we introduce and discuss the homotopy perturbation method, the adomian decomposition method and the variational iteration method for solving the stefan problem with kinetics. then, we give an example of the stefan problem with  kinetics and solve it by these methods.

In this paper we consider the model of phase relaxation introduced in [22], where an asymptotic analysis is performed toward integral formulation Stefan problem when parameter approaches zero. Assuming natural physical assumption that initial condition constrained, but taking more general boundary conditions, prove solution relaxed converges a stronger way to classical weak problem.

We present the Onsager–Stefan–Maxwell thermodiffusion equations, which account for Soret and Dufour effects in multicomponent fluids. Unlike transport laws derived from kinetic theory, this framework preserves structure of isothermal Stefan–Maxwell separating thermodynamic forces that drive diffusion force drives heat flow. The transport-coefficient matrix is symmetric, second law thermodynamic...

The non-local in space two-phase Stefan problem (a prototype phase change problems) can be formulated via a singular nonlinear parabolic integro-differential equation which admits unique weak solution. This formulation makes to part of the General Filtration Problems; class includes Porous Medium Equation. In this work, we prove that solutions both and Media problems are continuous.

the separation of olefin/paraffin mixtures is an important process in petrochemical industries, which is traditionally performed by low temperature distillation with a high-energy consumption, or complex extractive distillationand adsorption techniques. membrane separation process is emerging as an alternative for traditional separation processes with respect to low energy and simple operation....

The Stefan problem with small surface tension e is considered. Assuming that the classical Stefan problem (with s = 0) has a smooth free boundary T, we denote the temperature of the solution by 60 and consider an approximate solution 60 + su for the case where e ^ 0, e small. We first establish the existence and uniqueness of u , and then investigate the effect of u on the free boundary T. It i...

We present a method to embed local electroneutrality within Onsager–Stefan–Maxwell electrolytic-transport models, circumventing their formulation as differential systems with an algebraic constraint. Flux-explicit transport laws are developed for general multicomponent electrolytes, in which the ionic conductivity, component diffusivities, and transference numbers relate Stefan–Maxwell coeffici...

A lattice Boltzman model for the simulation of binary mixtures is presented. Contrary to previous models, the present formulation is able to simulate mixtures with different Schmidt numbers and arbitrary molecular mass ratio of the components. In the hydrodynamic limit, the Navier-Stokes and the Stefan-Maxwell binary diffusion equations are recovered. The model is used for the simulation of bin...