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The purpose of this paper is to introduce a robust mathematical model and finite element‐based numerical approach to solve solid oxide fuel cell (SOFC) problems.

A robust mathematical model is constructed by studying pros and cons of different SOFC and other fuel cell models. The finite element‐based numerical approach presented is a unified approach to solve multi‐disciplinary aspects arising from SOFC problems. The characteristic‐based split approach employed here is an efficient way of solving various flow, heat and mass transfer regimes in SOFCs.

The results presented show that both the model and numerical algorithm proposed are robust. Furthermore, the approaches proposed are general and can be easily extended to other similar problems of practical interest.

The model proposed is the first of this kind and the unified approach for solving flow, heat and mass transfer within a fuel cell is also novel.

Analytical methods are widely used in heat and fluid flow; the purpose of this paper is to couple Taylor series method and Bubbfil algorithm to solve nonlinear differential equations.

A series solution is obtained with some unknown constants, which can be determined by incorporating boundary conditions, and the constants are calculated by the Bubbfil algorithm.

This paper gives an analytical approach to a nonlinear equation arising in porous catalyst using Taylor series and Bubbfil algorithm, and a high accuracy can be achieved.

The coupled method of Taylor series and Bubbfil algorithm is a powerful method for nonlinear differential equations.

The proposed technology can be used in various numerical methods.

A new analytical method is proposed based on Taylor series and Bubbfil algorithm, which is a development of Newton’s iteration method and an ancient Chinese algorithm. The solution process is simple and easy to follow.

The purpose of this work is the study of the steady free convection in a square differentially heated cavity filled by a Brinkman bidisperse porous medium. An appropriate mathematical model considering the Brinkman, momentum and energy interphase terms is proposed. The dependence of the stream functions, isotherms and of the Nusselt numbers on the governing parameters is analysed.

The both phases of flow and heat transfer are solved numerically using a modified finite difference technique. The algebraic system obtained after discretization is solved using the SOR method. The results are found to be in a significant agreement with the ones presented by the literature for a Darcy bidisperse porous medium and a Brinkman monodisperse porous medium.

The effects of the governing parameters on stream functions, isotherms and Nusselt numbers are discussed. It has been found that in the case of the Brinkman bidisperse model, the Nusselt numbers decrease compared to the Darcy model, and this behaviour is significant in comparison to the Brinkman monodisperse case.

A mathematical model for the free convection inside a cavity filled by a non-Darcy bidisperse porous medium, based on the Brinkman equation, is used. The effect of Darcy number, Rayleigh number, modified inter-phase heat transfer parameter, modified thermal conductivity ratio and the inertial parameters is studied. To the best of the authors’ knowledge, this problem has not been studied before, and the results are new and original.

The purpose of this study is to indicate the effect of mounting heat generating porous matrix in a close cavity on the Brownian term of CuO-water nanofluid and its impact on improving the Nusselt number.

Because of the presence of heat source in porous matrix, couple of energy equations is solved for porous matrix and nanofluid separately. Thermal conductivity and viscosity of nanofluid were assumed to be consisting of a static component and a Brownian component that were functions of volume fraction of the nanofluid and temperature. To explain the effect of the Brownian term on the flow and heat fields, different parameters such as heat conduction ratio, interstitial heat transfer coefficient, Rayleigh number, concentration of nanoparticles and porous material porosity were investigated and compared to those of the non-Brownian solution.

The Brownian term caused the cooling of porous matrix because of rising thermal conductivity. Mounting the porous material into cavity changes the temperature distribution and increases Brownian term effect and heat transfer functionality of the nanofluid. Besides, the effect of the Brownian term was seen to be greatest at low Rayleigh number, low-porosity and small thermal conductivity of the porous matrix. It is noteworthy that because of decrement of thermal conduction in high porosities, the impact of Brownian term drops severely making it possible to obtain reliable results even in the case of neglecting Brownian term in these porosities.

The effect of mounting the porous matrix with internal heat generation was investigated on the improvement of variable properties of nanofluid.

This paper aims to present a three‐dimensional computational fluid dynamics (CFD) model that simulates the fluid flow, species transport and electric current flow in PEM fuel cells.

