MHD Axisymmetric Flow of a Third-Grade Fluid Between Porous Disks With Heat Transfer

T.Hayata; Anum Shafiq; M.Nawaz; A.Alsaedi

doi:10.3879/j.issn.1000-0887.2012.06.006

Volume 33 Issue 6

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2012 > 33(6): 710-725

T.Hayata, Anum Shafiq, M.Nawaz, A.Alsaedi. MHD Axisymmetric Flow of a Third-Grade Fluid Between Porous Disks With Heat Transfer[J]. Applied Mathematics and Mechanics, 2012, 33(6): 710-725. doi: 10.3879/j.issn.1000-0887.2012.06.006

Citation:

PDF( 1428 KB)

MHD Axisymmetric Flow of a Third-Grade Fluid Between Porous Disks With Heat Transfer

doi: 10.3879/j.issn.1000-0887.2012.06.006

¹Department of Mathematics, Quaid-i-Azam University, 45320, Islamabad 44000, Pakistan;²Department of Humanities and Sciences, Institute of Space Technology, P.O.Box 2750, Islamabad 44000, Pakistan;
Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O.Box 80257, Jeddah 21589, Saudi Arabia

Received Date: 2011-06-02
Rev Recd Date: 2012-02-08
Publish Date: 2012-06-15

Abstract

Abstract

The magnetohydrodynamic (MHD) flow of third-grade fluid between two permeable disks with heat transfer was investigated. The governing partial differential equations were converted into the ordinary differential equations by using suitable transformations. Transformed equations were solved by using homotopy analysis method (HAM). The expressions for square residual errors were defined and optimal values of convergencecontrol parameters were selected. The dimensionless velocity and temperature fields were examined for various dimensionless parameters. Skin friction coefficient and Nusselt number were tabulated to analyze the effects of dimensionless parameters.
- heat transfer,
- axisymmetric flow,
- third-grade fluid,
- porous disks,
- skin friction coefficient,
- Nusselt number

FullText(HTML)

References(31)

