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Lie group analysis of mixed convection flow with mass transfer over a stretching surface with suction or injection. (English) Zbl 1202.76055

Summary: The mixed convection flow with mass transfer over a stretching surface with suction or injection is examined. By using Lie group analysis, the symmetries of the equations are calculated. A four-finite parameter and one infinite parameter Lie group transformations are obtained. Two different cases are discussed, one for the scaling symmetry and the other for spiral symmetry. The governing partial differential equations are transformed into ordinary differential equations using these symmetries. It has been noted that the similarity variables and functions available in the literature become special cases of the similarity variables and functions discussed in this paper.

MSC:

76E06 Convection in hydrodynamic stability
17B81 Applications of Lie (super)algebras to physics, etc.
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References:

[1] B. C. Sakiadis, “Boundary-layer behavior on continuous solid surfaces: I. Boundary-layer equationsfor two-dimensional and axisymmetric flow,” AIChE Journal, vol. 7, pp. 26-28, 1961. · doi:10.1002/aic.690070108
[2] B. C. Sakiadis, “Boundary-layer behavior on continuous solid surfaces: II. The boundary layer ona continuous flat surface,” AIChE Journal, vol. 7, pp. 221-225, 1961. · doi:10.1002/aic.690070211
[3] L. J. Crane, “Flow past a stretching plate,” Journal of Applied Mathematics and Physics, vol. 21, pp. 645-647, 1970. · doi:10.1007/BF01587695
[4] F. K. Tsou, E. M. Sparrow, and R. J. Goldstein, “Flow and heat transfer in the boundary layer on a continuous moving surface,” International Journal of Heat and Mass Transfer, vol. 10, no. 2, pp. 219-235, 1967. · doi:10.1016/0017-9310(67)90100-7
[5] V. G. Fox, L. E. Erickson, and L. T. Fan, “Methods for solving the boundary layer equations formoving continuous flat surfaces with suction and injection,” AIChE Journal, vol. 14, pp. 726-736, 1969.
[6] L. E. Erickson, L. T. Fan, and V. G. Fox, “Heat and mass transfer on a moving continuous flat plate with suction or injection,” Industrial and Engineering Chemistry Fundamentals, vol. 5, no. 1, pp. 19-25, 1966. · doi:10.1021/i160017a004
[7] P. S. Gupta and A. S. Gupta, “Heat and mass transfer on a stretching sheet with suction or blowing,” The Canadian Journal of Chemical Engineering, vol. 55, pp. 744-746, 1977. · doi:10.1002/cjce.5450550619
[8] V. M. Soundalgekar and T. V. R. Murty, “Heat transfer in MHD flow with pressure gradient, suction and injection,” Journal of Engineering Mathematics, vol. 14, no. 2, pp. 155-159, 1980. · Zbl 0423.76088 · doi:10.1007/BF00037624
[9] L. J. Grubka and K. M. Bobba, “Heat transfer characteristics of a continuous stretching surface with variable temperature,” Journal of Heat Transfer, vol. 107, no. 1, pp. 248-250, 1985. · doi:10.1115/1.3247387
[10] M. E. Ali, “The effect of suction or injection on the Laminar boundary layer development overa stretched surface,” ournal of Engineering Sciences King Saud University, vol. 8, pp. 43-58, 1996.
[11] T. Hayat, M. Mustafa, and I. Pop, “Heat and mass transfer for Soret and Dufour’s effect on mixed convection boundary layer flow over a stretching vertical surface in a porous medium filled with a viscoelastic fluid,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 5, pp. 1183-1196, 2010. · Zbl 1221.80005 · doi:10.1016/j.cnsns.2009.05.062
[12] G. W. Bluman and S. Kumei, Symmetries and Differential Equations, vol. 81 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1989. · Zbl 0698.35001
[13] N. H. Ibragimov, Ed., CRC Handbook of Lie Group Analysis of Differential Equations, vol. 2, CRC Press, Boca Raton, Fla, USA, 1995. · Zbl 0864.35002
[14] P. J. Olver, Application of Lie Groups to Differential Equations, Springer, New York, NY, USA, 1989. · Zbl 0743.58003
[15] L. V. Ovsiannikov, Group Analysis of Differential Equations, Academic Press, New York, NY, USA, 1982. · Zbl 0485.58002
[16] M. Yürüsoy and M. Pakdemirli, “Exact solutions of boundary layer equations of a special non-Newtonian fluid over a stretching sheet,” Mechanics Research Communications, vol. 26, no. 2, pp. 171-175, 1999. · Zbl 0945.76556 · doi:10.1016/S0093-6413(99)00009-9
[17] M. Yürüsoy, M. Pakdemirli, and Ö. F. Noyan, “Lie group analysis of creeping flow of a second grade fluid,” International Journal of Non-Linear Mechanics, vol. 36, no. 6, pp. 955-960, 2001. · Zbl 1345.76009 · doi:10.1016/S0020-7462(00)00060-3
[18] S. Sivasankaran, M. Bhuvaneswari, P. Kandaswamy, and E. K. Ramasami, “Lie group analysis of natural convection heat and mass transfer in an inclined surface,” Nonlinear Analysis. Modelling and Control, vol. 11, no. 2, pp. 201-212, 2006. · Zbl 1125.93330
[19] S. Sivasankaran, M. Bhuvaneswari, P. Kandaswamy, and E. K. Ramasami, “Lie group analysis of natural convection heat and mass transfer in an inclined porous surface with heat generation,” International Journal Applied Mathematics and Mechanics, vol. 2, pp. 34-40, 2006. · Zbl 1125.93330
[20] M. Ali and F. Al-Yousef, “Laminar mixed convection boundary layers induced by a linearly stretching permeable surface,” International Journal of Heat and Mass Transfer, vol. 45, no. 21, pp. 4241-4250, 2002. · Zbl 1006.76511 · doi:10.1016/S0017-9310(02)00142-4
[21] K. A. Yih, “Free convection effect on MHD coupled heat and mass transfer of a moving permeable vertical surface,” International Communications in Heat and Mass Transfer, vol. 26, no. 1, pp. 95-104, 1999. · doi:10.1016/S0735-1933(98)00125-0
[22] C.-H. Chen, “Laminar mixed convection adjacent to vertical, continuously stretching sheets,” Heat and Mass Transfer, vol. 33, no. 5-6, pp. 471-476, 1998. · doi:10.1007/s002310050217
[23] M. K. Partha, P. V. S. N. Murthy, and G. P. Rajasekhar, “Effect of viscous dissipation on the mixed convection heat transfer from an exponentially stretching surface,” Heat and Mass Transfer/Waerme, vol. 41, no. 4, pp. 360-366, 2005. · doi:10.1007/s00231-004-0552-2
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