Heat and mass transfer influence on potential variation in a PEMFC membrane

Water transport in the membrane of a PEM fuel cell is provided essentially by a convective force, resulting from a pressure gradient, an osmotic force, due to a concentration gradient and an electric force caused by the protons migration from the anode to the cathode. Through these three types of force the two-dimensional behavior of electric potential has been studied in this paper. The adopted model in this work is based on the assumption of single phase and multi-species flow, supposed two-dimensional and transient in a porous medium. The species conservation equation is coupled with the energy equation through the diffusion coefficient of water and the heat convective flux. The set of governing equations in the form of convection–diffusion problem has been solved numerically using the finite volume method. The obtained results show the transient two-dimensional effect of heat and mass transfer on the voltage variation within the membrane.     

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.     

Experimental studies of natural convective mass transfer in a water-splitting system

The present research investigates the mass transfer processes at the electrode-electrolyte interface of a water-splitting, electrochemical cell using particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF). In a water-splitting device, mass transfer mechanisms usually involve simultaneous convection, diffusion, and migration. Mass transfer rate, at the electrode/electrolyte interface, depends on various factors, including electrode orientation, current density, type of redox agents and the products. The parameters considered here are cell voltage, the orientation of electrode, and the effect of concentration gradient induced by the reactants depletion and product formation at the interface on the mass transfer rate. The present study captures the instantaneous velocity and concentration fields using PIV and PLIF techniques. Conducting the experiments over various current densities and electrode-orientations, present study observes that the reactant depletion and product formation at the anode interface induces buoyancy which in turn causes natural convection even at low current densities. By utilizing the effect of orientation and the natural convection induced by the reactants and products, on the mass transfer rate, the limiting current density can be enhanced, and the supersaturation of products can be prevented at the interface.     

Laminar boundary-layer analysis of simultaneous mass and heat transfer in natural convection around A horizontal cylinder

An analytical study is presented of the combined heat and mass transfer characteristics of natural convection flow around a horizontal circular cylinder. The surface of the cylinder is assumed to be at uniform temperature and uniform concentration. Specific cases of diffusion of water vapour and naphthalene into air are studied. The results indicate that the local Nusselt number and the local wall shear stress increase and decrease from the pure free convection values as the buoyancy force from species diffusion assists and opposes, respectively, the thermal buoyancy force. The local Nusselt number and the local wall shear stress are found to increase with the decrease of the Schmidt number, whereas the surface mass transfer increases with increasing Schmidt number. The Sherwood number is found to become more effective as the thermal buoyancy force increases. The cumulative tangential mass flow rate is found to increase with the increase of the polar angle from the lower pole and is strongly dependent on the nature and magnitude of the concentration to thermal buoyancy force ratio, especially at low Schmidt number.     

Heat Transfer Control of Rayleigh-Benard Natural Convection of Air by Kelvin Force

Two-dimensional numerical computations are carried out to clarify the effect of Kelvin force on the Rayleigh-Benard natural convection of air in an enclosure under a magnetic field gradient. The computed results suggest that the Kelvin force could be utilized to control the heat transfer rate and the flow of the Rayleigh-Benard natural convection of air having a paramagnetic property. The transient characteristics of magnetothermal convection induced by the Kelvin force are also examined. Various phenomena caused by the Kelvin force are explained by considering the temperature dependence of the air's mass magnetic susceptibility according to Curie's law.     

Double diffusive unsteady free convection on two-dimensional and axisymmetric bodies in a porous medium

The unsteady laminar free convection flow of an incompressible electrically conducting fluid over two-dimensional and axisymmetric bodies embedded in a highly porous medium with an applied magnetic field has been studied. The unsteadiness in the flow field is caused by the variation of the wall temperature and concentration with time. The coupled nonlinear partial differential equations with three independent variables have been solved numerically using an implicit finite-difference scheme in combination with the quasilinearization technique. It is observed that the skin friction, heat transfer and mass transfer increase with the permeability parameter but decrease with the magnetic parameter. The results are strongly dependent on the variation of wall temperature and concentration with time. The skin friction and heat transfer increase or decrease as the buoyancy forces from species diffusion assist or oppose the thermal buoyancy force. However, the mass transfer is found to be higher for small values of the ratio of the buoyancy parameters than for large values.     

