Optimum dimensions of convecting–radiating fins:: Part I — longitudinal fins

The optimum dimensions of convective radiating extended surfaces or fins have been determined. Several fin shapes, profiles, have been analyzed including those treated by Gardner (Trans. ASME 69 (8) (1945) 621–631). Consideration is given to radiating fins and convective–radiating fins. In addition the cases of non-zero temperature sink, and the influence of the temperature dependent thermal conductivity and emissivity have been investigated. The results are generalized by expressing the fin’s optimum thickness, height, and heat dissipation in dimensionless form. They are presented graphically and in polynomial form the latter being particularly useful for computerized calculations.     

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.     

Numerical Method for Calculation of Complete Casting Processes—Part I: Theory

This article presents a method for calculation of the complete casting process, including the pouring of the liquid metal into the mold, its solidification, the deformation of the solidified cast, the formation of airgaps between the cast and the mold and their influence on the heat transfer, and the residual stresses. An original phase-change procedure is developed, valid for an arbitrary number of pure metals and/or alloys. A collocated version of a segregated finite-volume method is used to calculate both the liquid metal flow and the deformations and stresses in solids.     

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.     

Statistical phonon transport model for multiscale simulation of thermal transport in silicon: Part I – Presentation of the model

The Boltzmann transport equation can be used to model phonon transport in crystalline materials across multiple length scales. The statistical phonon transport model solves the Boltzmann transport equation in a statistical framework that incorporates a state-based phonon transport methodology. The statistical phonon transport model captures the anisotropy of the first Brillouin zone in addition to nonlinear dispersion. Three-phonon scattering is implemented conserving both energy and pseudo-momentum with probability limits based exclusively on the relative phonon populations available.     

Crack-opening-area analyses for circumferential through-wall cracks in pipes—Part I: analytical models

Leak-before-break (LBB) analyses for circumferentially cracked pipes are currently being conducted in the nuclear industry to justify elimination of pipe whip restraints and jet impingement shields which are present because of the expected dynamic effects from pipe rupture. The application of the LBB methodology requires calculation of leak rates. The leak rates depend on the crack-opening area of the through-wall crack in the pipe. In addition to LBB analyses which assume a hypothetical flaw size, there is also interest in the integrity of actual leaking cracks corresponding to current leakage detection requirements in NRC Regulatory Guide 1.45, or for assessing temporary repair of Class 2 and 3 pipes that have leaks, as are being evaluated in ASME Section XI. The objectives of this study were to review, evaluate, and refine current predictive models for performing crack-opening-area analyses of circumferentially cracked pipes. A three-phase effort was undertaken to accomplish this goal. It is described here in a series of three papers generated from this study. In this first paper (Part I — Analytical models), a comprehensive review is performed to determine the current state-of-the-art in predicting crack-opening displacements for circumferentially cracked pipes under pure bending, pure tension, and combined bending and tension loads. Henceforth, new and improved analytical models and some preliminary results are presented for cases where current methods are inadequate or there are no available methods. Also, based on this review, a number of appropriate predictive models are identified for a systematic evaluation of their accuracy. The results of their evaluations will be presented and examined in the forthcoming companion papers (Part II — Model validations [1] and Part III — Off-center cracks, restraint of bending, thickness transition, and weld residual stresses) [2].     

Modelling of hybrid energy system—Part I: Problem formulation and model development

A well designed hybrid energy system can be cost effective, has a high reliability and can improve the quality of life in remote rural areas. The economic constraints can be met, if these systems are fundamentally well designed, use appropriate technology and make use effective dispatch control techniques. The first paper of this tri-series paper, presents the analysis and design of a mixed integer linear mathematical programming model (time series) to determine the optimal operation and cost optimization for a hybrid energy generation system consisting of a photovoltaic array, biomass (fuelwood), biogas, small/micro-hydro, a battery bank and a fossil fuel generator. The optimization is aimed at minimizing the cost function based on demand and potential constraints. Further, mathematical models of all other components of hybrid energy system are also developed. This is the generation mix of the remote rural of India; it may be applied to other rural areas also.     

