Transient two-dimensional model of heat and mass transfer in a PEM fuel cell membrane

In the present work, a numerical study of heat and mass transfer within the membrane of a proton exchange membrane fuel cell is presented. The electrolyte membrane is considered an isotropic porous medium and ideal insulator for electrons and reactants. The adopted model in this study is based on the assumption of single-phase and multi-spices flow, supposed two-dimensional and unsteady. For the water transport, the major considered forces are; the convective force, resulting from the pressure gradient, the osmotic force, due to the concentration gradient and the electric force caused by the proton migration from the anode to the cathode. Based on a one-dimensional model, found in the literature, a transient two-dimensional one was proposed. The set of governing equations, written in velocity–pressure formulation, is solved by the implicit finite difference method. An alternating Direct Implicit scheme was used for the calculation. The numerical resolution gives the time- and space-dependent temperature and water concentration. The main focus lies on the influence of different cases of boundary conditions on water concentration and heat transfer variation with the intention of testing the reliability of the proposed computational fluid dynamic (CFD) code.     

Unsteady effects on natural convective heat transfer through porous media in cavity due to top surface partial convection

Numerical investigations of transient natural convection flow through a fluid-saturated porous medium in a rectangular cavity with a convection surface condition were conducted. Physical problem consists of a rectangular cavity filled with porous medium. The cavity is insulated except the top wall that is partially exposed to an outside ambient. The exposed surface allows convective transport through the porous medium, generating a thermal stratification and flow circulations. The formulation of differential equations is non-dimensionalized and then solved numerically under appropriate initial and boundary conditions using the finite difference method. The finite different equation handling the boundary condition of the open top surface is derived. The two-dimensional flow is characterized mainly by two symmetrical vortices driven by the effect of buoyancy. A lateral temperature gradient in the region close to the top wall induces the buoyancy force under an unstable condition. Unsteady effects of associated parameters were examined. It was found that the heat transfer coefficient, Rayleigh number and Darcy number considerably influenced characteristics of flow and heat transfer mechanisms. Furthermore, the flow pattern is found to have a local effect on the heat convection rate.     

Improving two-phase mass transportation under Non-Darcy flow effect in orientated-type flow channels of proton exchange membrane fuel cells

Orientated-type flow channels of proton exchange membrane fuel cells cause non-Darcy effect occurring in flow regions. Therefore, the species transportation is affected by inertial effect. However, how the inertial force affects convection and diffusion of different species has not been discussed before. Thus, a modified two-dimensional, non-isothermal, two-phase and steady state model considering non-Darcy effect is employed in this study, and reactants and products transportations through diffusion and convection under inertial effects are quantitatively analyzed for the first time. Simulation results reveal that the convective transportation of reactants increases more under the influence of inertial force; water vapor transportation through convection increases the water content in porous regions. At the same time, liquid water expels more rapidly from gas diffusion layers under baffle regions, and enlarging baffle volumes increases the regions where the liquid water is rapidly removed under the inertial effect.     

One dimensional transient numerical study of the mass heat and charge transfer in a proton exchange membrane for PEMFC

The objective of our study is to quantify the mass water transferred by various modes: diffusion, convection and migration. For the water transfer, the principal forces considered in the model are, the convection force, the osmotic force (i.e. diffusion) and the electric force (migration). The first of these forces results from a pressure gradient, the second of a concentration gradient and the third of a protons' migration from the anode to the cathode, which has an effect on the dipole of the water molecules (resistance force to the advancement). The numerical tool used to solve the equations' system is the finite element method. The results obtained numerically considering this method are concentration profiles and concentration variation with time and membrane thickness. These results illustrate the contribution of each mass transfer mode.     

Transient natural convection in an enclosure with vertical solutal gradients

Transient natural convection in an enclosure with vertical solutal gradients has been studied in this paper. Transfers in a rectangular cavity configuration translating hydrodynamic and thermal phenomena are numerically predicted by means of computational fluid dynamics (CFD) in transient regime.The objective of this numerical study is to give a fine knowledge of the hydrodynamic and thermal characteristics during energy storage in an enclosure filled with water stratified by downward salinity gradient. The enclosure is divided into three zones with different salinity level such as salt gradient pond (SGP). Water is heated by a heating device at the bottom of the cavity.The Navier–Stokes, energy and mass equations are discretized using finite-volume method, and a two-dimensional analysis of the hydrodynamic and thermal behaviors generated in transient regime in the cavity are performed. The mathematical modelling has allowed the prediction of the storage performances by developing parametrical study in view to search the convective heat transfer coefficient at the bottom of the enclosure. Velocity vector fields show the presence of recirculation zones caused only in the lower region and permit to explain the increase of the temperature in the lower convective zone (LCZ).This study shows also the importance of the salinity in the preservation of the high temperature in the bottom of the cavity, and the important reduction of the phenomenon of thermal transfer across the non-convective zone (NCZ).     

