Summary
The development of velocity and temperature fields of an incompressible viscous electrically conducting fluid, caused by an impulsive stretching of the surface in two lateral directions and by suddenly increasing the surface temperature from that of the surrounding fluid, is studied. The partial differential equations governing the unsteady laminar boundary-layer flow are solved numerically using an implicit finite difference scheme. For some particular cases, closed form solutions are obtained, and for large values of the independent variable asymptotic solutions are found. The surface shear stresses inx-andy-directions and the surface heat transfer increase with the magnetic field and the stretching ratio, and there is a smooth transition from the short-time solution to the long-time solution.
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Crane, L. J.: Flow past a stretching plate. ZAMP21, 645–647 (1970).
Gupta, P. S., Gupta, A. S.: Heat and mass tranfer on a stretching sheet with suction and blowing. J. Chem. Engng55, 744–746 (1977).
Chakrabarti, A., Gupta, A. S.: Hydromagnetic flow, heat and mass transfer over a stretching sheet. Quart. Appl. Math.33, 73–78 (1979).
Carragher, P., Crane, L. J.: Heat transfer on a continuous stretching sheet. ZAMM62, 564–565 (1982).
Dutta, B. K., Roy, P., Gupta, A. S.: Temperature field in flow over a stretching sheet with uniform heat flux. Int. Comm. Heat Mass Transfer28, 1234–1237 (1985).
Jeng, D. R., Chang, T. C. A., DeWitt, K. J.: Momentum and heat transfer on a continuous moving surface. J. Heat Transfer108, 532–539 (1986).
Dutta, B. K.: Heat transfer from a stretching sheet with uniform suction and blowing. Acta Mech.78, 255–262 (1989).
Andersson, H. I.: An exact solution of the Navier-Stokes equations for MHD flow. Acta Mech.113, 241–244 (1995).
Chiam, T. C.: Heat transfer with variable conductivity in a stagnation-point flow towards a stretching sheet. Int. Comm. Heat Mass Transfer23, 239–248 (1996).
Vajravelu, K. A., Hadjucolaou, A.: Convective heat transfer in an electrically conducting fluid at a stretching surface with uniform free stream. Int. J. Engng Sci.35, 1237–1244 (1997).
Wang, C. Y.: The three-dimensional flow due to a stretching flat surface. Phys. Fluids27, 1915–1917 (1984).
Stewartson, K.: On the impulsive motion of a flat plate in a viscous fluid, Part I. Quart. J. Mech. Appl. Math.4, 182–198 (1951).
Stewartson, K.: On the impulsive motion of a flat plate in a viscous fluid, Part II. Quart. J. Mech. Appl. Math.26, 142–153 (1973).
Hall, M. G.: The boundary layer over an impulsively started flat plate. Proc. Roy. Soc.310A, 401–414 (1969).
Dennis, S. C. R.: The motion of a viscous fluid past on impulsively started semi-infinite flat plate. J. Inst. Math. Appl.10, 105–117 (1972).
Watkins, C. A.: Heat transfer in the boundary layer over an impulsively started flat plate. J. Heat Transfer97, 482–484 (1975).
Smith, S. A.: The impulsive motion of a wedge in a viscous fluid. ZAMP18, 508–522 (1967).
Nanbu, K.: Unsteady Falkner-Skan flow. ZAMP22, 1167–1172 (1971).
Williams, J. C., Rhyne, T. H.: Boundary layer development on a wedge impulsively set into motion. SIAM J. Appl. Math.38, 215–224 (1980).
Eringen, A. C., Maugin, G. A.: Electrodynamics of continua, vol.2, New York: Springer 1990.
Abramowitz, M., Stegun, I. A.: Handbook of mathematical functions, vol.55. Providence. National Bureau of Standards. Amer. Math. Soc. 1972.
Merkin, J. H.: A note on the solution of a differential equation arising in boundary-layer theory. J. Engng Math.18, 31–36 (1984).
Blottner, F.: Finite-difference method of solution of the boundary-layer equations. AJAA J.8, 193–205 (1970).
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Takhar, H.S., Chamkha, A.J. & Nath, G. Unsteady three-dimensional MHD-boundary-layer flow due to the impulsive motion of a stretching surface. Acta Mechanica 146, 59–71 (2001). https://doi.org/10.1007/BF01178795
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DOI: https://doi.org/10.1007/BF01178795