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
Ames, W.F.: Nonlinear Partial Differential Equations in Engineering, vol. 18, 1st edn. Academic Press (1965)
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)
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)
Birkhoff, G.: Hydrodynamics. Princeton University Press (1960)
Carminati, J., Vu, K.: Symbolic computation and differential equations: Lie symmetries. J. Symb. Comput. 29, 95–116 (2000)
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)
Nield, D.A., Bejan, A.: Convection in Porous Media, 4th edn. Springer (2013)
Olver, P.J.: Applications of Lie Groups to Differential Equations, 2nd edn. Springer (1993)
Ovsiannikov, L.V.: Group Analysis of Differential Equations, 1st edn. Academic Press (1982)
Stephani, H.: Differential Equations: Their Solution Using Symmetries, 1st edn. Cambridge University Press (1989)
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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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DOI: https://doi.org/10.1007/978-3-030-11928-7_49
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Online ISBN: 978-3-030-11928-7
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