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First Thermal and Fluids Engineering Summer Conference

ISSN: 2379-1748
ISBN: 978-1-56700-430-4


Juan I. Ramos
Escuela de Ingenierias Industriales, Universidad de Malaga, Dr. Ortiz Ramos, s/n 29071 Malaga, Spain

DOI: 10.1615/TFESC1.fnd.012993
pages 1035-1049

KEY WORDS: Relativistic heat and mass transfer, flux-limited diffusion, reaction-diffusion equations, analytical and numerical solutions


A conservative time-linearized finite-difference technique and a finite-volume method are used to study one- and two-dimensional reactive-diffusive systems with flux-limited relativistic diffusion fluxes which depend nonlinearly on the concentration and temperature and their gradients. It is shown that the convection-like fluxes associated with the relativistic flux are small if either the relativistic length scale or the concentration and temperature gradients are small and that, when these fluxes are important, the concentration and temperature fronts are steeper and propagate at a smaller speed than those corresponding to Fourier’s and Fick’s laws. Numerical experiments performed with one-dimensional problems in fixed and moving domains and with two-dimensional problems in fixed domains are reported to illustrate the effects of the relativistic heat flux. It is shown that, for a Rankine vortex velocity field, the reaction fronts are characterized by thin and elongated spiral waves when the vortex circulation is not very large. For large circulations, it has been found that the importance of the relativistic contribution to wave propagation depends on the relativistic length scale, the vortex core radius, the diffusion coefficients and the value of the circulation, and the results show the formation of arms with a beak-shape tip connected to small filaments. It is also shown that, for large vortex circulations, the concentration of one of the reactants exhibits a periodic structure near the axis of the vortex characterized by spikes and complex dynamics between successive spikes.

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