Transient natural convective heat transfer in porous medium with solidification of binary mixture

In this paper an enthalpy porosity method associated with finite control volume scheme and SIMPLE iteration was employed to solve Navier–Stokes equation coupled with energy equation through Ergun equation and Boussinesq approximation for studying the effect of two-dimensional transient natural convective heat transfer from a closed region of porous medium with the different porosity on solidification in carbon–iron system. As shown in the results, it is fund that the thickness of solidification layer is increased with time due to thermal coupled flow induced by natural convection; and the wall temperature is faster changed in porous medium with larger porosity, which corresponds to slow the growth of the solidification layer in binary system.     

A two-energy equation model for dynamic heat and mass transfer in an adsorbent bed using silica gel/water pair

In this study, the influence of the adsorbent bed dimensions, convective heat transfer coefficient between the cooling fluid and adsorbent bed and the thermal conductivity of the solid adsorbent material on the transient distributions of the solid and gas phase temperature difference, differences in the adsorbate concentration predicted by the instantaneous equilibrium and linear driving force (LDF) models, solid phase temperature, gas pressure and adsorbate concentration inside the adsorbent bed of a solid sorption cooling system have been investigated numerically for a nearly isobaric adsorption process. Silica gel/water is selected as the working pair. A transient two-dimensional local thermal non-equilibrium model has been developed that takes into account both internal and external mass transfer resistances. The local volume averaging method has been used to derive the macro-scale governing conservation equations from the micro-scale equations. It has been found that generally, the effects of the parameters investigated on the transient distributions of the temperature difference between the phases, difference in adsorbate concentration between the instantaneous equilibrium and LDF models, and gas phase pressure gradients are negligible small. The thickness of the adsorbent bed for the given adsorbent bed length and thermal conductivity of the solid adsorbent material have a large influence on the transient distributions of the solid phase temperature and adsorbate concentration. On the other hand, the transient temperature and adsorbate concentration distributions are only slightly affected by the variation of the adsorbent bed length and convective heat transfer for the conditions studied.     

Performance analysis and optimization of a thermally non-symmetric annular fin

Considering thermally non-symmetric convective boundary conditions, optimum dimensions of an annular fin which has a rectangular cross-section are investigated. Two-dimensional heat diffusion equation is solved analytically to obtain temperature distribution and heat transfer rate. In this work, fin volume is fixed to obtain the dimensionless geometrical parameters of the fin with maximum heat transfer rates. The optimum geometry which maximizes the heat transfer rate for a given fin volume has been found employing NCONF routine in the IMSL Library. The derived condition of optimality gives an open choice to the designer.     

Modeling forced liquid convection in rectangular microchannels with electrokinetic effects

The effects of the electric double layer near the solid–liquid interface and the flow induced electrokinetic field on the pressure-driven flow and heat transfer through a rectangular microchannel are analyzed in this work. The electric double layer field in the cross-section of rectangular microchannels is determined by solving a non-linear, two-dimensional Poisson–Boltzmann equation. A body force caused by the electric double field and the flow-induced electrokinetic field is considered in the equation of motion. For steady-state, fully-developed laminar flows, both the velocity and the temperature fields in a rectangular microchannel are determined for various conditions. The flow and heat transfer characteristics withwithout consideration of the electrokinetic effects are evaluated. The results clearly show that, for aqueous solutions of low ionic concentrations and a solid surface of high zeta potential, the liquid flow and heat transfer in rectangular microchannels are significantly influenced by the presence of the electric double layer field and the induced electrokinetic flow.     

Transient thermal stress analysis of a functionally graded thick hollow cylinder with temperature-dependent material properties

This article deals with the study of temperature distribution and thermal stresses of a functionally graded thick hollow cylinder with temperature dependent material properties. All the material properties except Poisson’s ratio are assumed to be dependent on temperature and spatial coordinate z. The two-dimensional transient heat conduction equation is solved under convective heat transfer condition with varying point heat source. The influence of inhomogeneity parameters on the thermal and mechanical behavior is examined. Numerical computations are performed for ceramic-metal-based functionally graded material, in which alumina is selected as ceramic and nickel as metal.     

