Analysis of transport phenomena within PEM fuel cells – An analytical solution

Transport phenomena within PEM fuel cells are investigated and a comprehensive analytical solution is presented. The methodology couples the transport within the fuel cell supply channels and the substrate which is composed of five different layers. The layers are all treated as macroscopically homogeneous porous media with uniform morphological properties such as porosity and permeability. The locally volume-averaged equations are employed to solve for transport through the porous layers. The problem encompasses complex interfacial transport phenomena involving several porous–porous as well as porous–fluid interfaces. Chemical reactions within the catalyst layers are also included. The method of matched asymptotic expansions is employed to solve for the flow field and species concentration distributions. Throughout the analysis, the choice of the gauge parameters involved in the perturbation solutions for velocity and concentration is found to be inherently tied to the physics of the problem and therefore an important physical metric. The analytical solution is found to be in excellent agreement with prior computational simulations. The analytical results are used to investigate several aspects of transport phenomena and their substantial role in PEM fuel cell operation. The solution presented in this work provides the first comprehensive analytical solution representing fuel cell transport phenomena.     

Modeling of low-density lipoprotein (LDL) transport in the artery—effects of hypertension

A robust four-layer model is presented to describe the LDL transport in the arterial wall coupled with the transport in the lumen. The endothelium, intima, internal elastic lamina (IEL) and media are all treated as macroscopically homogeneous porous media and the volume-averaged porous media equations are employed to model various layers, with Staverman filtration and osmotic reflection coefficients introduced to account for selective permeability of each porous layer to certain solutes. The physiological parameters within the various layers are obtained from literature. The set of governing equations for fluid flow and mass transport is descretized using a finite element scheme based on the Galerkin method of weighted residuals. Filtration velocity and LDL concentration profiles are developed at different locations for various clinical conditions. The results are consistent with previous numerical and experimental studies. Effects of hypertension and boundary conditions are discussed based upon the present model. Furthermore, the effects of pulsatile flows on LDL transport in the arterial wall are studied in some detail. Compared to previous transport models, the newly developed model is found to be a more robust tool for investigation of LDL accumulation within different arterial wall layers for various clinical conditions. This will be helpful in understanding the role of transmural transport processes in the initiation and development of atherosclerosis.     

Effects of gender-related geometrical characteristics of aorta–iliac bifurcation on hemodynamics and macromolecule concentration distribution

Aorta–iliac bifurcation has been anatomically shown to be asymmetric. Also, statistical data reveal differences in the structural features of average male and female aorta–iliac bifurcation. In the present work, numerical simulations of the macromolecule transport at the aorta–iliac bifurcation are performed. The transport phenomena within the lumen and the arterial wall are coupled. The arterial wall is modeled as a four-layer porous wall, representing endothelium, intima, internal elastic lamina (IEL), and media layers. The layers are all treated as macroscopically homogeneous porous media with uniform morphological properties. The Staverman filtration coefficient is incorporated to account for selective permeability of each porous layer to macromolecules. Different geometrical attributes of the aorta–iliac bifurcation are studied, i.e. asymmetry and gender-dependence. Profiles of macromolecule concentration distributions are obtained for different cases. The results are discussed with regard to the shear stress distribution, which is believed to be one of the key factors in atherogenesis. The present study appears to be the first one to discuss the effects of gender and geometrical characteristics (e.g. asymmetry) on the transport phenomena at the aorta–iliac bifurcation.     

A multi-layer porous wall model for coronary drug-eluting stents

An analytical solution for solving the transient drug diffusion in adjoining porous wall layers faced with a drug-eluting stent is presented. The endothelium, intima, internal elastic lamina and media are all treated as homogeneous porous media and the drug transfer through them is modelled by a set of coupled partial differential equations. The classical separation of variables method for a multi-layer configuration is used. The model addresses the concept of penetration depth for multi-layer solids that is useful to treat the wall thickness by estimating a physical bound for mass diffusion. Drug concentration level and mass profiles in each layer at various times are given and discussed.     

