MHD flow and heat transfer in a thin liquid film on an unsteady stretching sheet by the homotopy analysis method

International Journal for Numerical Methods in Fluids

Volumn 63, Issue 3, 2010, Pages 357-373

  Noor, N F M ^a   Abdulaziz, O ^b   Hashim, I ^c  

^a Universiti Selangor   (Malaysia)

^b SANA A UNIVERSITY   (Yemen)

^c UNIVERSITI KEBANGSAAN MALAYSIA   (Malaysia)

Author keywords

Boundary layer; Heat transfer; Homotopy analysis method; MHD; Thin film; Unsteady stretching

Indexed keywords

HOMOTOPY ANALYSIS METHOD; HOMOTOPY ANALYSIS METHODS; MAGNETOHYDRODYNAMICS FLOWS; MHD; MHD FLOW; NUMERICAL RESULTS; SERIES SOLUTIONS; STRETCHING SURFACE; SURFACE TEMPERATURES; THIN LIQUID FILM; UNSTEADY STRETCHING SHEET;

BOUNDARY LAYERS; HEAT TRANSFER; LIQUID FILMS; MAGNETOHYDRODYNAMICS; NUMERICAL ANALYSIS; THIN FILMS;

HEAT EXCHANGERS;

EID: 77953572226     PISSN: 02712091     EISSN: 10970363     Source Type: Journal    
DOI: 10.1002/fld.2078     Document Type: Article

References (26)

1. Wang CY. Liquid film on an unsteady stretching sheet. Quarterly of Applied Mathematics 1990; 48:601-610.
2. Andersson HI, Aarseth JB, Dandapat BS. Heat transfer in a liquid film on an unsteady stretching surface. International Journal of Heat and Mass Transfer 2000; 43:69-74.
3. Liu IC, Andersson HI. Heat transfer in a liquid film on an unsteady stretching sheet. International Journal of Thermal Sciences 2008; 47:766-772.
4. Wang C. Analytic solutions for a liquid thin film on an unsteady stretching surface. Heat and Mass Transfer 2006; 42:759-766.
5. Dandapat BS, Santra B, Andersson HI. Thermocapillarity in a liquid film on an unsteady stretching surface. International Journal of Heat and Mass Transfer 2003; 46:3009-3015.
6. Dandapat BS, Santra B, Vajravelu K. The effects of variable fluid properties and thermocapillarity on the flow of a thin film on an unsteady stretching sheet. International Journal of Heat and Mass Transfer 2007; 50:991-996.
7. Chen CH. Marangoni effects on forced convection of power-law liquids in a thin film over a stretching surface. Physics Letters A 2007; 370:51-57.
8. Abel MS, Mahesha N, Tawade J. Heat transfer in a liquid film over an unsteady stretching surface with viscous dissipation in presence of external magnetic field. Applied Mathematical and Modelling, DOI: 10.1016/j.apm.2008.11.021.
9. Andersson HI, Aarseth JB, Braud N, Dandapat BS. Flow of a power-law fluid film on an unsteady stretching surface. Journal of Non-Newtonian Fluid Mechanics 1996; 62:1-8.
10. Chen CH. Heat transfer in a power-law fluid film over a unsteady stretching sheet. Heat and Mass Transfer 2003; 39:791-796.
11. Chen CH. Effect of viscous dissipation on heat transfer in a non-Newtonian liquid film over an unsteady stretching sheet. Journal of Non-Newtonian Fluid Mechanics 2006; 135:128-135.
12. Wang C, Pop I. Analysis of the flow of a power-law fluid film on an unsteady stretching surface by means of homotopy analysis method. Journal of Non-Newtonian Fluid Mechanics 2006; 138:161-172.
13. Liao SJ. Beyond Perturbation: Introduction to the Homotopy Analysis Method. Chapman & Hall: Boca Raton, 2004.
14. Liao SJ, Tan Y. A general approach to obtain series solutions of nonlinear differential equations. Studies in Applied Mathematics 2007; 119:297-354.
15. Liao SJ. Notes on the homotopy analysis method: some definitions and theorems. Communications in Nonlinear Science and Numerical Simulation 2009; 14:983-997.
16. Van Gorder RA, Vajravelu K. On the selection of auxiliary functions, operators, and convergence control parameters in the application of the homotopy analysis method to nonlinear differential equations: a general approach. Communications in Nonlinear Science and Numerical Simulation, DOI: 10.1016/j.cnsns.2009.03.008.
17. Abbasbandy S. The application of homotopy analysis method to solve a generalized Hirota-Satsuma coupled KdV equation. Physics Letters A 2007; 361:478-483.
18. Van Gorder RA, Vajravelu K. Analytic and numerical solutions to the LaneEmden equation. Physic Letters A 2008; 372:6060-6065.
19. Sajid M, Hayat T. Comparison of HAM and HPM methods in nonlinear heat conduction and convection equations. Nonlinear Analysis: Real World Applications 2008; 9:2296-2301.
20. Liang S, Jeffrey DJ. Comparison of homotopy analysis method and homotopy perturbation method through an evolution equation. Communications in Nonlinear Science and Numerical Simulation, DOI: 10.1016/j.cnsns.2009.02.016.
21. Hayat T, Khan M. Homotopy solutions for a generalized second-grade fluid past a porous plate. Nonlinear Dynamics 2005; 42:395-405.
22. Hayat T, Ellahi R, Asghar S. The influence of variable viscosity and viscous dissipation on the non-Newtonian flow: an analytical solution. Communication in Nonlinear Science and Numerical Simulation 2007; 12:300-313.
23. Abbasbandy S, Yürüsoy M, Pakdemirli M. The analysis approach of boundary layer equations of power-law fluids of second grade. Zeitschrift für Naturforschung A 2008; 63a:564-570.
24. Abdulaziz O, Hashim I. Fully developed free convection heat and mass transfer of a micropolar fluid between porous vertical plates. Numerical Heat Transfer, Part A 2009; 55:270-288.
25. Abdulaziz O, Noor NFM, Hashim I. Homotopy analysis method for fully developed MHD micropolar fluid flow between vertical porous plates. International Journal for Numerical Methods in Engineering 2008; DOI: 10.1002/nme.2509.
26. Sami Bataineh A, Noorani MSM, Hashim I. Solution of fully developed free convection of a micropolar fluid in a vertical channel by homotopy analysis method. International Journal for Numerical Methods in Fluids 2008; DOI: 10.1002/fld.1918.