An Extension of the Flow Boiling Correlation to Transition,Laminar, and Deep Laminar Flows in Minichannels and Microchannels

The thermal performance of rectangular plate fins circumscribing elliptic tubes is presented in this paper. Based on the assumption of uniform convective heat transfer the two-dimensional conduction equation has been formulated, and the solution has been obtained through the finite element method. Performance of rectangular plate fins for both inline and staggered arrangement of tubes has been investigated for a variation of geometric and thermo-geometric parameters. The necessity of optimizing the fin geometry for a given fin surface area has also been highlighted.     

Electrical cross effects in porous media with ice inclusions. 1. Diffusion mechanism

This paper is the first part of the theoretical work devoted to electrical cross effects in biporous media with ice inclusions. The fine-pored part of the medium is saturated by the electrolytic solution.A heat and mass transfer problem is formulated for an elementary cell of the medium on basis of diffusion mechanism. An equation set is proposed for finding the temperature, pressure, concentration, and electric potential fields. All the heat and mass flows through the cell depend on the cross thermodynamical forces.In the closed system the electric polarization induced by temperature gradient depends on the hydroconductivity of the fine-pored medium, the solution concentration and the ice content. At the low solution concentration and the high hydroconductivity the thermoelectric potential difference may be as great as 150 mV K^?1.In the open system the ice presence has no effect on the diffusion potential difference induced by concentration gradient.     

Buoyant convection in a cubical enclosure under time-periodic magnetizing force

A numerical investigation is made of buoyant convection of a paramagnetic fluid in a cubical enclosure under constant gravity g₀. Conventional buoyant convection arises by maintaining different temperatures at two opposite vertical sidewalls. The other walls are thermally insulated. To this basic layout, an electric wire is placed below the bottom horizontal wall to produce a magnetic field. The magnetizing force is induced, which modifies the convective flow and heat transfer characteristics. Comprehensive numerical solutions have been acquired to the governing equations. Of interest are the cases when the strength of the magnetizing force is time-periodic. The computed results reveal the presence of resonance, which is characterized by maximal amplification of the fluctuations of heat transport in the interior. The flow is shown to resonate to the basic mode of internal gravity oscillations. The study points to the feasibility of using the time-periodic magnetizing force as an effective regulator of the convective fluid system.     

Numerical analysis of convective and diffusive fuel transports in high-temperature proton-exchange membrane fuel cells

The fuel transports in high-temperature proton-exchange membrane fuel cells have been numerically examined. Both convective and diffusive fuel transports are analyzed in detail. The former is often neglected in straight flow channel configurations while it has been reported to become important for serpentine or interdigitated flow channel configurations. By using a two-dimensional isothermal model, we have performed numerical simulations of a high-temperature proton-exchange membrane fuel cell with a straight flow channel configuration. The present results show that even in a straight flow channel configuration, the convection can play a significant role in fuel transports for the anode side. Examination of the flow field data reveals that the anode gas mixture is transported toward the catalyst layer (CL) whereas the gas mixture in the cathode channel moves away from the reaction site. It is also observed that as the flow moves downstream, the flow rate decreases in the anode channel but increases in the cathode channel. Species transport data are examined in detail by splitting the total flux of fuel transport into convective and diffusive flux components. For oxygen transport in the cathode gas diffusion layer (GDL), diffusion is dominant; in addition, the convective flux has a negative contribution to the total oxygen flux and is negligible compared to the diffusion flux. However, for hydrogen transport to the reaction site, both convection and diffusion are shown to be important processes in the anode GDL. At high cell voltages (i.e., low current densities), it is even observed that the convective contribution to the total hydrogen flux is larger than the diffusive one.     

A way to explain the thermal boundary effects on laminar convection through a square duct

A way using the reformulation of the energy conservation equation in terms of heat flux to explain the thermal boundary effects on laminar convective heat transfer through a square duct is presented. For a laminar convection through a square duct, it explains that on the wall surface, the velocity is zero, but convection occurs for uniform wall heat flux (UWHF) boundary in the developing region due to the velocity gradient term; for uniform wall temperature (UWT) boundary, only diffusion process occurs on the wall surface because both velocity and velocity gradient do not contribute to convection; for UWHF, the largest term of the gradient of velocity components (the main flow velocity) on the wall surface takes a role in the convection of the heat flux normal to the wall surface, and this role exists in the fully developed region. Therefore, a stronger convection process occurs for UWHF than for UWT on the wall surface. The thermal boundary effects on the laminar convection inside the flow are also detailed.     

