Three-dimensional non-isothermal model development of high temperature PEM Fuel Cells

A three-dimensional non-isothermal mathematical model is developed in a triple mixed serpentine flow multichannel domain for a high temperature PEM Fuel Cell having a phosphoric acid doped PBI membrane as electrolyte and an active area of 25 cm² within Comsol Multiphysics. The inlet temperatures of cathode and anode reactants are taken as 438 K. Model predicts pressure, and temperature distribution along the channels and membrane current density distribution over the membrane electrodes. The model results are obtained at two different operation voltages, 0.45 V and 0.60 V. Resulting average current densities are respectively 0.313 A cm^?2 and 0.224 A cm^?2. The non-isothermal model results are compared to isothermal model results from a previous study and various other single channel non-isothermal model results available in the literature. The pressure drop at cathode compartment is predicted to be 6500 Pa, whereas it is found to be 6400 Pa for the isothermal model. The temperature difference within the system is found to be 0.18 K for the operation voltage of 0.6 V, whereas this value increases to 0.31 K for the operation voltage of 0.45 V. The temperature difference isocontours are illustrated for the whole cell. Considering changes in temperature, one can employ isothermal operation assumption for this system as an approximation and simplification for the governing equations, since the variation in the temperature within the cell is less than 1 K. It should be emphasized that multichannel model predictions are more realistic compared to single channel models. The model developed here can be extended to larger electrode active area and different multichannel configurations.     

Effect of viscous dissipation and pressure stress work in natural convection along a vertical isothermal plate. New results

The steady laminar boundary layer flow along a vertical stationary isothermal plate is studied taking into account the viscous dissipation and pressure stress work of the fluid. The results are obtained with the direct numerical solution of the boundary layer equations without any approximation. It was found that the variation of wall heat transfer and wall shear stress along the plate is quite different compared to that given by the approximate perturbation method.     

Entropy generation in a porous channel with hydromagnetic effect

An analytical work has been performed to study the First and Second Laws (of thermodynamics) characteristics of flow and heat transfer inside a vertical channel made of two parallel plates embedded in a porous medium and under the action of transverse magnetic field. Combined free and forced convection inside the channel is considered. Flow is assumed to be steady, laminar, fully developed of electrically conducting and heat-generating/absorbing fluid. Both vertical walls are kept isothermal at the same or different temperatures. Governing equations in Cartesian coordinate are simplified and solved analytically to develop expressions for velocity and temperature, entropy generation number and irreversibility distribution ratio. Velocity, temperature and entropy generation profiles are presented graphically.     

Analyses of heat and water transport interactions in a proton exchange membrane fuel cell

A two-phase non-isothermal model is developed to explore the interaction between heat and water transport phenomena in a PEM fuel cell. The numerical model is a two-dimensional simulation of the two-phase flow using multiphase mixture formulation in a single-domain approach. For this purpose, a comparison between non-isothermal and isothermal fuel cell models for inlet oxidant streams at different humidity levels is made. Numerical results reveal that the temperature distribution would affect the water transport through liquid saturation amount generated and its location, where at the voltage of 0.55 V, the maximum temperature difference is 3.7 °C. At low relative humidity of cathode, the average liquid saturation is higher and the liquid free space is smaller for the isothermal compared with the non-isothermal model. When the inlet cathode is fully humidified, the phase change will appear at the full face of cathode GDL layer, whereas the maximum liquid saturation is higher for the isothermal model. Also, heat release due to condensation of water vapor and vapor-phase diffusion which provide a mechanism for heat removal from the cell, affect the temperature distribution. Instead in the two-phase zone, water transport via vapor-phase diffusion due to the temperature gradient. The results are in good agreement with the previous theoretical works done, and validated by the available experimental data.     

