Summary
The forced convective heat and mass transfer along a semi-infinite vertical flat plate is investigated for non–Newtonian power law fluids in the presence of a strong nonuniform magnetic field, and the Hall currents are taken into account. The similarity solutions are obtained using transformations group theory. These are the only symmetry transformations admitted by the field equations. The application of one-parameter groups reduces the number of independent variables by one, and consequently the system of governing partial differential equations with boundary conditions reduces to a system of ordinary differential equations with the appropriate boundary conditions. Furthermore the similarity equations are solved numerically by using a fourth-order Runge-Kutta scheme with the shooting method. Numerical results for the velocity profiles, the temperature profiles and the concentration profiles are presented graphically for various values of the power-law viscosity index n, generalized Schmidt number Sc, generalized Prandtl number Pr, the magnetic parameter M and the Hall parameter m.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Vujanovic, B., Stauss, A. M., Djukic, D. J.: A variational solution of the Rayleigh problem for a power law non–Newtonian conducting fluid. Ing.-Arch. 41, 381–386 (1972).
Schowalter, W. R.: The application of boundary-layer theory to power-law pseudoplastic fluids: similar solutions. A.I.Ch.E. J. 6, 24–28 (1960).
Kapur, J. N., Srivastava, R. C.: Similar solutions of the boundary layer equations for power-law fluids. ZAMP 14, 383–388 (1963).
Lee, S. Y., Ames, W. F.: Similar solutions for non–Newtonian fluids. A.I.Ch.E. J. 12, 700–708 (1966).
Martinson, L. K., Pavlov, K. B.: Unsteady shear flows of a conducting fluid with a rheological power law. MHD 7, 182–189 (19 71).
Samokhen, V. N.: On the boundary-layer equation of MHD of dilatant fluid in a transverse magnetic field. MHD 3, 71–77 (1987).
Saponkov, Y.: Similar solutions of steady boundary-layer equations in magneto-hydrodynamic power law conducting fluids. Mech. Fluid Gas 6, 77–82 (1967).
Gorla, R. S. R., Krishnan, V., Pop, I.: Free convection of a power law fluid over the vertical frustum of a cone. Int. J. Engng Sci. 32, 1791–1800 (1994).
Wang, T.-Y.: Mixed convection from a vertical plate to non–Newtonian fluids with uniform surface heat flux. Int. Comm. Heat Mass Transf. 22, 369–380 (1995).
Chiam, T. C.: Solution for the flow of a conducting power-law fluid in a transverse magnetic field and with a pressure gradient using Crocco variables. Acta Mech. 137, 225–235 (1999).
Jumah, R. Y., Mujumdar, A. S.: Free convection heat and mass transfer of non–Newtonian power law fluids with yield stress from a vertical flat plate in saturate porous media. Int. Comm. Heat Mass Transf. 27, 485–494 (2000).
Massoudi, M.: Local non-similarity solutions for the flow of a non–Newtonian fluid over a wedge. Int. J. Non-Linear Mech. 36, 961–976 (2001).
Sato, H.: Hall effect in the viscous flow of ionized gas between parallel plates under transverse magnetic field. J. Phys. Soc. Japan 16, 1427–1433 (1961).
Sherman, A., Sutton, G. W.: Engineering magnetohydrodynamics. New York: McGraw-Hill 1965.
Hossain, M. A.: Effect of Hall current on unsteady hydromagnetic free convection flow near an infinite vertical porous plate. J. Phys. Soc. Japan 55, 2183–2190 (1986).
Hossain, M. A., Mohammad, K.: Effect of Hall current on hydromagnetic free convection flow near an accelerated porous plate. Jpn. J. Appl. Phys. 27, 1531–1535 (1988).
Hossain, M. A., Rashid, R. I. M. A.: Hall effects on hydromagnetic free convection flow along a porous flat plate with mass transfer. J. Phys. Soc. Japan 56, 97–104 (1987).
Pop, I.: The effect of Hall currents on hydromagnetic flow near an accelerated plate. J. Math. Phys. Sci. 5, 375–385 (1971).
Raptis, A., Ram, P. C.: Effects of Hall current and rotation. Astrophys. Space Sci. 106, 257–264 (1984).
Ram, P. C.: Hall effects on free convective flow and mass transfer through a porous medium. Wärme- und Stoffübertragung 22, 223–225 (1988).
Ram, P. C.: Hall effects on the hydromagnetic free convective flow and mass transfer through a porous medium bounded by an infinite vertical porous plate with constant heat flux. Int. J. Energy Res. 12, 227–231 (1988).