Final Shape of Precision Molded Optics: Part I—Computational Approach,Material Definitions and the Effect of Lens Shape

Coupled thermomechanical finite element models were developed in ABAQUS to simulate the precision glass lens molding process, including the stages of heating, soaking, pressing, cooling and release. The aim of the models was the prediction of the deviation of the final lens profile from that of the mold, which was accomplished to within one-half of a micron. The molding glass was modeled as viscoelastic in shear and volume using an n-term, prony series; temperature dependence of the material behavior was taken into account using the assumption of thermal rheological simplicity (TRS); structural relaxation as described by the Tool-Narayanaswamy-Moynihan (TNM)-model was used to account for temperature history dependent expansion and contraction, and the molds were modeled as elastic taking into account both mechanical and thermal strain. In Part I of this two-part series, the computational approach and material definitions are presented. Furthermore, in preparation for the sensitivity analysis presented in Part II, this study includes both a bi-convex lens and a steep meniscus lens, which reveals a fundamental difference in how the deviation evolves for these different lens geometries. This study, therefore, motivates the inclusion of both lens types in the validations and sensitivity analysis of Part II. It is shown that the deviation of the steep meniscus lens is more sensitive to the mechanical behavior of the glass, due to the strain response of the newly formed lens that occurs when the pressing force is removed.     

Bejan’s heatline analysis of natural convection in right-angled triangular enclosures: Effects of aspect-ratio and thermal boundary conditions

Natural convection in right-angled triangular enclosures with various top angles ($\phi$=15°, 30°, 45°) is studied in detail via heat flow analysis for various uniform isothermal and linear isothermal heating thermal boundary conditions. Detailed analysis on the effects of aspect-ratio and thermal boundary conditions on the fluid and heat flow inside the triangular enclosures have been carried out for a range of fluids (Pr = 7.2, 1000, 0.015) within Ra = 10³–10⁵. Interesting features of heat flow patterns under various thermal boundary conditions are ‘visualized’ by heatlines. The effect of increase in φ of triangular enclosures is such that the maximum heat flux at the top vertex decreases and the thermal mixing in cavity increases with the increase in $\phi$. It is found that, the fluid in the lower corners is adequately heated in presence of hot right wall compared to that in left wall heating cases. Further, the heat transfer characteristics, in terms of local and average Nusselt numbers, indicate that isothermal heating cases exhibit exponential decrease in Nu_l whereas linear heating cases interestingly show local intermediate maxima. Also, various qualitative and quantitative features of Nu and $\overline{Nu}$ are adequately explained based on heatlines. Finally, the correlations for $\overline{N{u}_l}$ and Ra are obtained for various fluid with all heating situations.     

Disclosure of the internal transport phenomena in an air-cooled proton exchange membrane fuel cell—Part I: Model development and base case study

In this study, the internal transport phenomena and mechanism inside an air-cooled proton exchange membrane fuel cell (PEMFC) are investigated. It helps to understand the factors that affect the performance of an air-cooled PEMFC and optimize the design of Membrane Electrode Assembly (MEA) and the flow field. This series article contains two parts. In this paper, i.e., Part Ⅰ of this series, a three-dimensional, two-phase flow, non-isothermal, steady-state Computational Fluid Dynamics (CFD) model is established to investigate the liquid water generation mechanism and the species distributions inside an air-cooled PEMFC single cell with a Base Case flow field design. Dry hydrogen and ambient air (the relative humidity and the stoichiometry are 60% and 150 separately) are considered for the simulation and validation. It is found that the liquid water appears mostly inside the cathode electrode underneath the cathode rib. Inside the anode gas diffusion layer (GDL), the mass fraction of H₂ underneath the cathode ribs is lower than that underneath the cathode channels, while the mass fraction of H₂O shows the opposite. The distributions of O₂ mass fraction and H₂O mass fraction inside the cathode GDL have the same trend as those of H₂ mass fraction and H₂O mass fraction inside the anode GDL. The membrane water content is periodically distributed from channel to channel and its value underneath the cathode rib is much larger than that underneath the cathode channel. The current density distribution is affected by the distribution of water content, i.e., the part underneath the cathode rib shows a larger current density than that underneath the cathode channel.     