Modified stability analysis of double-diffusive convection in viscoelastic fluid layer saturating porous media

The present analysis mathematically investigates the thermohaline convection problem in viscoelastic fluid layer saturating porous media by utilizing the modified Boussinesq approximation. By performing linear stability analysis, the Darcy–Rayleigh numbers for stationary and oscillatory modes of convection are derived. The effects of different parameters describing the problem are studied numerically. In nonlinear stability analysis, the heat and mass transfer rates in the form of Nusselt and Sherwood numbers, respectively, are obtained for oscillatory convection using the derived Ginzburg–Landau equation. From the results, it is observed that overstability is the preferred mode of instability in linear stability. It is found that in linear double-diffusive convection problems, the stress relaxation imparts a destabilizing effect whereas the strain retardation time, the coefficient of specific heat variation due to temperature, and the concentration gradient have a stabilizing effect on the system's stability. The numerical values of heat and mass transfer rates varied with the coefficient of specific heat showing that the heat transport decreases while the mass transport increases. Also, the stress relaxation time, the concentration gradient, and the gravity modulation's amplitude increase while the strain retardation time decreases the heat and mass transfer rates. The wavelength of oscillations remains unaltered with the variation of specific heat variation due to temperature. The modulation frequency does not affect the heat/mass transfer rate; though, the wavelength of oscillations decreases with increasing frequency.     

Scaling of boundary-layer flows driven by double-diffusive convection

The objective of this paper is to investigate natural convection driven by two buoyancy sources, such as heat and mass, in vertical boundary layers. Starting from the integral equations and using scale analysis, we derive the different asymptotic flow regimes encountered with different buoyancy forces and diffusion coefficients. Each type of flow is characterized by a set of scaling relations yielding the velocity, temperature and concentration distributions inside the fluid, and the heat and mass transfer coefficients. All our results are perfectly corroborated by numerical investigations in a wide range of parameters.     

MIXED CONVECTION HEAT AND MASS TRANSFER IN RADIALLY ROTATING RECTANGULAR DUCTS

The present work investigates mixed convection heat and mass transfer in the entrance region of radially rotating rectangular ducts with water film evaporation along the porous duct watts. Mechanisms of secondary vortex development in the ducts under various conditions are examined by a vorticity-velocity numerical method. Emphasis is placed on the rotation effects, including both Coriolis and centrifugal buoyancy forces, and the mass diffusion effect on the flow structure and heat transfer characteristics. Results are presented in particular for an air-water vapor system under various conditions. Predicted results show that the effects of liquid film evaporation along the porous duct walls on the mixed convection neat transfer are rather substantial. The magnitude of the evaporative latent heal transfer may be 10 times greater than that of sensible heat transfer. The predictions also demonstrate that the distributions of Nu, Sh?z?, and fRe are closely related to the emergence, disappearance, growth, and decay of the rotating-induced secondary vortices. Additionally, a higher Nu?z? is found for a rectangular duct with a larger aspect ratio ( γ = 2) due to the relatively stronger secondary flows.     

Coupling between finite volume method and lattice Boltzmann method and its application to fluid flow and mass transport in proton exchange membrane fuel cell

In this paper, a concentration distribution function reconstruction operator is derived to lift macroscopic parameter concentration to concentration distribution function in lattice Boltzmann method (LBM). Combined with a density–velocity distribution function reconstruction operator previously derived by the author’s group, the coupled finite volume method and LBM scheme (CFVLBM), previously proposed by the authors’ group is extended to simulate both fluid flow and mass transport processes. The accuracy of concentration distribution function reconstruction operator and the feasibility of CFVLBM are validated by two numerical examples, diffusion–convection–reaction problem and natural convection in a square cavity induced by concentration gradient. Finally, the CFVLBM is further adopted to simulate fluid flow and mass transport in the gas channel (GC) and gas diffusion layer (GDL) of a proton exchange membrane fuel cell (PEMFC). It is found that the CFVLBM can capture the pore-scale information of fluid flow and species transport in porous GDL and can save the computational resources.     