The model makes use of a general‐purpose CFD software as a basic tool incorporating fuel cell specific submodels for multi‐component species transport, electrochemical kinetics, water management and electric phase potential analysis in order to simulate various processes that occur in a PEM fuel cell.

Three dimensional results for the flow field, species transport, including waster formations, and electric current distributions are presented for two test flow configurations in the PEM fuel cell. For the two cases presented, reasonable predictions have been obtained, and this provides an insight into the effect of the flow designs to the operation of the fuel cell.

It is appreciated that the CFD modeling of fuel cells is, in general, still facing significant challenges due to the limited understanding of the complex physical and chemical processes existing within the fuel cell. The model is now under further development to improve its capabilities and undergoing further validations.

The model simulations can provide detailed information on some of the key fluid dynamics, physical and chemical/electro‐chemical processes that exist in fuel cells which are crucial for fuel cell design and optimization.

The model can be used to understand the operation of the fuel cell and provide and alternative to experimental investigations in order to improve the performance of the fuel cell.

The purpose of this paper is to present the research activity and results to research and development society on the field of ceramic microsystems.

The chemical reactor was developed as a non-conventional application of low temperature co-fired ceramic (LTCC) and thick-film technologies. In the ceramic reactor with a large-volume, buried cavity, filled with a catalyst, the reaction between water and methanol produces hydrogen and carbon dioxide (together with traces of carbon monoxide). The LTCC ceramic three-dimensional (3D) structure consists of a reaction chamber, two inlet channels, an inlet mixing channel, an inlet distributor, an outlet collector and an outlet channel. The inlet and outlet fluidic barriers for the catalyst of the reaction chamber are made with two “grid lines”.

A 3D ceramic structure made by LTCC technology was successfully designed and developed for chemical reactor – methanol decomposition.

Research activity includes the design and the capability of materials and technology (LTCC) to fabricate chemical reactor with large cavity. But further dimensions-scale-up is limited.

The technology for the fabrication of LTCC-based chemical reactor was developed and implemented in system for methanol decomposition.

The approach (large-volume cavity in ceramic structure), which has been developed, can be used for other type of reactors also.

The purpose of this paper is to use the variational iteration method (VIM) for studying boundary value problems (BVPs) characterized with dual solutions.

The VIM proved to be practical for solving linear and nonlinear problems arising in scientific and engineering applications. In this work, the aim is to use the VIM for a reliable treatment of nonlinear boundary value problems characterized with dual solutions.

The VIM is shown to solve nonlinear BVPs, either linear or nonlinear. It is shown that the VIM solves these models without requiring restrictive assumptions and in a straightforward manner. The conclusions are justified by investigating many scientific models.

The VIM provides convergent series solutions for linear and nonlinear equations in the same manner.

The VIM is practical and shows more power compared to existing techniques.

The VIM handles linear and nonlinear models in the same manner.

This work highlights a reliable technique for solving nonlinear BVPs that possess dual solutions. This paper has shown the power of the VIM for handling BVPs.

The purpose of this paper is to use the Adomian decomposition method (ADM) for solving boundary value problems with dual solutions.

The ADM has been previously demonstrated to be eminently practical with widespread applicability to frontier problems arising in scientific applications. In this work, the authors seek to determine the relative merits of the ADM in the context of several important nonlinear boundary value models characterized by the existence of dual solutions.

The ADM is shown to readily solve specific nonlinear BVPs possessing more than one solution. The decomposition series solution of these models requires the calculation of the Adomian polynomials appropriate to the particular system nonlinearity. The authors show that the ADM solves these models for any analytic nonlinearity in a practical and straightforward manner. The conclusions are supported by several numerical examples arising in various scientific applications which admit dual solutions.

This paper presents an accurate work for solving nonlinear BVPs that possess dual solutions. The authors have demonstrated the widespread applicability of the ADM for solving various forms of these nonlinear equations.

Nanotechnology promises to be the defining science of the 21st century. With its integration of the organic and inorganic worlds, it represents more than simply a continuation of the principles of microtechnology. Because of this it requires new structures of R&D management, and new communication processes. A number of recent foresight studies identify potential future applications for European industry and point to the strengths and weaknesses of Member States. But only new interdisciplinary research networks will enable Europe to harness the power of nanotechnology – or prepare its citizens for the benefits.