Two-level defect-correction Oseen iterative stabilized finite element method for the stationary conduction–convection equations

In this paper, a two-level defect-correction Oseen iterative finite element method is presented for the stationary conduction–convection equations based on local Gauss integration. The method combines the defect-correction method, the two-level strategy, and the locally stabilized method. The stability and convergence of the proposed method are deduced. Finally, numerical examples verify the theoretical results of the proposed algorithm and show that it is highly efficient and reliable for the considered problem.     

Green’s function method hybrid with the finite element method for ballistic phonon transport at low temperatures in nanostructures of arbitrary shape

An atomistic Green’s function method hybrid with the finite element method (FEM) is presented to analyze the ballistic phonon transport in a device with arbitrary geometries. Discretized by the FEM, the continuous system is transformed into a lattice system. In this analogy, the nodes play the role of atoms, and the stiffness matrix stands for the interaction between atoms. The method can be used to calculate the phonon transmission between the terminals of device, and the local density of states in the device. The validity of the method is demonstrated by the one- and three-dimensional cases and a comparison with the transfer matrix method. The method also can be used to investigate elastic waves in the acoustic metamaterials and phononic crystals.     

Using bubble functions in the multi-scale finite element modeling of the convection–diffusion–reaction equation

The Convection–diffusion–reaction (CDR) equation shows multi-scale behaviour in cases where it represents convection or reaction dominated transport processes. Bubble function enriched finite elements are used to generate stable and accurate solutions for this equation. To validate the approach, the numerical results obtained for a benchmark problem are compared with their corresponding analytical solution for both exponential and propagation regimes.     

On the numerical solution of generalized convection heat transfer problems via the method of proper closure equations – part I: Description of the method

ABSTRACT

The purpose of this paper is to introduce a new physical-based computational approach for the solution of convection heat transfer problems on co-located non-orthogonal grids in the context of an element-based finite volume method. The approach has already been presented in the context of two-dimensional incompressible flow problems without heat transfer. It has been shown that the pressure–velocity coupling on co-located grids can be correctly modeled via the so-called method of proper closure equations (MPCE). Here, MPCE is extended to the numerical simulation of natural, forced, and mixed convection heat transfer problems. It is shown that the couplings between pressure, velocity, and temperature can be conveniently handled on co-located grids by resorting again to the modified forms of the governing equations, i.e., the proper closure equations. The set of discrete equations is solved in a fully coupled manner in this study. Here, in part I of the paper, only the basic methodology is described; in part II, the results of application of the method to some test problems are presented.     

On the numerical solution of generalized convection heat transfer problems via the method of proper closure equations – part II: Application to test problems

ABSTRACT

In part I of this paper, a new physical-based computational approach for the solution of convection heat transfer problems on co-located non-orthogonal grids in the context of an element-based finite volume method was discussed. The test problems are presented here, in part II of the paper. These problems include five steady two-dimensional convection heat transfer problems. In all test cases, the convergence history, the required under-relaxations for the iterative solution of the linearized equations, and the order of accuracy of the method are discussed and the streamlines as well as isotherms are presented. The computational results show that the proposed method is second order accurate and might occasionally need mild under-relaxation in relatively complex problems. Excellent match between the computational results and the corresponding reliable published results is observed.     

Nonlinear free vibration of spherical shell panel using higher order shear deformation theory – A finite element approach

A nonlinear finite element model for geometrically large amplitude free vibration analysis of doubly curved composite spherical shell panel is presented using higher order shear deformation theory (HSDT). The nonlinearity is introduced in the Green–Lagrange sense. The governing equations of the vibrated shell panel are derived using the Variational approach. Frequency ratios (nonlinear frequency to linear frequency) of the spherical panels are determined as a function of shell amplitude ratio. The results are computed for different orthotropicity ratios, stacking sequences, thickness ratios, amplitude ratios and boundary conditions and also compared with those available in literature.     

Simulation on the thermal cycle of a welding process by space–time convection–diffusion finite element analysis

Welding plays an important role in manufacturing. But difficulties still exist for simulation of the welding process of large welded structures, due to the limitation of computer capacity, mathematical models and software. This paper is devoted to developing an algorithm that tries to simulate the thermal cycle during welding efficiently and accurately. A space–time finite element method (FEM) is proposed to solve the transient convection–diffusion thermal equation. The method has been applied to the steady-state thermal analysis of welds. A moving coordinate frame (Eulerian frame), in which the heat source is stationary, is used to improve the spatial resolution of a numerical analysis for the thermal cycle of welds effectively, as well as to incorporate the addition of the filler metal naturally. This method is suitable for the thermal analysis in the weld pool or/and weld joint region including starting and stopping transients.     

Kinetic analysis of thermal decomposition of date palm residues using Coats–Redfern method

Thermal degradation of different date palm residues (three fibrous materials and an agro-industrial by-product) under inert and oxidative atmospheres was investigated in order to identify the degradation mechanisms and kinetics of the main thermal decomposition stages using Coats–Redfern method. The corresponding kinetic parameters of the main degradation stages were also determined. The obtained results have shown that diffusion and reaction order models are the best mechanisms describing effectively thermal degradation of the different palm date residues under both atmospheres. The obtained kinetics parameters may help predicting the pyrolysis and combustion behavior of date palm residues as well as designing the suitable reactor.     

