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First integrals and bifurcations of a Lane-Emden equation of the second kind. (English) Zbl 1143.80005
Summary: First integrals admitted by an approximate Lane-Emden equation modelling a thermal explosion in a rectangular slab and cylindrical vessel are investigated. By imposing the boundary conditions on the first integrals we obtain a nonlinear relationship between the temperature at the center of the vessel and the temperature gradient at the wall of the vessel. For a rectangular slab the presence of a bifurcation indicates multivalued solutions for the temperature at the center of the vessel when the temperature gradient at the wall is fixed. For a cylindrical vessel we find a bifurcation indicating multivalued solutions for the temperature gradient at the walls of the vessel when the temperature at the center of the vessel is fixed.

80A20Heat and mass transfer, heat flow
80A32Chemically reacting flows (thermodynamic aspects)
34C23Bifurcation (ODE)
Full Text: DOI
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