Self-similar solutions of the magnetohydrodynamic boundary layer system for a dilatable fluid

Acta Mechanica

Volumn 188, Issue 1-2, 2007, Pages 103-119

  Zhang, Z ^a,b   Wang, J ^a,b  

^a Xiamen University ^*

^b XIAMEN UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; INITIAL VALUE PROBLEMS; MAGNETIC FIELD EFFECTS; MAGNETOHYDRODYNAMICS; ORDINARY DIFFERENTIAL EQUATIONS; PROBLEM SOLVING;

DILATABLE FLUIDS; MAGNETOHYDRODYNAMIC BOUNDARY LAYER SYSTEMS; NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS;

LAMINAR FLOW;

EID: 33751522700     PISSN: 00015970     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00707-006-0396-6     Document Type: Article

References (23)

1. Andersson, H. I.: MHD flow of a viscous fluid past a stretching surface. Acta Mech. 95, 227-230 (1992).
2. Andersson, H. I.: An exact solution of the Navier-Stokes equations for magnetohydrodynamic flow. Acta Mech. 113, 241-244 (1995).
3. Andersson, H. I., Bech, K. H., Dandapat, B. S.: Magnetohydrodynamic flow of a power-law fluid over a stretching sheet. Int. J. Non-Linear Mech. 27, 929-936 (1992).
4. Andersson, H. I., Irgens, F.: Gravity-driven film flow of power-law fluids along vertical walls. Non-Newtonian Fluid Mech. 27, 153-172 (1988).
5. Djukic, D. S.: On the use of Croccos equation for the flow of power-law fluids in a transverse magnetic field. AIChE J. 19, 1159-1163 (1973).
6. Djukic, D. S.: Hiemenz magnetic flow of power-law fluids. Trans. ASME J. Appl. Mech. 41, 822-823 (1974).
7. Falkner, V. M., Skan, S. W.: An analytic solution of a nonlinear singular boundary layer equations. Phil. Mag. 12, 865-896 (1931);
8. Aeronautical Research Council Reports and Memoranda 1314 (1930), London, UK.
9. Hartman, P.: Ordinary differential equations, 2nd ed. Boston: Birkhäuser 1982.
10. Ibrahim, F. N., Terbeche, M.: Solutions of the laminar boundary layer equations for a conducting power law non-Newtonian fluid in a transverse magnetic field. J. Phys. D Appl. Phys. 27, 740-747 (1994).
11. Oleinik, O. A., Samokhin, V. N.: Mathematical model in boundary layer theory, Differential Equations. Chapman & Hall/CRC: 1999.
12. Pavlov, K. B.: Magnetohydynamic flow of an incompressible viscous fluid caused by deformation of a plane surface. Magnitnaya Gidrodinamika 4, 146-147 (1974).
13. Pavlov, K. B.: On the theory of non-stationary MHD-flows of non-Newtonian fluid dilatable fluids. Magnitnaya Gidrodinamika 1, 3-13 (1981).
14. Sapunkov, Y. G.: Self-similar solutions of the boundary layer problems for non-Newtonian fluid in magnetic field. Izvest. Akad. Nauk SSSR, Mekh. Zhidk. Gaza 6, 77-82 (1967).
15. Sapunkov, Y. G.: Rayleigh problem of non-Newtonian electroconductive fluids. J. Appl. Tech. Phys. 2, 50-55 (1970).
16. Sarpkaya, T.: Flow of non-Newtonian fluids in a magnetic field. AICHE. J. 7, 324-328 (1961).
17. Schlichting, H.: Boundary-layer theory, 6th ed., New York: McGraw-Hill 1968.
18. Spinelli, R. A.: On the O.D.E of stagnation point flows of power law fluids. ZAMP 20, 479-486 (1969).
19. Vajravelu, K.: Hydromagnetic flow and heat transfer over a continuous, moving, porous, flat surface. Acta Mech. 64, 179-185 (1986).
20. Volosov, K. A., Pavlov, K. B., Fedotov, I. A.: On the theory of laminar boundary layer in a conducting non-Newtonian power law fluid in transversal magnetic field. Magnitnaya Gidrodinamika 4, 39-42 (1980).
21. Vujanovic, B., Strauss, A. M., Djukic, D. S.: A variational solution of the Rayleigh problem for a power-law Non-Newtonian conducting fluid. Ingenieur-Archiv 41, 381-386 (1972).
22. Wang, J., Gao, W.: Uniqueness, existence and nonexistence of normal solutions to a problem in boundary layer theory. Tohoku Math. J. 51, 539-553 (1999).
23. Zhang, Z., Wang, J., Shi, W.: A boundary layer problem arising in gravity-driven laminar film flow of power-law fluids along vertical walls. ZAMP 55, 769-780 (2004).