Is the H2 economy realizable in the foreseeable future? Part I: H2 production methods

The efforts on energy system decarbonization and improved sustainable energy efficiency in developed countries led energy enthusiasts to explore alternative highly effective pathways in accomplishing these goals. Specifically, the transition from hydrocarbon to H₂ economy using fuel cells and H₂ technologies is a sustainable and favorable approach forward in meeting stationary, transportation, industrial, residential, and commercial sectors. This review in three Parts brings out the capability of H₂ for enabling an energy revolution through much-needed flexibility in renewable energy resources. The review identifies the developments and challenges within the H₂ generation, storage, transportation, distribution, and usage - as well as applications along with national and international initiatives in the field, all of which suggest a pathway for a greener H₂ society. The review also highlights the opportunities and challenges in major energy sectors for H₂ technologies. Part I of the series highlights the importance of H₂ economy and initiatives from various agencies, and presents several H₂ generation methods.     

Optimization of Dimples in Microchannel Heat Sink with Impinging Jets——Part A: Mathematical Model and the Influence of Dimple Radius

With increasing heat fluxes caused by electronic components, dimples have attracted wide attention by researchers and have been applied to microchannel heat sink in modern advanced cooling technologies. In this work, the combination of dimples, impinging jets and microchannel heat sink was proposed to improve the heat transfer performance on a cooling surface with a constant heat flux 500 W/cm~2. A mathematical model was advanced for numerically analyzing the fluid flow and heat transfer characteristics of a microchannel heat sink with impinging jets and dimples(MHSIJD), and the velocity distribution, pressure drop, and thermal performance of MHSIJD were analyzed by varying the radii of dimples. The results showed that the combination of dimples and MHSIJ can achieve excellent heat transfer performance; for the MHSIJD model in this work, the maximum and average temperatures can be as low as 320 K and 305 K, respectively when mass flow rate is 30 g/s; when dimple radius is larger than 0.195 mm, both the heat transfer coefficient and the overall performance h/ΔP of MHSIJD are higher than those of MHSIJ.     

Local thermal non-equilibrium effects in the Darcy–Bénard instability with isoflux boundary conditions

The Darcy–Bénard problem with constant heat flux boundary conditions is studied in a regime where the fluid and solid phases are in local thermal non-equilibrium. The onset conditions for convective instability in the plane porous layer are investigated using a linear stability analysis. Constant heat flux boundary conditions are formulated according to the Amiri–Vafai–Kuzay Model A, where the boundary walls are assumed as impermeable and with a high thermal conductance. The normal mode analysis of the perturbations imposed on the basic state leads to a one-dimensional eigenvalue problem, solved numerically to determine the neutral stability condition. Analytical solutions are found for the limit of small wave numbers, and in the regime where the conductivity of the solid phase is much larger than the conductivity of the fluid phase. A comparison with the corresponding results under conditions of local thermal equilibrium is carried out. The critical conditions for the onset of convection correspond to a zero wave number only when the inter-phase heat transfer coefficient is sufficiently large. Otherwise, the critical conditions correspond to a nonzero wave number.     