Visualization experiments and pore network simulations for invasion-percolation transport of a non-wetting fluid through multiple porous layers

A similarity model experiment was developed to investigate the liquid water transport in hydrophobic porous layers of polymer electrolyte membrane fuel cells (PEMFCs). The dimensionless numbers in the similarity model experiment were closely matched to those in operating PEMFCs. This allowed the visual inspection of invasion-percolation transport of a non-wetting fluid with active capillary fingering in multiple porous layers, similar to the liquid water transport in porous layers of PEMFCs. The experimental results showed that inserting an intermediate layer between a fine layer and a coarse layer suppresses the capillary fingering of the non-wetting fluid inside the coarse layer. Thus, it could be expected that the steady-state volume of the non-wetting fluid in the multiple porous layers decreases as the thickness of the intermediate layer increases. In fact, this trend was quantitatively verified by measuring the volume of the breakthrough droplets formed by the non-wetting fluid that emerged out of multiple porous layers. In addition, pore network simulations were also conducted to reproduce the observed non-wetting fluid transport in multi-layer porous media, and relatively good agreements between experimental and numerical results were obtained.     

An investigation of convective transport in micro proton-exchange membrane fuel cells

The flow phenomena in a serpentine microchannel segment attached to a porous transport layer in a micro proton-exchange membrane fuel cell is investigated. Due to the presence of a porous transport layer, the fluid flow for this configuration exhibits different characteristics compared with that through a simple serpentine channel. The pressure drop and friction factor variation in the channel is examined for various values of Reynolds number and radii of curvature. Also, the effect of variation of permeability is investigated. There are two modes of fluid transport in this geometry—one through the serpentine channel and other via the porous media. With increasing permeability, more fluid is convected through the porous transport layer.     

Simulation of laminar impinging jet on a porous medium with a thermal non-equilibrium model

This work shows numerical simulations of an impinging jet on a flat plate covered with a layer of a porous material. Macroscopic equations for mass and momentum are obtained based on the volume-average concept. Two macroscopic models are employed for analyzing energy transport, namely the one-energy equation model, based on the Local Thermal Equilibrium assumption (LTE), and the two-energy equation closure, where distinct transport equations for the fluid and the porous matrix follow the Local Non-Thermal Equilibrium hypothesis (LNTE). The numerical technique employed for discretizing the governing equations was the finite volume method with a boundary-fitted non-orthogonal coordinate system. The SIMPLE algorithm was used to handle the pressure–velocity coupling. Parameters such as porosity, porous layer thickness, material permeability and thermal conductivity ratio were varied in order to analyze their effects on flow and heat transport. Results indicate that for low porosities, low permeabilities, thin porous layers and for high thermal conductivity ratios, a different distribution of local Nusselt number at the wall is calculated depending on the energy model applied. The use of the LNTE model indicates that it is advantageous to use a layer of highly conducting and highly porous material attached to the hot wall.     

Peristaltic flow of Buongiorno model nanofluids within a sinusoidal wall surface used in drug delivery

The current paper deals with the radiative heat transfer of the peristaltic flow of the Buongiorno model nanofluid through a two‐dimensional channel with a sinusoidal wall surface. A particular form of fluid transport occurring through progressive wave of expansion or contraction generating along a distensible tube containing fluid is known as peristaltic pumping, which takes place from the lower pressure region to the higher pressure region. Peristaltic transport finds several applications, such as blood pumping in heart, lung, and pharmacological delivery systems, and industrial applications—sanitary fluid transport, corrosive fluids transport, and so on. An approximate analytical solution is employed for the solution of the system of transformed differential equations with prescribed boundary conditions. The influences of physical parameters characterizing the flow phenomena are obtained and presented via graphs. The result warrants a good correlation with earlier studies in particular case. The following are the main findings: thermophoresis is favorable to enhance the fluid temperature near the channel center and also the axial velocity increases as an increase in the thermal buoyancy parameter. However, the main findings are elaborated in Section 3.     

An Investigation on Transport Properties Near the Wall in Porous Media by Fractal Models

A comprehensive investigation on the wall effects on the transport properties, permeability, thermal conductivity, and thermal dispersion conductivity is performed, based on the fractal models for these properties and the porosity variations near the wall in porous media. The results show that the fractal models for transport properties of porous media can provide good agreement with the conventional models in the region near the wall in porous media. This indicates that the fractal models for transport properties of porous media also hold in the region near the wall in porous media if the wall effects are taken into account.     

