Mathematical modelling of non-isothermal silica transport and deposition in a porous medium

The problem of transport and deposition of silica in non-isothermal flows, either in a porous medium or a single fracture, is investigated. Analytic solutions are obtained using the method of characteristics for both the one-dimensional problem of constant rate injection into a channel or packed column and the radially symmetric problem of the flow away from a reinjection well. Silica deposition is represented by a first order rate equation. Studies on the temperature effects of reinjection into a hot or cold reservoir are undertaken using the one-dimensional model. The strong dependence of the rate of silica deposition on temperature is confirmed by the model. The radial flow model is applied to some field data from the Otake geothermal field, Japan. The model produces a good match to the permeability decline observed in the wells. Mathematical models of silica deposition resulting from non-isothermal flow in a single fracture are successfully tested against some previously reported numerical results.     

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.     

Free convection in a non-Newtonian fluid along a horizontal plate embedded in porous media with internal heat generation

Similarity solutions for the problem of free convection flow over a non-isothermal horizontal plate embedded in porous media are investigated in the presence of internal heat generation. The porous medium is saturated with non-Newtonian power law fluid. Numerical results are obtained for the effect of power law temperature profile and fluid index on the heat transfer characteristics.     

Flow and heat transfer in a moving fluid over a moving non-isothermal surface

Heat transfer characteristics for a boundary layer forced convective flow past a moving parallel flat non-isothermal surface in the presence of heat source/sink are obtained. The cases of surface temperature varying directly or inversely with power-law exponent are considered. The similarity solutions are obtained. The numerical results are validated by comparing them with the available results in the literature for some special cases. It is found that dual solutions exist when the surface and the fluid move in the opposite directions. Furthermore, exact and analytical solutions are provided for some parametric regimes.     

Numerical investigation of transport phenomena in high temperature proton exchange membrane fuel cells with different flow field designs

In this work, a three-dimensional, non-isothermal, steady-state model for high temperature proton exchange membrane fuel cells with phosphoric acid polybenzimidazole membrane has been developed using computational fluid dynamics. The importance of the gas flow field design on the transport characteristics and cell performance is revealed by solving the mass, momentum, species, energy, and charge conservation equations. The numerical results show that the best cell performance is provided by the fuel cell with serpentine flow channel flow field. However, the pressure drop is also very high due to the large length of the serpentine channel. In addition, the velocity, oxygen mass fraction, and temperature distributions are unevenly distributed over the entire active area of the fuel cell having straight channels with small manifolds, especially at low cell voltages when a large amount of oxygen is required. The cell performance and durability can be significantly affected by the uniformity of the reactants within the fuel cell. It is suggested that the flow field configurations must be optimized to obtain uniform distributions of the reactants, maximize the cell performance, and minimize the pressure drop penalty. The present results provide detailed information about transport characteristics within fuel cells and give guidelines for design and manufacturing of current collectors.     

Creeping flow of a polymeric liquid passing over a transverse slot with viscous dissipation

Numerical simulations for the non-isothermal flow of a nylon-6 fluid passing over a transverse slot with heat dissipation are considered with a differential-type non-isothermal White-Metzner model describing the non-Newtonian behavior of the melt. The results obtained in the study are computed by using the elastic-viscous split-stress finite element method incorporating the non-consistent streamline-upwind scheme. As a verification of the numerical scheme, the algorithm is first applied to compute the corresponding isothermal flow of the upper-convected Maxwell fluid, a special case of the melt, characterized by constant viscosity and relaxation time. Hole pressure was evaluated for various Deborah numbers (De), and compared with that derived from the Higashitani-Pritchard (HP) theory. The agreement between the two is found to be satisfactory for creeping flow in the De range for which the HP theory is valid. Subsequently, hole pressure and other flow characteristics were predicted. Furthermore, the effects of heat-transfer, shear-thinning, and slot geometry on hole pressure were also investigated.     

Three-dimensional model for stacks of tubular high temperature proton exchange membrane fuel cells incorporating a thin layer approach for the membrane electrode assembly

A three-dimensional, non-isothermal, steady state model for stacks of tubular high temperature proton exchange membrane fuel cells (HT PEM FCs) is developed. It is based on a thin layer approach for the membrane-electrode assembly while retaining Butler-Volmer kinetics, concentration and Ohmic losses on both electrodes. It solves for flow, temperature and concentration fields as well as locally resolved current densities for multiple cells. Single cell results for the polarization curve compare well with experimental data for single tubular HT PEM FCs. The model allows for efficient simulations of stacks of multiple tubular HT PEM FCs with a shared air channel in which the interactions between local FC performance and flow, temperature and concentration fields pose a major design challenge. The effects of flow field design, flow rate and cell distance in a stack of 7 tubular cells are investigated and basic approaches for the design of such stacks are derived.     