Electrocatalysts for ethanol and ethylene glycol oxidation reactions. Part I: Effects of the polyol synthesis conditions on the characteristics and catalytic activity of Pt–Sn/C anodes

In this work, Pt–Sn/C electrocatalysts with nominal Pt:Sn ratio of 1:1 (at.%) were synthesized by a polyol/alcohol process. The effect of different ethylene glycol:ethanol:water (EG:EtOH:H₂O) volume ratios on the physicochemical characteristics (i.e., Pt:Sn ratio and SnOx formation) of the Pt–Sn/C alloys was evaluated. In some cases, no water was used for the synthesis. Afterwards, the electrocatalytic activity of the alloys for the Ethanol and the Ethylene Glycol Oxidation Reaction (EOR and EGOR, respectively) was studied. XRD characterization showed that the degree of alloying calculated by using Vegard's law ranges from about 15% (synthesis in the presence of water) to roughly 49% (synthesis in the absence of water). The average particle size was calculated with the Scherrer equation to be within 1.8–4.7 nm, smaller sizes obtained in the absence of water. The chemical analysis by EDS indicated the formation of oxides regardless of the presence or not of water during the synthesis. The oxides were attributed to the presence of SnO_x phases in the materials. The electrochemical characterization showed that the synthesis conditions have an important effect on the electrocatalytic activity of the Pt–Sn/C materials for the EOR and the EGOR. As a result, the alloys synthesized in the absence of H₂O delivered a higher performance for both reactions.     

Improved solvation routes for the Bunsen reaction in the sulphur iodine thermochemical cycle: Part I – Ionic liquids

The Bunsen reaction is central to the Sulphur Iodine cycle, however large excesses of both water and iodine are currently employed to enable phase separation of the two acids produced. This causes separation issues later in the cycle and induces a large thermal burden for water evaporation. The use of solvents in the reaction has the potential to reduce these large excesses, thereby increasing the cycle efficiency. This paper investigates ionic liquids as solvents for the Bunsen reaction. Several potential ionic liquids are identified based on their anion properties. The extraction of HI into the ionic liquid is then investigated experimentally. [FAP]⁻ ionic liquids were examined but their extreme hydrophobicity prevented water being taken up into the organic phase, severely retarding the extraction of acid by the solvent. Results for the [TMPP]⁻ ionic liquid showed discrepancies in the component balance and it is thought that the solvent may be susceptible to hydrolysis. The extraction of acid by the [Tf₂N]⁻ ionic liquids was more promising, the amount of acid extracted being of the order of 20%. However, the amount of protons and iodide ions extracted by the solvents were not equivalent and evidence is presented demonstrating the presence of an ion exchange mechanism. None of the ionic liquids tested are therefore suitable for use in the Bunsen reaction, however the properties of an ionic liquid can be tailored by the choice of anion and cation. Further investigation of ionic liquids is necessary before they can be conclusively ruled out.     

On the importance of the long-term seasonal component in day-ahead electricity price forecasting: Part II — Probabilistic forecasting

A recent electricity price forecasting study has shown that the Seasonal Component AutoRegressive (SCAR) modeling framework, which consists of decomposing a series of spot prices into a trend-seasonal and a stochastic component, modeling them independently and then combining their forecasts, can yield more accurate point predictions than an approach in which the same autoregressive model is calibrated to the prices themselves. Here, we show that further accuracy gains can be achieved when the explanatory variables (load forecasts) are deseasonalized as well. More importantly, considering a novel extension of the SCAR concept to probabilistic forecasting and applying two methods of combining predictive distributions, we find that (i) SCAR-type models nearly always significantly outperform the autoregressive benchmark but are in turn outperformed by combined SCAR forecasts, (ii) predictive distributions computed using Quantile Regression Averaging (QRA) outperform those obtained from historical simulation and bootstrap methods, and (iii) averaging over predictive distributions generally yields better probabilistic forecasts of electricity spot prices than averaging over quantiles. Given that probabilistic forecasting is a concept closely related to risk management, our study has important implications for risk officers and portfolio managers in the power sector.     

