The general form of the maxwell stefan equation is shown below. Most electromagnetic components, devices, and products are affected by another branch of physics, whether it be heat transfer, structural mechanics, or acoustics, to name a few. Twodimensional pem fuel cells modeling using comsol. Comsol multiphysics is a crossplatform finite element analysis, solver and multiphysics simulation software. This is the maxwellstefan equation, an equation that forms the basis for the mathematical description of mass transfer of chemical species in a mixture 2. It allows conventional physicsbased user interfaces and coupled systems of partial differential equations pdes. Comsol multiphysics software was applied to analyze the steam methane reforming in the chemical reactor investigated. It will be really great if someone can help me with the primary syntaxes and function. Fick diffusion coefficient d ij maxwell stefan diffusion coefficient between species i and j e charge on a proton e youngs modulus f net force force acting per unit mass of component i f i body force g gibbs free energy gex excess gibbs free energy. These release notes provide information regarding new functionality in existing products.

Ansys maxwell is a software specializedoptimized for lf. Apr 30, 2014 the maxwell stefan formulation describes diffusion from first principles. If you have an earlier build number, contact your comsol sales representative to get the official release of comsol 4. The pdes used to model diffusion problems might include ficks laws, the convection diffusion equation, or more complex methods for concentrated mixtures, like maxwell stefan diffusion. In the absence of chemical reactions source terms and convective contributions, the maxwellstefan formulation results in zero net mass flux. Thus, unlike fick diffusion, maxwell stefan diffusion can describe multicomponent mixtures. A complete mathematical model of protein gel swelling was established. This is the maxwellstefan equation, an equation that forms the basis for. This can be easily done if i use ficks equation but it does not look straighforward if one uses maxwell stefan. Which is the most suitable software comsol vs ansys. The comsol discussion forum covers a wide variety of simulation topics. The necessary equations are formulated as the maxwellstefan description of diffusion.

The model is solved with commercial software comsol multiphysics 3. It is easy to download the latest version of the comsol software if you have a comsol access account with your license number linked to it. Comsol multiphysics is a finite element method fem based software that facilitates such analysis. Maxwellstefan theory for diffusion through zeolite membrane. Simplifications of these equations for diluted mixtures give, for example, ficks first law of diffusion and the nernstplanck equations for diffusion. Solution of a maxwell stefan diffusion problem file. H gas channel inlet o 2 gas channel inlet pvim membrane at. However, because this ideal model faced convergence issues due to the complexity of the maxwell stefan diffusion equations, a simpler model is presented. Comsol provides an ide and unified workflow for electrical, mechanical, fluid, acoustics and chemical applications. These properties make mass transport systems described by ficks second law easy to simulate numerically.

Ns equation and the pure diffusion equation in pem fuel cell modeling. Learn more about these chemical reaction engineering features below. A onedimensional transport model for multicomponent solute. Pdf twodimensional pem fuel cells modeling using comsol. Comsol multiphysics modeling environment with customized user interfaces. When defining and solving these problems, the fluid is modeled as incompressible by default but can. Modeling the chemical, diffusional, and thermal processes of a microreactor by. This apparatus have been modeled with comsol multiphysics software. Warning your internet explorer is in compatibility mode and may not be displaying the website correctly. The diffusion coefficient is most simply understood as the magnitude of the molar flux through a surface. Comsol is promoted to be a very good tool to solve multiphysics problems. A 1d steady state model for a spherical catalyst shape is developed in comsol multiphysics software using transport of dilute species and heat conduction interfaces.

A onedimensional transport model for multicomponent solute in. They can be calculated using the boundary conditions. While the maxwellstefan equations are successfully used in engineering applications, they seem much less known in the mathematical literature. This example illustrates the use of the maxwell stefan diffusion model available with the transport of concentrated species interface. It solves for the fluxes in terms of mass fraction. This matlab function simulates the 1962 bulb diffusion experiment of duncan and toor, an experiment that validated the accuracy of maxwellstefan diffusion.