Effect of flow field design on the performance of elevated-temperature polymer electrolyte fuel cells

In our previous work, operation of polymer electrolyte fuel cell (PEFC) at 95°C was investigated in detail and it was found that dry operation of PEFC at elevated temperatures makes the parallel flow field design a viable design option for high temperature applications such as for automobiles. In this work, a three-dimensional, non-isothermal PEFC model is used to compare the performance of a 25 cm² fuel cell with serpentine and parallel flow field design operated at 95°C under various inlet humidity conditions. Numerical results show that the parallel flow field provides better and more uniformly distributed performance over the whole active area which makes the parallel flow field a better design compared to the serpentine flow field for PEFCs operated at elevated temperature and low inlet relative humidity. Copyright © 2006 John Wiley & Sons, Ltd.     

Non-isothermal dynamic modelling and optimization of a direct methanol fuel cell

A non-isothermal dynamic optimization model of direct methanol fuel cells (DMFCs) is developed to predict their performance with an effective optimum-operating strategy. After investigating the sensitivities of the transient behaviour (the outlet temperature, crossovers of methanol and water, and cell voltage) to operating conditions (the inlet flow rates into anode and cathode compartments, and feed concentration) through dynamic simulations, we find that anode feed concentration has a significantly larger impact on methanol crossover, temperature, and cell voltage than the anode and cathode flow rates. Also, optimum transient conditions to satisfy the desired fuel efficiency are obtained by dynamic optimization. In the developed model, the significant influence of temperature on DMFC behaviour is described in detail with successful estimation of its model parameters.     

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.     

Combination of the fictitious domain method and the sharp interface method for direct numerical simulation of particulate flows with heat transfer

In this paper, the fictitious domain (FD) method and the sharp interface (SI) method are combined for the direct numerical simulations of particulate flows with heat transfer in three dimensions. The flow field and the motion of particles are solved with the FD method. The temperature field is solved in both fluid and solid media with the SI method. The accuracy of the proposed FD/SI method is validated via two problems: the natural convection in a two- dimensional cavity with fixed solid particles, and the flow over a cold sphere. The method is then applied to the natural convection in a three dimensional cavity with a fixed sphere, the motion of a spherical particle in a non-isothermal fluid, and the rising of spherical catalyst particles in an enclosure. The effects of the thermal conductivity ratio are examined in the first and third problems, respectively, and the significant effects of the thermal expansion coefficient ratio on the particle motion are demonstrated in the second problem.     

Non-isothermal flow of a polymeric fluid past a submerged circular cylinder

In this paper, non-isothermal flow of a polymeric liquid past a circular cylinder in an infinite domain is investigated numerically. A non-Newtonian fluid, known as a differential-type White-Metzner model, is used in the flow simulation. The computer code developed is based on the elastic-viscous split-stress finite element method incorporating the streamline-upwind Petrov-Galerkin scheme. Numerical solutions for several cases are obtained. Global flow characteristics, such as drag coefficient and heat transfer coefficient, are derived. The effects of fluid elasticity, inertia, and shear-thinning on drag and heat transfer are also investigated.     

A droplet size dependent multiphase mixture model for two phase flow in PEMFCs

A droplet size dependent multiphase mixture model is developed in this paper, and the droplet size in the gas channel can be considered as a parameter in this multiphase mixture model, which includes the effect of gas diffusion layer (GDL) properties and the gas drag function and cannot be considered in the commonly used multiphase mixture model in the references. The three-dimensional two phase and non-isothermal simulation of the PEMFCs with a straight flow field is performed. The effect of droplet size on the liquid remove, the effect of liquid water on the heat transfer and the effect of gas flow pattern on the heat and mass transfer are mainly investigated. The simulation results show that the large droplet is hard to be dragged by the gas, so it produces large water saturation. The results of the heat transfer show that the liquid water hinders the heat transfer in the GDL and catalyst layer, so it produces the large relative high temperature area, and there are large temperature difference and water saturation in the PEMFCs operated with coflow pattern compared with counter flow pattern.     

Calibration of low-pressure MEMS gas sensor for detection of hydrogen gas

Detection of hydrogen by sensors are significant for improvement and safe usage of hydrogen gas as an energy source. In this paper, the application of the MEMS gas sensor for detection of hydrogen gas is numerically studied to develop the application of this device in different industrial applications. The flow feature and force generation mechanism inside a rectangular enclosure with heat and cold arms as the non-isothermal walls are inclusively discussed. In this study, the pressure of hydrogen is varied from 62 to 1500 pa correspond to Knudsen number from 0.1 to 4.5 to investigate all characteristics of the thermal-driven force inside the MEMS sensor. In order to simulate a rarefied gas inside the micro gas detector, Boltzmann equations are applied to obtain high precision results. To solve these equations, Direct Simulation Monte Carlo (DSMC) approach is used as a robust method for the non-equilibrium flow field. The effects of length, thickness and temperature of arms are comprehensively investigated in different ambient pressures. In addition, the effect of various hydrogen concentrations on the Knudsen force is studied. Our findings show that maximum Knudsen force occurs at P = 387 pressure and intensifies when the length of the arms is increased from 50 μm to 150 μm. In addition, the obtained results demonstrate that the generated force is highly sensitive to hydrogen gas species and this enables device for detection of hydrogen gas.     