Effect of boron on the hydrogen-induced grain boundary embrittlement in α-Fe

The influence of interstitial impurities such as B and C on the H-induced Fe Σ5(310) symmetrical tilt grain boundary embrittlement was investigated using the projector augmented-wave method. It was shown that in contrast to hydrogen, both boron and carbon decrease the grain boundary energy more significantly than the surface one. This results in an increase in the Griffith work, i.e. the grain boundary strengthening. The strengthening of grain boundary is more pronounced with increased number of B atoms whereas the increase of H concentration makes the process of intergranular brittle cleavage fracture easier. The grain boundary energy is lowered with an increased number of B atoms indicating a strong driving force for segregation. Our estimations of the Griffith work for the Fe Σ5(310) grain boundary containing both B and H atoms show an increase in comparison with the undoped grain boundary. It is revealed that improved cohesion of Fe Σ5(310) grain boundary due to B is mainly a chemical effect, whereas both elastic and chemical contributions to the Griffith work in case of H are negative, i.e. they are embrittling contributions.     

Modeling of the transport phenomena in GMAW using argon–helium mixtures. Part I – The arc

This article presents a numerical investigation on the transient transport phenomena in the arc which include the arc plasma generation and interactions with moving droplets and workpiece for pure argon and three argon–helium mixtures (75% Ar + 25% He, 50% Ar + 50% He, and 25% Ar + 75% He) during the gas metal arc welding (GMAW) process. The results indicate that the arcs in various shielding gases behave very differently due to the significant differences in thermophysical properties, including the ionization potential and the electrical conductivity, thermal conductivity, specific heat, and viscosity at high temperatures. For the same welding power input, it was found the increase of helium content in the mixtures results in (1) the change of plasma arc shape from bell-like to cone-like and (2) the change of arc pressure distribution along the workpiece surface from Gaussian-like to flat-top with decreasing peak value. Detailed explanations to the physics of the very complex but interesting transport phenomena are given.     

Lignites from the Plains region of Alberta,Canada—Part 2: Elemental geochemistry

Mineralogy and elemental concentration of two coal seams in Alberta, Canada, were determined using X-ray diffractometry and X-ray fluorescence (XRF). Minerals consist mainly of quartz and calcium minerals, the latter as calcite and vaterite, and oxalate (whewellite). Clay minerals are present as kaolinite, reflecting peat deposition in an acidic environment. Most elements in the coal show depletion compared to Clarke values. Some elements are associated with mineral matter (e.g., Ti, Ba, Si, Al, K, Mg, and Y) and increase with ash. Na, Mn, Sr, and Cu are associated with macerals. High phosphorous and strontium in one interval may be related to the high concentration of whewellite.     

D'Alembert's Solution in Thermoelasticity—Impact of a Rod Against a Heated Barrier: Part I. A Case of Uncoupled Strain and Temperature Fields

The problem of impact of a thermoelastic rod against a heated rigid barrier is considered, in so doing lateral surfaces and free end of the rod are heat insulated, while there is either free heat exchange between the rod and the rigid obstacle within contacting end or ideal thermal contact, as a particular case. The rod's thermoelastic behavior is described by the Green–Naghdi theory of thermoelasticity. D'Alembert's method, which is based on the analytical solution of equations of the hyperbolic type describing the dynamic behavior of the thermoelastic rod, is used as the method of solution. This solution involves four arbitrary functions which are determined from the initial and boundary conditions and are piecewise constant functions. The procedure developed enables one to analyze the influence of thermoelastic parameters on the values to be found, as well as to investigate numerically the longitudinal coordinate dependence of the desired functions at each fixed instant of the time beginning from the moment of the rod's collision with the barrier up to the moment of its rebound. The case of uncoupled stress and temperature fields is examined in the first part of the paper, while the case of coupling thermoelasticity is considered in detail in the companion paper. It has been shown that the possibility for generating the reflected thermal wave from the incident elastic wave at the free rod's end is unavailable in the case of the uncoupled strain and temperature fields, and that the rod's rebound may occur either at the moment of arrival at the contact place of the reflected elastic wave from the incident thermal wave or at the time when the reflected elastic wave from the incident elastic wave reaches the contact point.