Calculation procedure for mass transfer in fuel cells

An analysis of mass transfer losses, or concentration over-potentials in fuel cells is provided. An elementary theory, based on an equivalent film thickness, as proposed in some texts, is derived. This is followed by a more rigorous theoretical treatment of mass transfer theory, for which the mass transfer factor is obtained as a function of the driving force. The solution for the driving force is derived, for the well-known one-dimensional convection–diffusion problem. It is shown that mass transfer in planar and square geometries approximates this idealised situation. A linearised theory, appropriate for low mass flow rates is also presented. The methodology is illustrated using the simple example of a solid oxide fuel cell (SOFC). It is shown that the simplified theory is only applicable for very dilute binary mixtures. A step-by-step procedure for computing mass transfer in fuel cells is detailed, together with a discussion of the scope and range of application of the results.     

Numerical study of heat and mass transfer in MHD flow of nanofluid in a porous medium with Soret and Dufour effects

This article models the transport mechanism of mass and heat energy under temperature and concentration gradients. Mathematical models in the form of partial differential equations based on conservation laws for fluid flow and transfer of heat and mass subjected to thermal diffusion and diffusion thermos, heat generation porous medium, and buoyancy forces are developed under boundary layer approximations. These models along with models of nanostructures are solved numerically using the shooting method with the Runge–Kutta method of order five. Convergent solutions are obtained and are used for parametric analysis regarding thermal enhancement of a working fluid having nanoparticles of CuO, Al₂O₃, and TiO₂. Numerical experiments are performed and it is observed that the transport of heat is accelerated when the compositional gradient is increased. Similarly, a significant rise in the transport across concentration is noted when the temperature gradient is increased. The magnetohydrodynamic flow experienced retardation when the porous medium parameter and Hartmann number are increased. The temperature increased when the friction force produced heat and that heat is distributed to the particles of the fluid. Hence, viscous dissipation is responsible for widening the thermal boundary layer region.     

Effect of transpiration on combined heat and mass transfer in mixed convection along a vertical plate

The effect of transpiration velocity on the heat and mass transfer characteristics of mixed convection flow along a permeable vertical flat plate under the combined effects of thermal and mass diffusion is analysed. The diffusion-thermo and thermo-diffusion effects as well as the interfacial velocities due to mass diffusion are negligibly small. The plate is maintained at a uniform temperature and species concentration. Numerical results for the local skin-friction, the local Nusselt number and the local Sherwood number, as well as for the velocity, the temperature and the concentration profiles, are presented for diffusion of common species into air only. In general, it has been found for thermally assisted flow that the local surface shear-, heat-, and mass-transfer rates decrease owing to suction of fluid. This trend reversed for blowing of fluid. In addition this trend is higher for species of larger Schmidt number as well as for increasing buoyancy force.     

Effect of spatially varying acceleration on the combined heat and mass transfer in free convection along a plate

An analysis is performed to study the combined heat and mass transfer characteristics in free convection along a plate under the influence of spatially varying acceleration. The plate is maintained at a uniform temperature and/or a uniform concentration. The governing nonsimilar coupled boundary layer equations are solved by the local nonsimilarity approach. Numerical results of the local Nusselt number, the local Sherwood number and the local wall shear stress are presented for the diffusion of common gases and vapors into air for the linear variation of the gravity force along the plate. Analysis covers the range both when the concentration buoyancy force assists as well as mildly opposes the thermal buoyancy force.     