Heat transfer in a viscoelastic boundary layer flow over a stretching sheet

Studies are made on the viscoelastic fluid flow and heat transfer characteristics over a stretching sheet with frictional heating and internal heat generation or absorption. The heat transfer analysis has been carried out for the cases of prescribed surface temperature (PST) and prescribed surface heat flux (PHF). The momentum equation is decoupled from the energy equation for the present incompressible boundary layer flow problem with constant physical parameters. Exact solution for the velocity field and the skin-friction are obtained. Also, the solutions for the temperature and heat transfer characteristics are obtained in terms of Kummer’s function. The work due to deformation in energy equation, which is essential while formulating the viscoelastic boundary layer flow problems, is considered. This paper examines the effect of viscoelastic parameter, Eckert number, Prandtl number and non-uniform heat source/sink parameter on temperature distribution, wall temperature gradient for PST-case and wall temperature for PHF-case.     

Heat transfer in a turbulent particle-laden channel flow

The objective of this paper is twofold: (i) to present and analyze particle temperature statistics in turbulent non-isothermal fully-developed turbulent gas–solid channel flow for a large range of particle inertia in order to better understand particle heat transfer mechanisms; (ii) to examine the performance of a recent Probability Density Function (PDF) model provided by Zaichik et al. (2011) [1]. In order to achieve such objectives, a Direct Numerical Simulation (DNS) coupled with a Lagrangian Particle Tracking (LPT) was used to collect fluid and particle temperature statistics after particles reach a statistically stationary regime. A non-monotonic behavior of particle temperature statistics is observed as inertia increases. The competition between different mechanisms (filtering inertia effect, preferential concentration, production of fluctuating quantities induced by the presence of the mean velocity and/or mean temperature gradients) are responsible for such a behavior. This competition is investigated from the exact transport equations of particle temperature statistical moments, fluid statistics conditionally-averaged at particle location, and instantaneous particle distribution in the flow field. Using these data, the accuracy of a PDF model is also assessed in the second part. From this assessment, it is seen that, despite the assumptions made, the model leads to a satisfactory prediction of most of the particle temperature statistics for not too high particle inertia.     

质子交换膜燃料电池内部传热传质三维模拟

针对常规流场质子交换膜燃料电池提出了三维非等温数学模型。模型考虑了电化学反应动力学以及反应气体在流道和多孔介质内的流动和传递过程,详细研究了水在质子膜内的电渗和扩散作用。计算结果表明,反应气体传质的限制和质子膜内的水含量直接决定了电极局部电流密度的分布和电池输出性能;在电流密度大于0.3~0.4A/cm2时开始出现水从阳极到阴极侧的净迁移;高电流密度时膜厚度方向存在很大的温度梯度,这对膜内传递过程有较大影响。     

Modeling of high temperature proton exchange membrane fuel cells with novel sulfonated polybenzimidazole membranes

In this study, a three-dimensional, steady-state, non-isothermal numerical model of high temperature proton exchange membrane fuel cells (HT-PEMFCs) operating with novel sulfonated polybenzimidazole (SPBI) membranes is developed. The proton conductivity of the phosphoric acid doped SPBI membranes with different degrees of sulfonation is correlated based on experimental data. The predicted conductivity of SPBI membranes and cell performance agree reasonably with published experimental data. It is shown that a better cell performance is obtained for the SPBI membrane with a higher level of phosphoric acid doping. Higher operating temperature or pressure is also beneficial for the cell performance. Electrochemical reaction rates under the ribs of the bipolar plates are larger than the values under the flow channels, indicating the importance and dominance of the charge transport over the mass transport.     

Numerical Research on the Influence of Deborah Number on Flow and Heat Transfer of Maxwell Fluid in a Tube with Laminar Pulsating Flow

The flow and heat transfer characteristics of Maxwell fluid in a pipe under pulsating pressure gradient were studied. The governing equations were made dimensionless. The Rubin boundary condition was adopted. The flow field was solved theoretically and the temperature field was obtained using finite volume method. A general model suitable for various fluctuating characteristics and physical parameters was established. The Deborah number(De) was used to characterize the fluidity of the fluid. The influence of De on flow and temperature fields was evaluated. The Nusselt number and start-up process of Maxwell fluid were studied. Results showed that the influence of De on flow field was greater than that on temperature field. The effect of De on Nusselt number was irregular and related to the oscillation parameters. The over-shooting amplitude and oscillation time of axis center velocity in start-up flow grow larger with De.     

Mass transfer performance of the LiCl solution dehumidification process

The driving force of the solution dehumidification process is investigated in this work, in which the parameters without the solute are used. The isothermal and non-isothermal equilibrium curves under some thermal conditions are calculated for the dehumidification process related to the LiCl solution as desiccant. Experiments based on the obtained equilibrium curves were performed for the structured packing tower with a height of 0.2 m and 0.3 m respectively. The temperature variation for the solution decreased with an increase in the solution flow rate and increased with an increasing airflow rate. But the temperature variation for the air did not display a marked trend. The average driving force and the overall mass transfer coefficients are calculated. The average driving force is investigated for different solution flow rates. The overall volumetric mass transfer coefficient increased with an increasing solution flow rate.