The effect of diffusioosmosis on water transport in polymer electrolyte fuel cells

An analytical study of the effect of diffusioosmosis caused by the concentration gradient of hydrogen ions on the isothermal transport of water in a fully hydrated membrane of a polymer electrolyte fuel cell (PEFC) is presented. A capillary tube or slit with a negatively charged wall is chosen to model the nanopores of the membrane. The electric double layer adjacent to the capillary wall may have an arbitrary thickness relative to the capillary radius and its electrostatic potential distribution is determined as the solution of the Poisson–Boltzmann equation. Solving a modified Navier–Stokes equation, the fluid velocity in the axial direction of the capillary induced by the macroscopic electric field and protonic concentration gradient is obtained as a function of the radial position in closed forms. The results for the local and averaged electrokinetic velocities in the capillary show that the effect of diffusioosmosis on the water transport in the membrane of a PEFC can be significant in comparison with that of electroosmosis under low-potential-difference operations.     

Analytical characterization of heat transport through biological media incorporating hyperthermia treatment

Modeling and understanding heat transport and temperature variations within biological tissues and body organs are key issues in medical thermal therapeutic applications, such as hyperthermia cancer treatment. The biological media can be treated as a blood saturated tissue represented by a porous matrix. A comprehensive analytical investigation of bioheat transport through the tissue/organ is carried out including thermal conduction in tissue and vascular system, blood–tissue convective heat exchange, metabolic heat generation and imposed heat flux. Utilizing local thermal non-equilibrium model in porous media theory, exact solutions for blood and tissue phase temperature profiles as well as overall heat exchange correlations are established for the first time, for two primary tissue/organ models representing isolated and uniform temperature conditions, while incorporating the pertinent effective parameters, such as volume fraction of the vascular space, ratio of the blood and the tissue matrix thermal conductivities, interfacial blood–tissue heat exchange, tissue/organ depth, arterial flow rate and temperature, body core temperature, imposed hyperthermia heat flux, metabolic heat generation, and blood physical properties. A simplified solution based on the local thermal equilibrium between the tissue and the blood is also presented.     

Critical assessment of arterial transport models

Works pertinent to arterial transport models are analyzed and a critical assessment of the models utilized in the study of fluid flow and mass transfer within the arteries is presented with an emphasis on the role of porous media. Arterial transport models are assessed and classified based on their ability to physically prescribe the arterial anatomy as well as the related transport processes. Pertinent models such as wall-free, homogeneous-wall, and multi-layer models as well as the governing equations and different types of boundary conditions utilized in each model are analyzed.     

Analysis of 2D flow and heat transfer modeling in fracture of porous media

Heat and mass transfer between porous media and fluid is a complex coupling process,which is widely used in various fields of engineering applications,especially for natural and artificial fractures in oil and gas extraction.In this study,a new method is proposed to deal with the flow and heat transfer problem of steady flow in a fracture.The fluid flow in a fracture was described using the same method as Mohais,who considered a fracture as a channel with porous wall,and the perturbation method was used to solve the mathematical model.Unlike previous studies,the shear jump boundary condition proposed by Ochoa-Tapia and Whitaker was used at the interface between the fluid and porous media.The main methods were perturbation analysis and the application of shear jump boundary conditions.The influence of permeability,channel width,shear jump degree and effective dynamic viscosity on the flow and heat transfer in the channel was studied by analysing the analytical solution.The distribution of axial velocity in the channel with the change of the typical parameters and the sensitivity of the heat transfer was obtained.     

Enhancement of heat transfer: Combined convection and radiation in the entrance region of circular ducts with porous inserts

Using porous ceramic inserts in high temperature equipment has been proven to be an effective means to enhance combined convective–radiative heat transfer. The porous ceramic insert was referred to as a convection-to-radiation converter (CRC) by previous investigators. We consider a novel application of CRC cores in a partial by pass flow system for heat transfer enhancement. Both hydrodynamically and thermally developing laminar flow is considered in the entrance region of a circular pipe with a porous insert located at the center. The momentum and Darcy–Brinkman equations are applied to the flow field in the annular gas layer and central porous layer respectively. The energy equation is coupled with the radiative transfer equation by the radiation source term. The radiative transfer is simulated by the newly developed integral equations [X.L. Chen, W. Sutton, Radiative transfer in finite cylindrical media using transformed integral equations, J. Quant. Spectrosc. Radiat. Transfer 77 (3) (2003) 233–271; W. Sutton, X.L. Chen, A general integration method for radiative transfer in 3-D non-homogeneous cylindrical media with anisotropic scattering, J. Quant. Spectrosc. Radiat. Transfer 84 (2004) 65–103] to avoid singularity problem and give high accuracy. The working fluid and porous medium are both considered as participating media. Finally, this highly non-linear system of equations is solved by a mixed iteration method. The results are compared between the cases with and without the porous insert. The porous insert enhances both convective and radiative transfer by about 35% and 105% respectively at the most. The effects of important parameters on this enhancement are discussed in detail.     