When modeling diffusion, it is often a good idea to begin with the assumption that all diffusion coefficients are equal and independent of temperature, pressure, etc. The friction between the solute species and the soil skeleton wall, which is proportional to the relative velocity between the solute species and the soil skeleton, is introduced. This is the measure of the rate of the diffusion process. Estimates of na and nb can be obtained from application of the ficks law assuming simple binary diffusion. Thus, unlike fick diffusion, maxwellstefan diffusion can describe multicomponent mixtures. But somehow i am not able to code it using ode45, more likely i am not able to write the system to solve using ode45. Several different mathematical parameters had to be applied and solved. Solution of a system of odes with polymath and matlab. The maxwellstefan diffusion or stefanmaxwell diffusion is a model for describing diffusion in multicomponent systems. Modelling of multicomponent diffusion and swelling in protein gels.

The maxwell stefan diffusion or stefan maxwell diffusion is a model for describing diffusion in multicomponent systems. The comsol multiphysics geometry and cad environment 320. Sauer1,2,3 1 electrochemical energy conversion and storage systems group, institute for power electronics and electrical drives isea, rwth aachen university, germany 2 juelich aachen research alliance, jaraenergy, germany 3 institute for power generation and storage systems. In the bottom of a stefan tube there is a quiescent liquid with a mixture of acetone component 1 and methanol component 2. Noting the increased use of this product in analytical electrochemistry, the authors aim to.

Comparison of darcys law, the brinkman equation, the. Species transport in the gas diffusion layers of a pem comsol. The model couples the maxwell stefan application mode to the navier. A modified multicomponent solute diffusion equation described with diffusion flux was derived in detail based on the classical maxwell stefan diffusion theory. This paper will present the model developed in comsol of an electrolytesupported planar button sofc and a summary of the parametric study done for the same model. For characterizing the thermal profile, convective, conductive, and radiataive heat transfer modes were all included. For a comprehensive analysis, use the comsol multiphysics software and the acdc module to see how multiple physics affect your design.

Temperature based correlations for diffusivities of ft products in wax are widely used and a comparison of diffusion flux models wilke, wilkebosanquet, maxwell stefan, and dusty gas to describe species transportkinetic interactions for fts has not been reported in literature. Comsol multiphysics is a modeling package that solves. Modelling of multicomponent diffusion and swelling in. Simplifications of these equations for diluted mixtures give, for example, ficks first law of diffusion and the nernstplanck equations for diffusion and migration. The swelling process of protein gels in this thesis involved multicomponent diffusion, chemical ionisation and mechanical deformation. Oct 27, 2004 in the bottom of a stefan tube there is a quiescent liquid with a mixture of acetone component 1 and methanol component 2.

Ode45 in maxwellstefan equation matlab answers matlab. Parametric study will be conducted to analyze the effects of various parameters on the performance of pem fuel cells. The maxwell stefan ms equations maxwell 1866, stefan 1871 describe the process of diffusion, where diffusive fluxes, j i, of species through a plane, across which no net transfer of moles occurs, depend on all n1 independent driving forces in a mixture of n species. In this case, it is a liquid mixture of acetone and methanol that evaporates into air. The concentration isosurfaces reveal mass transfer through diffusion. Which is the most suitable software comsol vs ansys maxwell. This is the maxwell stefan equation, an equation that forms the basis for the mathematical description of mass transfer of chemical species in a mixture 2. The paper reports the results of a heat transfer modeling of a membrane reactor for methane steam reforming, study developed in order to analyze the importance of temperature for methane conversion and hydrogen yield. The transportkinetics interactions in the porous catalyst are analysed using various diffusion flux models such as wilke, wilkebosanquet, stefanmaxwell, and dusty gas models. In the module transport of diluted and concentrated species one can model a diffusion. A onedimensional transport model for multicomponent solute in saturated soil was developed based on the maxwell stefan diffusion theory and the mcl equation.

Browse the threads and share your ideas with the comsol community. Comparison of diffusion flux models for fischertropsch. A onedimensional transport model for multicomponent. The equations that describe these transport processes have been developed independently and in parallel by james clerk maxwell for dilute gases and josef stefan for fluids. The maxwellstefan formulation describes diffusion from first principles. It models multicomponent gasphase diffusion in a stefan tube in 1d. The mass flux is zero at the walls of the gas channel and gde, this boundary condition is usually taken as insulating. These are symmetric, so that an ncomponent system requires nn12 independent coefficients to parameterize the rate of diffusion of its components.

