeable shrinking sheet with prescribed surface heat flux. WSEAS Trans on Math, 9(5), 365-375 (2010)

F. M. Ali, R. Nazar, N. M. Arifin, and I. Pop : Unsteady flow and heat transfer past an axisymmetric permeable

shrinking sheet with radiation effect. Int. J. Numer. Method in Fluids, (2010), DOI: 10.1002/fld.2435.

N. F. M. Noor and I. Hashim : MHD flow and heat transfer adjacent to a permeable shrinking sheet embedded in a porous medium. Sains Malaysiana. 38(4) (2009) 559-565.

C. Midya “Study of boundary layer flow and heat transfer over an axisymmetrically shrinking sheet with suction†Journal of Global Research in Mathematical Archives, 2013, Vol. 1, No. 3, pp. 70-77.

J. N. Reddy, An introduction to finite element method, Tata McGraw Hill, second edition, 2003.