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

Abstract

The Generalized Integral Transform Technique (GITT) is reviewed as a hybrid numerical–analytical 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.     

Analytical solution of the advection–diffusion transport equation using a change-of-variable and integral transform technique

This paper presents a formal exact solution of the linear advection–diffusion transport equation with constant coefficients for both transient and steady-state regimes. A classical mathematical substitution transforms the original advection–diffusion equation into an exclusively diffusive equation. The new diffusive problem is solved analytically using the classic version of Generalized Integral Transform Technique (GITT), resulting in an explicit formal solution. The new solution is shown to converge faster than a hybrid analytical–numerical solution previously obtained by applying the GITT directly to the advection–diffusion transport equation.     

Optimization of hydrogen generation process from the hydrolysis of activated Al–NaCl–SiC composites using Taguchi method

Novel Al–NaCl–SiC composites for hydrogen generation were prepared by mechanical ball milling. NaCl is a well-known salt for the activation of Al. SiC, which is much harder and more rigid than NaCl, was added as a milling aid. In this optimization study Taguchi method was used for design of experiments. In the experimental design using the L16 (4 ? 3) orthogonal array, 4-levels of NaCl and SiC ratios and mechanical milling times were used. Confirmation tests were carried out for the optimum levels determined by Taguchi method. An analysis of variance was performed to determine the relative importance of the control factors and their contribution to the performance characteristic. It was found that NaCl has the greatest effect on hydrogen generation performance, followed by mechanical milling time and SiC ratio. The highest values of these parameters were determined as optimum levels for maximum hydrogen generation. X-ray diffraction (XRD), scanning electron microscopy (SEM), and energy-dispersive spectroscopy (EDS) analyzes were performed to investigate the relation between hydrogen generation performance and morphology of milled powders. The grain (crystal) dimensions of some milled powders were calculated from the XRD data using the Scherrer equation. Grain refinement, reduction in grain size during mechanical milling was used as a measure of the severity of plastic deformation. It was observed that the grain sizes were reduced to a few tens of nanometers with the ball milling process.     

Natural convection flow of Cu–Water nanofluid in horizontal cylindrical annuli with inner triangular cylinder using lattice Boltzmann method

In this paper the lattice Boltzmann method is used to investigate the effect of nanoparticles on natural convection heat transfer in two-dimensional horizontal annulus. The study consists of an annular-shape enclosure, which is created between a heated triangular inner cylinder and a circular outer cylinder. The inner and outer surface temperatures were set as hot (T_h) and cold temperatures (T_c), respectively and assumed to be isotherms. The effect of nanoparticle volume fraction to the enhancement of heat transfer was examined at different Rayleigh numbers. Furthermore, the effect of vertical, horizontal, and diagonal eccentricities at various locations is examined at Ra = 10⁴. The result is presented in the form of streamlines, isotherms, and local and average Nusselt number. Results show that the Nusselt number and the maximum stream functions increase by augmentation of solid volume fraction. Average Nusselt number increases when the inner cylinder moves downward, but it decreases, when the location of inner cylinder changes horizontally.     

A mechanical–electrical finite element method model for predicting contact resistance between bipolar plate and gas diffusion layer in PEM fuel cells

Contact resistance between the bipolar plate (BPP) and the gas diffusion layer (GDL) plays a significant role on the power loss in a proton exchange membrane (PEM) fuel cell. There are two types of contact behavior at the interface of the BPP and GDL, which are the mechanical one and the electrical one. Furthermore, the electrical contact behavior is dependent on the mechanical one. Thus, prediction of the contact resistance is a coupled mechanical–electrical problem. The current FEM models for contact resistance estimation can only simulate the mechanical contact behavior and moreover they are based on the assumption that the contact surface is equipotential, which is not the case in a real BPP/GDL assembly due to the round corner and margin of the BPP.     

An alternative space–time meshless method for solving transient heat transfer problems with high discontinuous moving sources

ABSTRACT

The aim of this work is the development of a space–time diffuse approximation meshless method (DAM) to solve heat equations containing discontinuous sources. This work is devoted to transient heat transfer problems with static and moving heat sources applied on a metallic plate and whose power presents temporal discontinuities. The space–time DAM using classical weight function is convenient for continuous transient heat transfer. Nevertheless, for problems including discontinuities, some spurious oscillations for the temperature field occur. A new weight function, respecting the principle of causality, is used to eradicate the physically unexpected oscillations.     

Numerical solution for the hyperbolic heat conduction problems in the radial–spherical coordinate system using a hybrid Green's function method

The hyperbolic heat conduction problems in the radial–spherical coordinate system are investigated by the hybrid Green's function method. The present method combines the Laplace transform for the time domain, Green's function for the space domain and ?-algorithm acceleration method for fast convergence of the series solution. Three different examples problems have been analyzed by the present method. It is found that the present method does not exhibit numerical oscillations at the wave front and the numerical solutions are stable.     