Wave Instability of Mixed Convection Flow Along a Vertical Flat Plate

Abstract

An analysis is performed to investigate the linear wave instability of laminar mixed convection flow over an isothermal vertical flat plate, in which the buoyancy force arises solely from the temperature gradients in the fluid. In the stability analysis, the main flow and thermal fields are treated as nonparallel, and are obtained by the local nonsimilarity solution method The eigenvalue problem consisting of the linearized system of coupled differential equations for the velocity and temperature disturbances are solved by a direct Runge-Kutta numerical integration scheme along with a filtering technique to remove the “parasitic errors” inherent in the numerical integration of the disturbance equations. Neutral stability curves and critical Reynolds numbers are presented for a range of buoyancy parameters covering both assisting and opposing flow situations for two representative Prandtl numbers of 0.7 and 7. It is found that the flow becomes more stable as the buoyancy force increases for assisting flow and less stable as the buoyancy force increases for opposing flow. The curve of Grashof number versus Reynolds number that separates the unstable flow region from the stable one is also presented.     

Analytical fuel cell modeling; non-isothermal fuel cells

The isothermal fuel cell model, given in an earlier publication, will be generalized to describe the behaviour of non-isothermal fuel cells of co-flow type. To this end the temperalure distribution inside a fuel cell in steady state is investigated analytically. A simplified relation between the local temperature and the fuel utilization is derived and its practical significance elucidated. Furthermore, it is shown that the solution of the non-isothermal model is accurately approximated by analytical expressions obtained from a so-called quasi-isothermal approach. This new approach yields a similar expression for the cell voltage as derived from the isothermal model. The quasi-isothermal approach is also used to make a clear comparison between the isothermal and the non-isothermal fuel cell model.     

Three-dimensional polymer melt flow in sudden expansions: Non-isothermal flow topology

Three-dimensional, non-isothermal, polymer melt flow in sudden expansion is numerically investigated. The main goal of the paper is to study the general features of the flow field. The generalized Newtonian formulation is adopted, and the mathematical model corresponds to the laminar, incompressible Navier–Stokes equations. A second order finite difference scheme is used to discretize the governing equations in a collocated mesh. The non-Newtonian flow behaviour is modelled by the Cross constitutive relation, in which temperature effects are accounted for. The simulations show that, despite the high viscosity exhibited by polymer melts, a complex three-dimensional flow structure is found close to the expansion section, characterized by a spiral motion. The results also indicate that viscous dissipation causes limited effect in temperature rise and viscosity variations. The latter was found mostly affected by the shear rate.     

Hydromagnetic plane and axisymmetric flow near a stagnation point with heat generation

The steady, laminar, forced convection flow of an electrically-conducting and heat-generating/absorbing fluid at the stagnation point of an isothermal two-dimensional porous body and an axisymmetric body in the presence of a uniform applied magnetic field has been studied. The governing equations are transformed into ordinary differential equations using similarity variables. The obtained results are solved numerically by an implicit finite-difference method. A parametric study of all the physical parameters involved in the problem has been performed and graphical results for the velocity and temperature profiles as well as the skin-friction coefficient and the wall heat transfer are presented and discussed.     

First law analysis for viscous dissipation in liquid flows in micro-channels

This paper focuses on temperature rise due to the viscous dissipation in liquids flowing through micro-channels. In the past, equations for the prediction of the temperature rise have been obtained as a function of the friction factor, Reynolds number and Eckert number or a similar form, starting from Navier–Stokes equation and energy equation under the assumption of fully developed laminar flow by researchers. The temperature rises calculated from the equations have been compared with experimental data and the equations have been validated. However, in this paper, a new equation for the prediction of the temperature rise is simply obtained from the first law of thermodynamics without restriction of fully developed laminar flow.     

Heat transfer due to double laminar slot jets impingement onto an isothermal wall within one side closed long duct

In this study, heat transfer due to double impinging vertical slot jets onto an isothermal wall was investigated numerically for laminar flow regime. Navier–Stokes and energy equations were discretized with a finite volume procedure on a non-staggered grid arrangement using SIMPLEM (SIMPLE-Modified) algorithm. The effect of the jet Reynolds number, the jet-isothermal bottom wall spacing, and the distance between two jets on heat transfer and flow field was examined. Air was chosen as the working fluid (Pr = 0.71). It is found that multi-cellular flow is formed in the impingement region due to interaction between two jets and entrainment effects in the duct. The mean Nusselt number increases almost linearly with increasing of Reynolds number at isothermal surface. When Reynolds number of the first jet is higher than second one the heat transfer is enhanced significantly.     

