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Symmetry Group of Heat Transfer Flow in a Porous Medium

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Advanced Intelligent Systems for Sustainable Development (AI2SD’2018) (AI2SD 2018)

Abstract

In this paper, the symmetry group is performed for the heat transfer flow in a porous medium, this flow is described by coupled partial differential equations. Thanks to the method of the symmetry group, the symmetries of the coupled equations are given. The similarity variables and reduction equations generated from the symmetry transformations are provided. Such similarity reductions are computed and exact solutions are given such solutions are important in engineering applications and on the theory of nonlinear science.

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References

  1. Ames, W.F.: Nonlinear Partial Differential Equations in Engineering, vol. 18, 1st edn. Academic Press (1965)

    Google Scholar 

  2. Amtout, T., Er-Riani, M., El Jarroudi, M., Cheikhi, A.: Preliminary group classification for the flow of a thermodependent fluid in porous medium. Int. J. Nonlin. Mech. 104, 19–27 (2018)

    Article  Google Scholar 

  3. Afify, A.A., Uddinc, Md.J.: Lie symmetry analysis of a double-diffusive free convective slip flow with a convective boundary condition past a radiating vertical surface embedded in a porous medium. J. Appl. Mech. Tech. Phys. 5(57), 925–936 (2016)

    Google Scholar 

  4. Birkhoff, G.: Hydrodynamics. Princeton University Press (1960)

    Google Scholar 

  5. Carminati, J., Vu, K.: Symbolic computation and differential equations: Lie symmetries. J. Symb. Comput. 29, 95–116 (2000)

    Article  MathSciNet  Google Scholar 

  6. Lee, J., Kandaswamy, P., Bhuvaneswari, M., Sivasankaran, S.: Lie group analysis of radiation natural convection heat transfer past an inclined porous surface. J. Mech. Sci. Technol. 22, 1779–1784 (2008)

    Article  Google Scholar 

  7. Nield, D.A., Bejan, A.: Convection in Porous Media, 4th edn. Springer (2013)

    Google Scholar 

  8. Olver, P.J.: Applications of Lie Groups to Differential Equations, 2nd edn. Springer (1993)

    Google Scholar 

  9. Ovsiannikov, L.V.: Group Analysis of Differential Equations, 1st edn. Academic Press (1982)

    Google Scholar 

  10. Stephani, H.: Differential Equations: Their Solution Using Symmetries, 1st edn. Cambridge University Press (1989)

    Google Scholar 

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Correspondence to Tarik Amtout .

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Amtout, T., Er-Riani, M., el Jarroudi, M. (2019). Symmetry Group of Heat Transfer Flow in a Porous Medium. In: Ezziyyani, M. (eds) Advanced Intelligent Systems for Sustainable Development (AI2SD’2018). AI2SD 2018. Advances in Intelligent Systems and Computing, vol 915. Springer, Cham. https://doi.org/10.1007/978-3-030-11928-7_49

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