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**Thermal diffusion and diffusion thermo effects on the viscous fluid flow with heat and mass transfer through porous medium over a shrinking sheet.**
*(English)*
Zbl 1266.76021

Summary: The motion of the viscous, incompressible fluid through a porous medium with heat and mass transfer over a shrinking sheet is investigated. The cross-diffusion effect between temperature and concentration is considered. This phenomenon is modulated mathematically by a set of partial differential equations which govern the continuity, momentum, heat, and mass. These equations are transformed to a set of ordinary differential equations by using similarity solutions. The analytical solutions of these equations are obtained. The velocity, temperature, and concentration of the fluid as well as the heat and mass transfer with shear stress at the sheet are obtained as a function of the physical parameters of the problem. The effects of Prandtl number, mass transfer parameter, the wall shrinking parameter, the permeability parameter, and Dufour and Soret numbers on temperature and concentration are studied. Also, the effects of mass transfer parameter, permeability parameter, and shrinking strength on the velocity and shear stress are discussed. These effects are illustrated graphically through a set of figures.

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\textit{N. Eldabe} and \textit{M. A. Zeid}, J. Appl. Math. 2013, Article ID 584534, 11 p. (2013; Zbl 1266.76021)

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### References:

[1] | B. C. Sakiadis, “Boundary-layer behavior on continuous solid surface: I. Boundary-layer equations for two-dimensional and axisymmetric flow,” AIChE Journal, vol. 7, pp. 26-28, 1961. |

[2] | B. C. Sakiadis, “Boundary-layer behavior on continuous solid surface: II. Boundary-layer equations for two-dimensional and axisymmetric flow,” AIChE Journal, vol. 7, pp. 221-225, 1961. |

[3] | L. J. Crane, “Flow past a stretching plate,” Journal of Applied Mathematics and Physics, vol. 21, no. 4, pp. 645-647, 1970. |

[4] | 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. |

[5] | C. K. Chen and M. I. Char, “Heat transfer of a continuous, stretching surface with suction or blowing,” Journal of Mathematical Analysis and Applications, vol. 135, no. 2, pp. 568-580, 1988. · Zbl 0652.76062 |

[6] | M. Ferdows, M. Ota, A. Sattar, and M. Alam, “Similarity solutions for MHD through vertical porous plate with suction,” Journal of Computational and Applied Mathematics, vol. 6, pp. 15-25, 2005. · Zbl 1150.76550 |

[7] | J. R. Lin, L. J. Liang, and R. D. Chien, “Magneto-hydrodynamic flow of a second order fluid over a stretching sheet with suction,” Journal of the Chinese Institute of Engineers, vol. 30, no. 1, pp. 183-188, 2007. |

[8] | 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. |

[9] | C. K. Chen and M. I. Char, “Heat transfer of a continuous, stretching surface with suction or blowing,” Journal of Mathematical Analysis and Applications, vol. 135, no. 2, pp. 568-580, 1988. · Zbl 0652.76062 |

[10] | R. S. R. Gorla, D. E. Abboud, and A. Sarmah, “Magnetohydrodynamic flow over a vertical stretching surface with suction and blowing,” Heat and Mass Transfer, vol. 34, no. 2-3, pp. 121-125, 1998. |

[11] | S. Yao, T. Fang, and Y. Zhong, “Heat transfer of a generalized stretching/shrinking wall problem with convective boundary conditions,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 2, pp. 752-760, 2011. · Zbl 1221.76062 |

[12] | T. Fang, S. Yao, and I. Pop, “Flow and heat transfer over a generalized stretching/shrinking wall problem-Exact solutions of the Navier-Stokes equations,” International Journal of Non-Linear Mechanics, vol. 46, pp. 1116-1127, 2011. |

[13] | T. Fang, “Boundary layer flow over a shrinking sheet with power-law velocity,” International Journal of Heat and Mass Transfer, vol. 51, no. 25-26, pp. 5838-5843, 2008. · Zbl 1157.76010 |

[14] | T. Fang, W. Liang, and C. F. Lee, “A new solution branch for the Blasius equation- shrinking sheet problem,” Computers & Mathematics with Applications, vol. 56, no. 12, pp. 3088-3095, 2008. · Zbl 1165.76324 |

[15] | T. Fang and J. Zhang, “Closed-form exact solutions of MHD viscous flow over a shrinking sheet,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 7, pp. 2853-2857, 2009. · Zbl 1221.76142 |

[16] | T. Fang, J. Zhang, and S. Yao, “Slip MHD viscous flow over a stretching sheet-an exact solution,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 11, pp. 3731-3737, 2009. |

[17] | M. Miklav\vci\vc and C. Y. Wang, “Viscous flow due to a shrinking sheet,” Quarterly of Applied Mathematics, vol. 64, no. 2, pp. 283-290, 2006. · Zbl 1169.76018 |

[18] | C. Y. Wang, “Stagnation flow towards a shrinking sheet,” International Journal of Non-Linear Mechanics, vol. 43, no. 5, pp. 377-382, 2008. |

[19] | M. S. Alam and M. M. Rahman, “Dufour and Soret effects on mixed convection flow past a vertical porous flat plate with variable suction,” Nonlinear Analysis. Modelling and Control, vol. 11, no. 1, pp. 3-12, 2006. · Zbl 1109.76057 |

[20] | H. A. M. El-Arabawy, “Soret and dufour effects on natural convection flow past a vertical surface in a porous medium with variable surface temperature,” Journal of Mathematics and Statistics, vol. 5, no. 3, pp. 190-198, 2009. · Zbl 1423.80018 |

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