Predictions of concentration in the pyrolysis of biomass materials—I

The present work involves the prediction of the concentration profiles in the case of pyrolysis of different lignocellulosic materials in isothermal and non-isothermal conditions. The operative temperature range is from 573 to 973 K for isothermal conditions, and for non-isothermal conditions, the heating rate ranges from 5 to 80 K/min (5, 20, 40, 60 and 80 K/min).

The concentration for the above mentioned conditions is predicted for various biomass components, viz. cellulose, hemicellulose and lignin. Based on the concentration profiles of different biomass materials, it is possible to predict the pyrolysis behavior over a wide range of temperatures under isothermal and non-isothermal conditions for a large number of biomass materials, provided the activation energy and the frequency factor for the various reaction steps are known. It is also possible to ascertain the degree of combustibility of different biomass materials.

The simulation model utilizes a 4th order Runge-Kutta Predictor-Corrector method to solve the coupled ordinary differential equations. Based on thermogravimetric analysis done elsewhere, it is considered that temperature and time have a linear relationship. The above technique enables us to predict concentration profiles of different biomass materials for the entire range of pyrolysis. The concentration vs time data is plotted graphically for both isothermal and non-isothermal conditions utilizing the Harvard Graphics package on a PC-A/T personal computer.     

Fully developed natural convection in an isothermal vertical annular duct

The gevernine equation for fully developed laminar natural convection in a vertical annulus have been analytically solved for the isothermal wall boundary conditions. The resulting flow rates and Nusselt numbers are a function of a annulus gap and a non-dimensional temperature ration. These results are compared to those obtained from a finite-difference solution of the developing flow. It is concluded that fullt developed conditions may be assumed for Grashof numbers smaller than 10.     

Mixed convection boundary layer flow past an isothermal horizontal circular cylinder with temperature-dependent viscosity

The problem of steady laminar mixed convection boundary layer flow past an isothermal horizontal circular cylinder placed in a viscous and incompressible fluid of temperature-dependent viscosity is theoretically considered in this paper. The partial differential equations governing the flow and heat transfer are shown to be non-similar. Full numerical solutions of these governing equations are obtained using an implicit finite-difference scheme known as the Keller-box method. The solutions are obtained for various values of the Prandtl number Pr, the mixed convection parameter λ and the viscosity/temperature parameter θ_r. The obtained results show that the flow and heat transfer characteristics are significantly influenced by these parameters.     

Stokes flow and heat transfer past a circular cylinder in a square cavity with suction/injection on sidewalls

The laminar viscous fluid flow past a circular cylinder placed in a square cavity of a uniform cross‐section is generated by applying injection/suction at the adjacent sidewalls. The temperature on the side walls without suction and on the boundary of the cylinder is kept constant, and constant heat flux is maintained on the walls with suction. The streamline flow pattern and isothermal lines are drawn. The flow is assumed to be Stokesian. Hence, the resulting biharmonic equation is solved for stream function by expressing it in two coupled equations, and a 5‐point formula is used to solve these equations. Fictitious nodes are introduced for derivative boundary conditions for stream function by using a central difference scheme, and a 3‐point backward difference formula is used for derivative boundary conditions on temperature.     

Physical Effects of Variable Fluid Properties on Laminar Gas Microconvective Flow

The physical effects of variable fluid properties on heat transfer and frictional flow characteristics of laminar gas microconvective flow are investigated in this research. The fully developed flow through a microtube is studied numerically by using 2D continuum‐based governing equations. The physical effects induced due to variations in gas density with pressure and temperature, and gas viscosity, thermal conductivity, and specific heat with temperature are analyzed. Numerical results reveal that the heat transfer and frictional flow characteristics of laminar gas microflow are drastically affected by these physical effects. Hence, this research suggests that these physical effects need to be well considered in the applications of laminar gas microconvection based on large temperature gradients, for example, the design of microchannel heat sinks, and the flow cannot be generally considered as a constant property flow, as in conventional channels.     