References

[1]	Fetecau C, Mahmood A, Jamil M. Exact solutions for the flow of a viscoelastic fluid induced by a circular cylinder subject to a time dependent shear stress[J]. Communications in Nonlinear Science and Numerical Simulation, 2010, 15(12): 3931-3938.
[2]	Jamil M, Fetecau C, Imran M. Unsteady helical flows of Oldroyd-B fluids[J]. Communications in Nonlinear Science and Numerical Simulation, 2011, 16(3): 1378-1386.
[3]	Jamil M, Rauf A, Fetecau C, Khan N A. Helical flows of second grade fluid to constantly accelerated shear stresses[J]. Communications in Nonlinear Science and Numerical Simulation, 2011, 16(4): 1959 -1969.
[4]	Tan W C, Masuoka T. Stability analysis of a Maxwell fluid in a porous medium heated from below[J]. Physics Letters A, 2007, 360(3): 454-460.
[5]	Tan W C, Masuoka T. Stokes’ first problem for an Oldroyd-B fluid in a porous half space[J]. Physics of Fluids, 2005, 17(2): 023101-7.
[6]	Sajid M, Hayat T. Non-similar series solution for boundary layer flow of a third-order fluid over a stretching sheet[J]. Applied Mathematics and Computation, 2007, 189(2): 1576-1585.
[7]	Sajid M, Hayat T, Asghar S. Non-similar analytic solution for MHD flow and heat transfer in a third order fluid over a stretching sheet[J]. International Journal of Heat and Mass Transfer, 2007, 50(9/10): 1723-1736.
[8]	Hayat T, Mustafa M, Asghar S. Unsteady flow with heat and mass transfer of a third grade fluid over a stretching surface in the presence of chemical reaction[J]. Nonlinear Analysis: Real World Applications, 2010, 11(4): 3186-3197.
[9]	Abbasbandy S, Hayat T. On series solution for unsteady boundary layer equations in a special third grade fluid[J]. Communications in Nonlinear Science and Numerical Simulation, 2011, 16(8): 3140-3146.
[10]	Sahoo B. Hiemenz flow and heat transfer of a third grade fluid[J]. Communications in Nonlinear Science and Numerical Simulation, 2009, 14(3): 811-826.
[11]	Sahoo B, Do Y. Effects of slip on sheet driven flow and heat transfer of a third-grade fluid past a stretching sheet[J]. International Communication in Heat and Mass Transfer, 2010, 37(8): 1064-1071.
[12]	von Krmn T. ber laminare and turbulente reibung[J]. Zeitschrift für Angewandte Mathematik und Mechanik, 1921, 1(4): 233-255.
[13]	Cochran W G. The flow due to a rotating disk[J]. Mathematical Proceedings of the Cambridge Philosophical Society, 1934, 30(3): 365-375.
[14]	Benton E R. On the flow due to a rotating disk[J]. Journal of Fluid Mechanics, 1966, 24(781/800): 133-137.
[15]	Takhar H S, Chamkha A J, Nath G. Unsteady mixed convection flow from a rotating verticle cone with a magnetic field[J]. Heat and Mass Transfer, 2003, 39(4): 297-304.
[16]	Maleque K A, Sattar M A. The effects of variable properties and Hall current on steady MHD laminar convective fluid flow due to a porous rotating disk[J]. International Journal of Heat and Mass Transfer, 2005, 48(23/24): 4963-4972.
[17]	Stuart J T. On the effect of uniform suction on the steady flow due to a rotating disk[J]. The Quarterly Journal of Mechanics and Applied Mathematics, 1954, 7(4): 446-457.
[18]	Sparrow E M, Beavers G S, Hung L Y. Flow about a porous-surface rotating disk[J]. International Journal of Heat and Mass Transfer, 1971, 14: 993-996.
[19]	Miklavcic M, Wang C Y. The flow due to a rough rotating disk[J]. Zeitschrift für Angewandte Mathematik und Physik ZAMP, 2004, 55(2): 235-246.
[20]	Hayat T, Nawaz M. Unsteady stagnation point flow of viscous fluid caused by an impulsively rotating disk[J]. Journal of the Taiwan Institute of Chemical Engineers, 2011, 42(1): 41-49.
[21]	Liao S J. Beyond Perturbation: Introduction to Homotopy Analysis Method[M]. Boca Raton: Chapman and Hall, CRC Press, 2003.
[22]	Liao S J. On the analytic solution of magnetohydrodynamic flows of non-Newtonian fluids over a stretching sheet[J]. Journal of Fluid Mechanics, 2003, 488: 189-212.
[23]	Liao S J. On the homotopy analysis method for nonlinear problems[J]. Applied Mathematics and Computation, 2004, 147(12): 499-513.
[24]	Liao S J. Notes on the homotopy analysis method: some definitions and theorems[J]. Communications in Nonlinear Science and Numerical Simulation, 2009, 14(4): 983-997.
[25]	Liao S J. An optimal homotopy analysis approach for strongly nonlinear differential equations[J]. Communications in Nonlinear Science and Numerical Simulation, 2010, 15(8): 2003-2016.
[26]	Rashidi M M, Domairry G, Dinarvand S. Approximate solutions for the Burger and regularized long wave equations by means of the homotopy analysis method[J]. Communications in Nonlinear Science and Numerical Simulation, 2009, 14(3): 708-717.
[27]	Abbasbandy S, Shirzadi A. A new application of the homotopy analysis method: solving the Sturm-Liouville problems[J]. Communications in Nonlinear Science and Numerical Simulation, 2011, 16(1): 112-126.
[28]	Bataineh A S, Noorani M S M, Hashim I. Approximate analytical solutions of systems of PDEs by homotopy analysis method[J]. Computer and Mathematics With Applications, 2008, 55(12): 2913-2923.
[29]	Hashim I, Abdulaziz O, Momani S. Homotopy analysis method for fractional IVPs[J]. Communications in Nonlinear Science and Numerical Simulation, 2009, 14(3): 674-684.
[30]	哈亚特 T, 纳瓦兹 M, 奥拜达特 S. 微极流体在两个伸展平面之间的不稳定轴对称MHD流动[J]. 应用数学和力学, 2011, 32(3): 344-356 (Hayat T, Nawaz M, Obaidat S. Axisymmetric magnetohydrodynamic flow of a micropolar fluid between unsteady stretching surfaces[J]. Applied Mathematics and Mechanics (English Edition), 2011, 32(3): 361-374).
[31]	Fosdick R L, Rajagopal K R. Thermodynamics and stability of fluids of third grade[J]. Proc Roy Soc London, 1980, 369(1738): 351-377.