Coupled heat and mass transfer in mixed convection over a wedge with variable wall temperature and concentration in porous media: The entire regime

A boundary layer analysis is used to investigate both heat and mass transfer characteristics of mixed convection about a wedge in saturated porous media under the coupled effects of thermal and mass diffusion. The surface of the wedge is maintained at a variable wall temperature (VWT) and variable wall concentration (VWC). The nonsimilar governing equations are obtained by using a suitable transformation and solved by Keller box method. Numerical results are presented for the local Nusselt number and the local Sherwood number. Increasing the buoyancy ratio N, the exponent of wall temperature/concentration n and the wedge angle parameter λ increases the local Nusselt number and the local Sherwood number. As mixed convection parameter χ varies from 0 to 1, the local Nusselt number and the local Sherwood number decrease initially, reach a minimum in the intermediate value of χ and then increase gradually. It is apparent that the Lewis number has a pronounced effect on the local Sherwood number than it does on the local Nusselt number. Furthermore, increasing the Lewis number decreases (increases) the local heat (mass) transfer rate.     

Three-Dimensional Mixed Convection Heat and Mass Transfer in a Rectangular Duct: Case of Longitudinal Rolls

This article presents numerical study of 3-D thermosolutale mixed convection (TSMC) in horizontal rectangular channels. The contribution of this work is to characterize the travelling wave's appearance and to generalize the behavior of Poiseuille-Rayleigh-Benard (PRB) systems for a broad range of dimensionless parameters, which control the double diffusive mixed convection. The numerical results consist of analyzing the flow regimes of the steady longitudinal thermoconvectives rolls for the case of purely thermal mixed convection (TMC) and for both thermal and mass transfer (TSMC). The transition from opposed volume forces to cooperating ones at fixed Rayleigh (Ra), Reynolds (Re), and Lewis (Le) numbers, considerably affects the birth and the development of the longitudinal rolls (noted R_//). The heat and mass transfers distribution, presented by the average Nusselt and Sherwood numbers, are also examined.     

A Single-Component Nonhomogeneous Lattice Boltzmann Model for Natural Convection in Al2O3/Water Nanofluid

Natural convection heat transfer in Al₂O₃/water nanofluid is analyzed using the single-component nonhomogeneous lattice Boltzmann method (SCNHLBM). There exists a contradictory observation between the numerical and experimental works in the literature with respect to the heat transfer of nanofluids in natural convection. Nanofluid is treated as a single component with nonhomogeneous particle distribution introduced by a concentration transport equation of nanoparticles by considering the Brownian and thermophoretic diffusions. The average Nusselt number is found to deteriorate with increasing nanoparticle volume fraction; thus the trend of the experimental results is captured using SCNHLBM. Addition of Brownian and thermophoretic diffusion results in additional thermal diffusion and hence reduces the convective transport of heat. The contribution of Brownian and thermophoretic diffusions in heat transfer deterioration is revealed.     

Convection heat and mass transfer in a hydromagnetic flow of a second grade fluid in the presence of thermal radiation and thermal diffusion

The convection heat and mass transfer in a hydromagnetic flow of a second grade fluid past a semi-infinite stretching sheet in the presence of thermal radiation and thermal diffusion are considered. The governing coupled non-linear partial differential equations describing the flow problem are transformed into non-linear ordinary differential equations by method of similarity transformation. The resulting similarity equations are solved numerically using Runge-Kutta shooting method. The results are presented as velocity, temperature and concentration fields for different values of parameters entering into the problem. The skin friction, rate of heat transfer and mass transfer are presented numerically in tabular form. In addition, the results obtained showed that these parameters have significant influence on the flow, heat and mass transfer.     

Simultaneous mass and heat transfer under mixed convection along a vertical cone

Steady laminar binary mixed convection flow along a vertical circular cone under the combined buoyancy effects of thermal and species diffusion is studied analytically. The analysis is confined to mass diffusion processes with low concentration levels. In the analysis the surface of the cone is assumed to be at a uniform temperature and uniform concentration. Numerical results for the local Sherwood number, local Nusselt number and local friction factor are presented. Representative temperature, concentration and velocity profiles are also shown. The analysis covers the diffusion of common gases and vapours into air. Considerations are given to the situations where the buoyancy forces assist and oppose the forced convection flow for various possible combinations of the thermal and species diffusion processes.