Simulations of post-filling process considering the cooling effect of the mold cooling systems

Simulation of the post-filling process has been developed and performed to study the compressible polymer melt flow during the packing phase and the pressure development inside the mold cavity for the entire post-filling process. A mixed finite-element/finite-difference numerical scheme is implemented to solve the non-isothermal, compressible viscous flow equations. The transient, non-isothermal mold cavity surface temperatures which depend on the mold cooling channel arrangement and coolant flow conditions are also incorporated during simulation using hybrid finite-element/shape-factor method. It has been found that the difference in the pressure profile variation during the post-filling stage is quite distinguished for cases assuming constant mold wall temperature and cases with the consideration of the cooling effect of the cooling system configuration.     

Numerical investigation of non-isothermal phase change phenomena in vertical Bridgman crystal growth

The non-isothermal phase change phenomena during the vertical Bridgman growth process for HgCdTe are numerically investigated using an interface capturing finite element scheme. The influence of the growth parameters such as Bi, Ste, U and the flow parameters including Gr_T and Gr_S on the non-isothermal phase change phenomena are obtained. Some new features about the melt/crystal interface shape, the temperature field near the interface and the flow field are revealed by comparing the non-isothermal phase change with the isothermal phase change. Furthermore, the comparison of the non-isothermal interfacial characteristics between the pure diffusion, the natural convection and the double-diffusive convection is made and the obvious differences are presented.     

Mixed free and forced convection in the incompressible boundary layer along a rotating vertical cylinder with fluid injection

We examine the steady incompressible laminar boundary layer flow along a vertical cylinder with isothermal walls. The mixed free and forced convection regime is studied while injection/suction of fluid can take place through the cylinder surface. The two-dimensional boundary layer equations are solved using an efficient finite difference scheme, and velocity and temperature profiles, as well as skin friction, heat transfer and pressure coefficients, are calculated. It is proved that fluid injection can considerably reduce the skin friction and heat transfer at the wall. Also, significant differences are reported when the present results are compared with published results for the zero mass transfer case.     

Friction factors in smooth trapezoidal silicon microchannels with different aspect ratios

An experiment has been conducted to measure the friction factor of laminar flow of deionized water in smooth silicon microchannels of trapezoidal cross-section with hydraulic diameters in the range of 25.9-291.0 μm. It is shown that the friction constant of these microchannels is greatly influenced by the cross-sectional aspect ratio, W_b/W_t. Based on the 334 data points, a correlation equation for the friction constant of a fully developed laminar flow of water in these microchannels is obtained in terms of the cross-sectional aspect ratio. The experimental data is found to be in good agreement with an existing analytical solution for an incompressible, fully developed, laminar flow under no-slip boundary condition. It is confirmed that the Navier-Stokes equations are still valid for the laminar flow of deionized water in smooth silicon microchannels having hydraulic diameter as small as 25.9 μm. For smooth channels with larger hydraulic diameters of 103.4-291.0 μm, transition from laminar to turbulent flow is found at Re=1500-2000.     

Interfacial heat transfer coefficient for non-equilibrium convective transport in porous media

The literature has documented proposals for macroscopic energy equation modeling for porous media considering the local thermal equilibrium hypothesis and laminar flow. In addition, two-energy equation models have been proposed for conduction and laminar convection in packed beds. With the aim of contributing to new developments, this work treats turbulent heat transport modeling in porous media under the local thermal non-equilibrium assumption. Macroscopic time-average equations for continuity, momentum and energy are presented based on the recently established double decomposition concept (spatial deviations and temporal fluctuations of flow properties). Interfacial heat transfer coefficients are numerically determined for an infinite medium over which the fully developed flow condition prevails. The numerical technique employed for discretizing the governing equations is the control volume method. Preliminary laminar flow results for the macroscopic heat transfer coefficient, between the fluid and solid phase in a periodic cell, are presented.