On the mass transport in membraneless flow batteries with flow-by configuration

Lisbôa, Kleber Marques; Cotta, Renato M.

doi:10.1016/j.ijheatmasstransfer.2018.02.002

Cited by 19 publications

(16 citation statements)

References 42 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The velocity is assumed to be composed of a base flow and an infinite number of vortices, as proposed in previous works (Lisboa and Cotta, 2018a, 2018b; Lisboa et al , 2018). This proposition automatically satisfies the continuity equation, allowing one to skip the analysis of the mass conservation principle.…”

Section: Formulation and Solution Methodologymentioning

confidence: 99%

“…Even though this three-dimensional formulation automatically satisfies the continuity equation and eliminates the pressure field, likewise the streamfunction-only formulation, it fails to condense all the information of the flow, upon integral transformation, into a single set of transformed ordinary differential equations. To overcome this difficulty, a vector eigenfunction expansion has been recently proposed for the integral transform solution of steady-state fluid flow problems (Lisboa and Cotta, 2018a, 2018b; Lisboa et al , 2018). In this novel approach, a physically inspired eigenfunction expansion was introduced, which is capable of recovering the streamfunction-only formulation for two-dimensional problems, albeit not limited to this situation.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Vector eigenfunction expansion in the integral transform solution of transient natural convection

Lisbôa

Cotta³

2019

HFF

Self Cite

View full text Add to dashboard Cite

Purpose The purpose of this work is to revisit the integral transform solution of transient natural convection in differentially heated cavities considering a novel vector eigenfunction expansion for handling the Navier-Stokes equations on the primitive variables formulation. Design/methodology/approach The proposed expansion base automatically satisfies the continuity equation and, upon integral transformation, eliminates the pressure field and reduces the momentum conservation equations to a single set of ordinary differential equations for the transformed time-variable potentials. The resulting eigenvalue problem for the velocity field expansion is readily solved by the integral transform method itself, while a traditional Sturm–Liouville base is chosen for expanding the temperature field. The coupled transformed initial value problem is numerically solved with a well-established solver based on a backward differentiation scheme. Findings A thorough convergence analysis is undertaken, in terms of truncation orders of the expansions for the vector eigenfunction and for the velocity and temperature fields. Finally, numerical results for selected quantities are critically compared to available benchmarks in both steady and transient states, and the overall physical behavior of the transient solution is examined for further verification. Originality/value A novel vector eigenfunction expansion is proposed for the integral transform solution of the Navier–Stokes equations in transient regime. The new physically inspired eigenvalue problem with the associated integmaral transformation fully shares the advantages of the previously obtained integral transform solutions based on the streamfunction-only formulation of the Navier–Stokes equations, while offering a direct and formal extension to three-dimensional flows.

show abstract

Section: Formulation and Solution Methodologymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Vector eigenfunction expansion in the integral transform solution of transient natural convection

Lisbôa

Cotta³

2019

HFF

Self Cite

View full text Add to dashboard Cite

show abstract

“…However, in the studies, it is found that the diffusion in the direction transverse to the flow creates a mixing region around the laminar interface where the solution contains both fuel and oxidant . This mixing region needs to be controlled carefully as mixed potential will be resulted if either reactant reaches its counterelectrode, which hinders the cell performance . Consequently, there is an inherent size limitation for MFC, which makes MFC suffer from small single cell output power.…”

Section: Introductionmentioning

confidence: 99%

Design of a radial vanadium redox microfluidic fuel cell: A new way to break the size limitation

Bei

Liu

et al. 2019

Int J Energy Res

View full text Add to dashboard Cite

Summary Microfluidic fuel cell (MFC) suffers from small single cell output power due to the inherent cell size limitation as microscale geometries are prerequisite to prevent reactant crossover between the anode and cathode. To meet the power demand of practical applications, previous works mainly focus on the creating of MFC stacks with multiple cells connected in series, parallel, or mixture of both series and parallel to increase the output power. Yet, low energy efficiency is observed because of the flow distribution nonuniformity and shunt current losses. In this work, a high performance radial vanadium redox MFC is presented to address the size limitation issue by adding a separate layer between the porous electrodes of the conventional plate‐frame MFC. Specific cell characteristics are detailed by mathematical modeling, and parametric studies are performed to evaluate the influences of the geometrical and operational parameters on the cell performance. The results show that this new radial MFC can provide a higher fuel utilization and meanwhile an improved cell performance under a fixed electrode size compared with the conventional plate‐frame MFC. Moreover, the electrode size limitation due to the reactant crossover between the anode and cathode is broken as the influences of the electrode size on the mixing region are greatly reduced. In the case with the electrode size equal to 18 mm × 18 mm, single cell output power of 0.35 mW with a fuel utilization of 53.33% is obtained under the reactant concentration of 2 mol L−1 and flow rate of 300 μL min−1.

show abstract

“…This particular emphasis is here chosen in light of recent progresses that are allowing for further generalization of this hybrid method. First, a single domain reformulation strategy has been successfully employed in a number of problems involving heterogeneous media and complex geometries [55][56][57][58][59], with recent extensions to the solution of fluid flow and heat or mass transfer within channels and cavities partially filled with a saturated porous medium [60][61][62][63]. Second, a novel interpretation of the eigenfunction expansion proposal in handling the Navier-Stokes equations [60], has unified the treatment of the two-and threedimensional primitive variables formulations into a vector eigenfunction expansion representing all velocity components with one set of transformed potentials and an appropriately chosen vector eigenfunction basis.…”

Section: Introductionmentioning

confidence: 99%

“…The agreement is shown to be perfect to the graph scale, hence demonstrating the capability of the method described in section 4 of dealing with flow problems in heterogeneous media. Further calculations can be performed, aiming at determining the current density under mass-transport-limited conditions, for which the reader is referred to[61].…”

mentioning

confidence: 99%

A review of hybrid integral transform solutions in fluid flow problems with heat or mass transfer and under Navier–Stokes equations formulation

Cotta

Lisbôa

Curi

et al. 2019

Numerical Heat Transfer, Part B: Fundamentals

View full text Add to dashboard Cite

The Generalized Integral Transform Technique (GITT) is reviewed as a hybrid numericalanalytical approach for fluid flow problems, with or without heat and mass transfer, here with emphasis on the literature related to flow problems formulated through the full Navier-Stokes equations. A brief overview of the integral transform methodology is first provided for a general nonlinear convection-diffusion problem. Then, different alternatives of eigenfunction expansion strategies are discussed in the integral transformation of problems for which the fluid flow model is either based on the primitive variables or the streamfunction-only formulations, as applied to both steady and transient states. Representative test cases are selected to illustrate the different eigenfunction expansion approaches, with convergence being analyzed for each situation. In addition, fully converged integral transform results are critically compared to previously reported simulations obtained from traditional purely discrete methods.

show abstract

On the mass transport in membraneless flow batteries with flow-by configuration

Cited by 19 publications

References 42 publications

Vector eigenfunction expansion in the integral transform solution of transient natural convection

Vector eigenfunction expansion in the integral transform solution of transient natural convection

Design of a radial vanadium redox microfluidic fuel cell: A new way to break the size limitation

A review of hybrid integral transform solutions in fluid flow problems with heat or mass transfer and under Navier–Stokes equations formulation

Contact Info

Product

Resources

About