# A Stefan problem for exothermic non-catalytic reactions

01 Jun 1985-International Journal of Heat and Mass Transfer (Pergamon)-Vol. 28, Iss: 6, pp 1237-1239

TL;DR: Resolution numerique par la methode de l'enthalpie d'un probleme de Stefan de fusion provoque par la reaction exothermique entre 2 solides as mentioned in this paper.

Abstract: Resolution numerique par la methode de l'enthalpie d'un probleme de Stefan de fusion provoque par la reaction exothermique entre 2 solides

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TL;DR: In this article, a model describing the combustion of porous condensed materials in which a reactant melts and spreads through the pores of the sample is presented. But the model does not take into account the relative motion of the components and exhibits a dependence of the structure of the product on the mode of propagation of the combustion front.

Abstract: We formulate and analyze a model describing the combustion of porous condensed materials in which a reactant melts and spreads through the pores of the sample. Thus there is liquid motion relative to the porous solid matrix. Our model describes the cases when the melt either fills all the pores or when some gas remains in the pores. In each case the melt occupies a prescribed volume fraction of the mixture. We employ both analytical and numerical methods to find uniformly propagating combustion waves, to analyze their stability and to determine behavior in the instability region. The principal physical conclusion which follows from our analysis is that the flow of the melted component can result in nonuniform composition of the product. Unlike models which do not take into account the relative motion of the components, this model exhibits a dependence of the structure of the product on the mode of propagation of the combustion front. Thus, if the initial mixture is uniform, models which do not al...

16 citations

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TL;DR: In this article, the authors discuss the advances made and remaining problems in the chemical synthesis and calcination of ceramic powders, self-propagating high temperature synthesis of ceramics, chemical vapor infiltration and ceramic melt infiltration.

Abstract: Reaction engineering methodology is uniquely suitable to solve many synthesis, analytical and processing problems associated with the fabrication of advanced ceramic materials. This review discusses the advances made and remaining problems in the chemical synthesis and calcination of ceramic powders, self-propagating high temperature synthesis of ceramics, chemical vapor infiltration and ceramic melt infiltration. The problems associated with advanced ceramics fabrication are of practical importance and scientific interest, and more reaction engineers should get involved in their solution.

14 citations

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TL;DR: In this paper, a mathematical model was developed to investigate the effect of various processing parameters on pressure-assisted combustion synthesis of NiTi intermetallics, including preheat and ambient temperature, particle size, initial porosity, and pressure differential.

Abstract: A mathematical model is developed to investigate the effect of various processing parameters on pressure-assisted combustion synthesis of NiTi intermetallics. Specifically, preheat and ambient temperature, particle size, initial porosity, and pressure differential are studied to determine their influence on propagation behavior and final porosity. The governing equations are solved using a high-order-implicit numerical scheme capable of accommodating the steep spatial and temporal gradients of properties. The predicted results appear plausible and consistent with the trends presented in the available literature.

9 citations

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TL;DR: In this paper, a two-dimensional model for combustion of porous condensed phase materials is proposed, in which a reactant melts and spreads through the void space of a porous solid.

Abstract: We formulate a two-dimensional model describing the combustion of porous condensed phase materials in which a reactant melts and spreads through the void space of a porous solid. The melt may completely fill the pores, or some gas may remain in the pores. In each case, the volume fraction of melt is prescribed. In the limit of large activation energy, we analytically find a one-dimensional basis state consisting of a uniformly propagating combustion wave with a planar reaction front and a planar melting front. We find that the uniformly propagating solution with planar fronts is linearly unstable to traveling waves transverse to the propagation direction of the basic state above some critical Zeldovich number. The critical wave number associated with this critical Zeldovich number is generally unique and nonzero. However, the critical wave number can be zero for certain parameter values. For other special parameter values, the neutral stability curve may have two minima, so that two wave numbers lose stability at the same Zeldovich number.

6 citations

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TL;DR: In this paper, a mathematical model is developed to investigate the effect of thermal conductivity on the combustion synthesis of intermetallics, and the governing equations are solved using a high-order-implicit numerical scheme capable of accommodating the steep spatial and temporal gradients of properties.

Abstract: A mathematical model is developed to investigate the effect of thermal conductivity on the combustion synthesis of intermetallics. The governing equations are solved using a high-order-implicit numerical scheme capable of accommodating the steep spatial and temporal gradients of properties. A parametric study is then performed to elucidate reaction characteristics (propagation type, steady-state propagation velocity, peak temperature, etc.) in terms of the thermal conductivity ratio, κ=kp/kr. The predicted results appear plausible and consistent with the trends presented in the available literature.

5 citations

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TL;DR: An implicit scheme for one dimensional problems, based upon the above development, is described which can cope with any size phase change temperature range and the influence of internal heating, simultaneously.

Abstract: After highlighting the problems associated with the conventional numerical implementations of Stefan problems using the enthalpy formulation, a simple development is described which leads to very accurate solutions. The extension of this technique to two dimensional problems is then demonstrated using a straightforward explicit method. An implicit scheme for one dimensional problems, based upon the above development, is then described which can cope with any size phase change temperature range and the influence of internal heating, simultaneously. Finally, the utility of this scheme is demonstrated by its application to a welding problem.

463 citations

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TL;DR: In this paper, the authors trace out the broad characteristics of a class of higher order finite difference schemes which are applicable to the solution of parabolic partial differential equations associated with viscous fluid flow problems.

Abstract: This paper attempts to trace out the broad characteristics of a class of higher order finite difference schemes which are applicable to the solution of parabolic partial differential equations associated with viscous fluid flow problems. The basic method developed here uses the approach of the compact implicit techniques applied to the full spatial operator. The resulting spatial approximation, referred to here as the operator compact implicit method can be implemented with a variety of temporal integration schemes. In particular, a simple factorization technique is employed to resolve higher space dimension problems in terms of simple tridiagonal systems. The operator compact implicit method is compared to standard techniques and to some of the newer compact implicit methods. Stability characteristics, computational efficiency and the results of numerical experiments are discussed.

122 citations