Effect of operating parameters on dynamic response of water-to-gas membrane humidifier for proton exchange membrane fuel cell vehicle

An analytic multi-dimensional dynamic model of a membrane type humidifier has been developed for the study of transient responses of the humidifier under proton exchange membrane fuel cell vehicle operating conditions. The dynamic responses of heat and mass transfer and fluid flow in a membrane humidifier are mathematically formulated and modeled with a newly developed pseudo-multi-dimensional concept. The model is used to analyze the performance of the humidifier under various operating conditions and the dynamic response of the humidifier under transient operating conditions. The simulation results show that, in the case of the water-to-gas type membrane humidifier modeled in this study, the time constant of water diffusion in the membrane is less than 1 s. Thus, the delay of the response of the humidifier induced by the vapor diffusion in the membrane is not significant in vehicle operation. However, it is also found that the dynamic behavior is mainly due to the thermal resistance and heat capacity of the membrane humidifier.     

Transient simulations of heat transfer in human eye undergoing laser surgery

A validated two-dimensional computational model of the human eye solving the discretized form of the bio-heat transfer equation using finite volume formulation has been developed. Using the model, the transient temperature evolution and associated thermal effects in various regions of the human eye subjected to laser radiation during retinopathy are investigated. It is shown that the transient evolution of the retinal temperature during laser heating could reach values higher than that required for irreversible cell damage. This is because the time scale for spatial diffusion of heat towards the choroid, containing blood vessels for cooling, is much larger than that of the actual laser surgical process (100 ms). This excess temperature could cause cell damage to the adjoining retinal region due to heat diffusion. Based on the simulation results, a method is proposed to maintain the retinal pigmented epithelium (RPE) temperature close to the required 60 °C by pulsating the laser source between suitable maximum and minimum heat flux values.     

Effect of electromagnetic field on the thermal performance of longitudinal trapezoidal porous fin using DTM–Pade approximant

The heat transfer and thermal distribution through porous fins have gotten a lot of attention in recent years due to their extensive applications in the manufacturing and engineering field. In porous fins, the impact of magnetic field aids in improved heat transfer enhancement. Also, the combination of an electric effect and a magnetic field considerably enhances heat transfer. In this direction, the thermal distribution through a convective–radiative longitudinal trapezoidal porous fin with the impact of an internal heat source and an electromagnetic field is discussed in the present analysis. The governing heat equation is nondimensionalized with nondimensional terms, and the transformed nonlinear ordinary differential equation is solved analytically using the DTM–Pade approximant algorithm. Furthermore, the graphical discussion is presented to explore the impact of various nondimensional parameters, such as convection-conduction parameter, fin taper ratio, thermomagnetic field, radiation–conduction parameter, internal heat generation parameter, and thermoelectrical field on the temperature gradient of the fin. The investigation's key findings disclose that as the magnitude of the convection–conduction parameter, fin taper ratio, and radiation–conduction parameter increase, the thermal distribution through the fin reduces. The thermal distribution inside the fin increases for the heat-generating parameter, thermoelectric, and thermomagnetic fields.     

Heat transfer enhancement in medium temperature thermal energy storage system using a multitube heat transfer array

An experimental energy storage system has been designed using an horizontal shell and tube heat exchanger incorporating a medium temperature phase change material (PCM) with a melting point of 117.7 °C. Two experimental configurations consisting of a control unit with one heat transfer tube and a multitube unit with four heat transfer tubes were studied. The thermal characteristics in the systems have been analysed using isothermal contour plots and temperature time curves. Temperature gradients along the three directions of the shell and tube systems; axial, radial and angular directions have been analysed and compared. The phase change in the multitube system was dominated by the effect of convective heat transfer compared to conductive heat transfer in the control system. The temperature gradient in the PCM during phase change was greatest in the radial direction for both the control and multitube systems. The temperature gradients recorded in the axial direction for the control and multitube systems during the change of phase were respectively 2.5 and 3.5% that of the radial direction, indicating essentially a two-dimensional heat transfer in the PCM. The onset of natural convection through the formation of multiple convective cells in the multitube system significantly altered the shape of the solid liquid interface fluid flow and indicates the requirement for an in-depth study of multitube arrangements.     

Characterization of heat transfer modes of tube side convective condensation under the influence of an applied DC voltage

An experimental study was performed to determine the modes of heat transfer in horizontal tube side convective condensation under an applied DC high voltage. Experiments were performed with R134a in a horizontal, single-pass, counter-current heat exchanger. A 8 kV DC voltage was applied through a central rod electrode with the tube wall grounded for mass flux in the range 45–156 kg/m² s. The average quality across the test section was 45%, which corresponds to an initially stratified flow with the liquid level below the central electrode. The high-voltage electric field results in an interfacial electric body force which extracts the liquid from the bottom stratum towards the vapour core. This results in a phase redistribution with a resultant increase in heat transfer. The increase in heat transfer can be attributed to a change of the heat transfer mode in the lower section of the tube from convective condensation to film condensation.