Pop, I., Watanabe, T.: Hall effects on magnetohydrodynamic free convection about a semi-infinite vertical flat plate, Int. J. Eng. Sci. 32, 1903–1911 (1994).
Acharya, M., Dash, G. C., Singh, L. P.: Effect of chemical and thermal diffusion with Hall current on unsteady hydromagnetic flow near an infinite vertical porous plate. J. Phys. D: Appl. Phys. 28, 2455–2464 (1995).
Aboeldahab, E. M., Elbarbary, E. M. E.: Hall current effect magnetohydrodynamic free convection flow past a semi-infinite vertical plate with mass transfer. Int. J. Engng. Sci. 39, 1641–1652 (2001).
Asghar, S., Parveen, S., Hanif, S., Siddiqui, A. M., Hayat, T.: Hall effects on the unsteady hydromagnetic flows of an Oldroyd-B fluid. Int. J. Engng Sci. 41, 609–619 (2003).
Aboeldahab, E. M., Salem, A. M.: Hall current effect on MHD free convection flow of a non–Newtonian power-law fluid at a stretching surface transfer. Int. Comm. Heat Mass Transf. 31, 343–354 (2004).
Birkhoff, G.: Hydrodynamics. New York: Dover 1955.
Morgan, A. J. A.: The reduction by one of the number of independent variables in some systems of partial differential equations. Quart. J. Math. 3, 250–259 (1952).
Hansen, A. G.: Similarity analyses of boundary value problems in engineering. Englewood Cliffs: Prentice Hall 1965.
Na, T. Y.: Computational methods in engineering boundary value problems. New York: Academic Press 1982.
Seshadri, R., Na, T.Y.: Group invariance in engineering boundary value problems. New York: Springer 1985.
Na, T.Y., Hansen, A. G: Similarity solutions of a class of laminar, three-dimensional, boundary, layer equations of power law fluids. Int. J. Non-Linear Mech. 2, 373–385 (1967).
Pakdemirli, M.: Similarity analysis of boundary-layer equations of a class of non–Newtonian fluids. Int. J. Non-Linear Mech. 29, 187–196 (1994).
Fan, J. R., Shi, J. M., Xu, X. Z.: Similarity solution of mixed convection with diffusion and chemical reaction over a horizontal moving plate. Acta Mech. 126, 59–69 (1998).
Abd-el-Malek, M. B., Badran, N. A.: Group method analysis of unsteady free-convective laminar boundary-layer flow on a nonisothermal vertical circular cylinder. Acta Mech. 85, 193–206 (1990).
Abd-el-Malek, M. B., Badran, N. A., Hassan, H. S.: Solution of the Rayleigh problem for a power law non–Newtonian conducting fluid via group method. Int. J. Engng Sci. 40, 1599–1609 (2002).
Megahed, A. A., Komy, S. R., Afify, A. A.: Similarity analysis in magnetohydrodynamics: effects of Hall and ion-slip currents of a gas past a semi-infinite vertical flat Plate. Acta Mech. 151, 185–194 (2001).
Megahed, A. A., Komy, S. R., Afify, A. A.: Similarity analysis in magnetohydrodynamics: Hall effects on free convection flow and mass transfer past a semi-infinite vertical flat Plate. Int. J. Non-Linear Mech. 38, 513–520 (2003).
Timol, M. G., Kalthia, N. L.: Similarity solutions of three-dimensional boundary-layer equations of non–Newtonian fluids. Int. J. Non-Linear Mech. 21, 475–481 (1986).
Chiam, T. C.: Hydromagnetic flow over a surface stretching with a power-law velocity. Int. J. Engng Sci. 33, 429–435 (1995).
Moran, M. J., Gaggioli, R. A.: Reduction of the number of variables in systems of partial differential equations with auxiliary conditions. SIAM J. App. Math. 16, 202–215 (1968).
Wang, T.-Y.: The analysis of conjugate problems of conduction and convection for non–Newtonian fluids past a flat plate. Int. Comm. Heat Mass Transf. 24, 337–348 (1997).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Afify, A.A., Aboeldahab, E.M. & Mohamed, E.S. Similarity analysis in magnetohydrodynamics: Hall effects on forced convective heat and mass transfer of non–Newtonian power law fluids past a semi-infinite vertical flat plate. Acta Mechanica 177, 71–87 (2005). https://doi.org/10.1007/s00707-005-0235-1
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00707-005-0235-1