Vapor that evaporates from this pool of liquid diffuses to the top of the tube. Modelling of multicomponent diffusion and swelling in protein gels 2011. Simultaneous multicomponent diffusion of gases the parameters n a and n b the molar fluxes of components a and b respectively are unknown. All of the features listed below are implemented through associated physics interfaces. When i read the users guide, i found that all introductions are referred to. Which is the most suitable software comsol vs ansys maxwell for femm. Diffusion equation comsol multiphysics modeling software. Fick diffusion coefficient d ij maxwellstefan diffusion coefficient between species i and j e charge on a proton e youngs modulus f net force force acting per unit mass of component i f i body force g gibbs free energy gex excess gibbs free energy. Comsol multiphysics is a generalpurpose simulation software for modeling designs, devices, and processes in all fields of engineering, manufacturing, and scientific research. On the help menu, click about comsol multiphysics to check your version.

Numerical simulations were conducted with the finite element software comsol multiphysics, and the case of two heavy metal ion species was chosen as an example. The model incorporates stokesbrinkman, maxwellstefan, and nonlinear butlervolmer equations, computed and solved with comsol multiphysics software v4. In this module, the electron density and mean energy are computed by solving a pair of drift diffusion equations using a drift diffusion interface. In dilute species transport, the flux due to diffusion is given by ficks first law, which only depends on a single property of the solutes interaction with the solvent. Simply log in and follow the onscreen product download directions. Modeling of htpem fuel cell startup process by using comsol multiphysics y. Figure 4 shows the oxygen isoconcentration surfaces in a gas diffusion cathode for a fuel cell. Excerpt from the proceedings of the comsol conference 2007, boston. For multicomponent gas diffusion, the maxwell stefan diffusion model was used. Modeling and simulation of planar sofc to study the. In addition to using multiphysics modeling for your own projects, you can also turn your models into simulation applications and. Using maxwell stefan equation for diffusion, i want to set anisotrpic values for the diffusion coefficients.

Modeling of single cell solid oxide fuel cells using comsol. Anisotropic diffusion coefficients in maxwellstefan equation. To try to reduce this mass transport limitation, operation at high pressure, increase co2 solubility by adding chemical compounds or the use of gas diffusion electrodes 5. Finally, maxwell stefan equations were implemented in order to capture the concentration and temperature. Maxwell stefan s diffusion and convection equations explained the material transport, solved for both anode and cathode flow channel by using a transport of concentrated species interface. The following matlab project contains the source code and matlab examples used for solution of a maxwell stefan diffusion problem. This matlab function simulates the 1962 bulb diffusion experiment of duncan and toor, an experiment that validated the accuracy of maxwell stefan diffusion. This work proposes a 3d multiphysics model to predict and optimize the gde cell behavior, specifically for the cl and the gdl.

The gas chosen to insert in the retentate gas chamber is co2 and the inert gas is argon. Modeling the chemical, diffusional, and thermal processes of. This application mode models concentrated solutions where the species in solution interact with each other as well as the solvent. Finally, maxwellstefan equations were implemented in order to capture the concentration and temperature. The real problem of a proton exchange membrane pem fuel cell modeling involves different scales, multiple variables and processes, coupling of solvers. Diffusion coefficient understanding the diffusion coefficient. As of update 2, the new rotordynamics module is available as an optional addon to the structural mechanics module. Modeling the chemical, diffusional, and thermal processes. Solution of a maxwell stefan diffusion problem in matlab. A significant advantage with the maxwellstefan diffusion formulation, in comparison with ficks law, is the inclusion of a conservation of mass.

Diffusion of electrolyte solutions through protein gels was modelled using the generalised maxwell stefan gms equation. For my master thesis i want to write a chapter to compare those 3 models and to justify my choice. A onedimensional transport model for multicomponent solute in saturated soil was developed based on the maxwellstefan diffusion theory and the mcl equation. About the maxwell stefan equation in comsol, can it be used for liquids. Nov 26, 2014 dear experts, using maxwell stefan equation for diffusion, i want to set anisotrpic values for the diffusion coefficients. On the maxwellstefan approach to multicomponent di. This example illustrates the use of the maxwellstefan diffusion model available with the transport of concentrated species interface. Transport of the heavy species is determined by solving a modified form of maxwell stefan equations using the heavy.

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