Comparative finite element analysis of the stress–strain states in three different bonded solid oxide fuel cell seal designs

One of the critical issues in designing and fabricating a high performance planar solid oxide fuel cell (pSOFC) stack is the development of the appropriate materials and techniques for hermetically sealing the metal and ceramic components. A second critical issue is ensuring that the brittle ceramic cell constituents, i.e. the electrodes and electrolyte, exhibit high mechanical reliability by mitigating potential sources of thermal-mechanically induced stresses that can lead to fracture during operation and/or shutdown. A foil-based sealing approach is currently being developed that appears to offer good hermeticity and mechanical integrity, while minimizing the generation of high stresses in either of the joint's substrate materials. Based on the concept's viability, demonstrated in prior experimental work, numerical analyses were conducted to evaluate the behavior and benefits of the seal in a configuration prototypic of current pSOFC stack designs. This paper presents recent results from finite element (FE) simulations of a planar cell using the foil-based seal, along with companion analyses of the more conventionally employed glass-ceramic and brazed joints. The stresses and deformations of the components were evaluated at isothermal operating and shutdown temperatures. The results indicate that the foil seal is able to accommodate a significant degree of thermal mismatch strain between the metallic support structure and the ceramic cell via elastic deformations of the foil and plasticity in the foil-to-cell braze layer. Consequently the cell stresses in this type of seal are predicted to be much lower than those in the glass-ceramic and brazed designs, which is expected to lead to improved stack reliability. This ability to accommodate large thermal strain mismatches allows the design requirement of thermal expansion matching between ceramic and metal stack components to be relaxed and expands the list of candidate materials that can be considered for the metal frames and interconnects.     

Optimization of catalyst preparation conditions for hydrogen generation in the presence of Co–B using taguchi method

Efficient hydrogen generation is a significant prerequisite of future hydrogen economy. Therefore, the development of efficient non-noble metal catalysts for hydrolysis reaction of sodium borohydride (NaBH₄) under mild conditions has received extensive interest. Since the transition metal boride based materials are inexpensive and easy to prepare, it is feasible to use these catalysts in the construction of practical hydrogen generators. In this work, temperature, pH, reducing agent concentration, and reduction rate were selected as independent process parameters and their effects on dependent parameter, such as hydrogen generation rate, were investigated using response surface methodology (RSM). According to the obtained results of the RSM prediction, maximum hydrogen generation rate (53.69 L. min^?1g_cat^-1) was obtained at temperature of 281.18 K, pH of 5.97, reducing agent concentration of 31.47 NaBH₄/water and reduction rate of 7.16 ml min^?1. Consequently, after validation studies it was observed that the RSM together with Taguchi methods are efficient experimental designs for parameter optimization.     

Numerical simulations of a coupled radiative–conductive heat transfer model using a modified Monte Carlo method

Radiative–conductive heat transfer in a medium bounded by two reflecting and radiating plane surfaces is considered. This process is described by a nonlinear system of two differential equations: an equation of the radiative heat transfer and an equation of the conductive heat exchange. The problem is characterized by anisotropic scattering of the medium and by specularly and diffusely reflecting boundaries. For the computation of solutions of this problem, two approaches based on iterative techniques are considered. First, a recursive algorithm based on some modification of the Monte Carlo method is proposed. Second, the diffusion approximation of the radiative transfer equation is utilized. Numerical comparisons of the approaches proposed are given in the case of isotropic scattering.     

Individual effects of four types of rotation modulation on Rayleigh–Bénard convection in a ferromagnetic fluid with couple stress

The effect of trigonometric sine, square, triangular, and sawtooth wave types of rotation modulation on Rayleigh–Bénard convection in a ferromagnetic fluid with couple stress is investigated in this paper using linear and nonlinear analyses. The expression for the critical Rayleigh number and the correction Rayleigh number is deduced from the three-mode linearized Lorenz model using the Venezian approach. The effect of rotation modulation on heat transport is studied using the generalized fifth-order Lorenz model. The study reveals that the Taylor number stabilizes the no-modulation system and decreases the heat transport, and this situation remains so in the presence of rotation modulation. It is found that the effect of all four types of modulation is to stabilize the system and diminish heat transport. It is also observed that the sawtooth wave type of modulation has the least diminishing effect on heat transport and the square wave type of modulation diminishes the most.     

Validation of H/O conduction in doped ceria–carbonate composite material using an electrochemical pumping method

A hydrogen and oxygen electrochemical pump technique has been employed to elucidate the conduction of proton and oxygen ion in a doped ceria–carbonate composite electrolyte for intermediate temperature solid oxide fuel cells. The composite material shows efficient conductivities of both of the two ions at 650 °C. The molten carbonate phase is important for the migration of both of the two ions. The mechanism of the conduction of proton and oxygen ion is also discussed.