Analytical determination of permeability of porous fibrous media with consideration of electrokinetic phenomena

Flow behavior in porous fibrous media with consideration of electrokinetic phenomena is investigated based on a linearized Poisson–Boltzmann equation and Navier–Stokes equation. An analytical solution of effective permeability of porous fibrous media as functions of porosity, dimensionless local averaging net charge density and dimensionless electric resistance number is derived in this paper. The influences of the electrokinetic phenomena can be measured by the dimensionless electric resistance number, which is proportional to the square of the liquid dielectric constant, the solid surface Zeta potential and inversely proportional to the liquid dynamic viscosity, electric conductivity and the square of the maximum pore radius. The analytical results show that when the dimensionless electric resistance number is small and the porosity is large, the dimensionless total flow rate shows a nearly uniform distribution. When the dimensionless electric resistance number is large, the resistant effects of the electrical double layer (EDL) become so significant that the superficial velocity decreases. The effective permeability of the porous fibrous media decreases correspondingly. Furthermore, the theoretical predicted effective permeability values are compared with experimental data, and good agreement is observed between the two. It shows that the mathematical model for the effective permeability of porous fibrous media with consideration of electrokinetic phenomena is satisfactory.     

Formation of a low reflective surface on crystalline silicon solar cells by chemical treatment using Ag electrodes as the catalyst

A new method was developed for making a porous silicon layer as an anti-reflective coating on the top of crystalline silicon solar cells. The porous silicon layer was formed in a mixed solution of H₂O₂ and HF by using screen-printed Ag front electrodes as the catalyst. With the help of the catalytic effect, porous silicon layers were formed by treatment in a solution chemically milder than conventional solutions. The multi-crystalline silicon solar cell covered with the porous silicon layer showed a surface reflectance below 15% in a wavelength region of 400–800 nm.     

Investigations of solar cells with porous silicon as antireflection layer

The possibility of using porous silicon layers as antireflection coating instead of the antireflection coatings in common silicon solar cells was investigated. A technology for the manufacture of porous silicon antireflection layers was developed. The comparison of the photovoltaic and optical characteristics of investigated samples of solar cells with ZnS antireflection coating and with porous silicon antireflection coating is presented. It is shown that the formation of the porous layer under optimal technological regimes leads to significant improvement of the main photovoltaic parameters–short-circuit current and open-circuit voltage.     

VOF modelling of gas–liquid flow in PEM water electrolysis cell micro-channels

In this study, the gas–liquid flow through an interdigitated anode flow field of a PEM water electrolysis cell (PEMEC) is analysed using a three-dimensional, transient, computational fluid dynamics (CFD) model. To account for two-phase flow, the volume of fluid (VOF) method in ANSYS Fluent 17.2 is used. The modelled geometry consists of the anode channels and the anode transport layer (ATL). To reduce the complexity of the phenomena governing PEMEC operation, the dependence upon electro-chemistry is disregarded. Instead, a fixed source of the gas is applied at the interface between the ATL and the catalyst layer. An important phenomenon that the model is able to capture is the gas–liquid contact angle on both the channel wall and ATL-channel interface. Particularly, the latter interface is crucial in capturing bubble entrainment into the channel. To validate the numerical simulation, photos taken of the gas–liquid flow in a transparent micro-channel, are qualitative compared against the simulation results. The experimental observations confirm the models prediction of long Taylor bubbles with small bubbles in between. From the simulation results, further intriguing details of the flow are revealed. From the bottom to the top of the outgoing channel, the film thickness gradually increases from zero to 200 μm. This increase in the film thickness is due to the particular superficial velocity field that develops in an interdigitated flow. Here both the superficial velocities change along the length of the channel. The model is capable of revealing effect of different bubble shapes/lengths in the outgoing channel. Shape and the sequence of the bubbles affect the water flow distribution in the ATL. The model presented in this work is the first step in the development of a comprehensive CFD model that comprises multiphase flow in porous media and micro-channel, electro-chemistry in catalyst layers, ion transport in membrane, hydrogen evolution, etc. The model can aid in the study of gas–liquid flow and its impact on the performance of a PEMEC.