This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems. Although we discuss the main points in the application of the finite element method to electromagnetic design, including formulation and implementation, those who seek deeper understanding of the finite element method should consult some of the works listed in the bibliography section.

Introduction to the Finite Element Method

Thermal energy storage technologies and systems for concentrating solar power plants

Pool boiling characteristics of nano-fluids

Thermal energy storage has recently attracted increasing interest related to thermal applications such as space and water heating, waste heat utilization, cooling and air-conditioning. Energy storage is essential whenever there is a mismatch between the supply and consumption of energy. Use of phase change material (PCM) capsules assembled as a packed bed is one of the important methods that has been proposed to achieve the objective of high storage density with higher efficiency. A proper designing of the thermal energy storage systems using PCMs requires quantitative information about heat transfer and phase change processes in PCM. This paper reviews the development of available latent heat thermal energy storage technologies. The different aspects of storage such as material, encapsulation, heat transfer, applications and new PCM technology innovation have been carried out.

Heat transfer characteristics of thermal energy storage system using PCM capsules: A review

An overview of thermal energy storage systems

http://ihtcdigitallibrary.com/download/article/5020b80651519816/IHTC16-21811-2_N.pdf

Layout optimization of passive micro mixers with cylindrical obstacles

The effect of superficial velocity of liquid and gas on elongated bubble length is experimentally studied using water and air as the working fluid inside mini channels of tube diameters less than 3mm. A high speed CMOS camera is used to identify the slug length. The reduction in tube diameter results in squeezing of bubbles and thereby results in elongated bubble flow pattern distinguishing it from slug flow pattern. At low superficial gas velocities inside mini/micro channels, such pattern dominates which is the subject of interest in the present study. The experimental set-up used in this study is designed for adiabatic co-current flow of air-water mixtures in round horizontal tubes. Both the liquid and gas streams flowed separately through a bank of rota meters and Coriolis mass flow meters before entering the gas-liquid mixer. The gas-liquid mixer installed upstream of the test section (the observation zone), ensures that the two phases get thoroughly mixed before entering the test section. Flow patterns were observed and the video graphs were recorded in a computer and subsequently analyzed frame by frame with appropriate image processing technique to determine various flow regimes. The decreasing tube diameter results in the elongated bubble flow pattern over a wider range in the flow regime map of mini channels which would be of a slug flow pattern in conventional tube diameters. The region of slug flow is differentiated from elongated bubble flow based on flow visualizations. The analysis of measured length of elongated bubble acts as a good indicator for identifying the change of flow regime in mini channels.

Effect of tube diameter on elongated bubble length in mini channels

Flooding is the limiting condition of stable countercurrent gas-liquid flow in columns and has been the subject of extensive research over a number of decades. An exhaustive review of the subject, as pertaining to unpacked columns, has been given by Bankoff and Lee.1 While a number of correlations exist in the literature to predict the onset of flooding, the topic of the mechanism of flooding has been debated and discussed widely in the recent literature. Briefly, there are two schools of thought on the flooding mechanism: (1) the formation and upward transport of large waves from the bottom of the column near the gas injection/liquid withdrawal point, and (2) the destabilization of the liquid film near the liquid inlet resulting in the formation of large waves. Direct visual evidence of formation of large waves at the liquid exit under flooding conditions has been reported by a number of researchers.2,3,4 However, this idea was opposed by Zabaras and Dukler.5 They measured the local instantaneous wall shear stress using an electrochemical method just below the liquid feed, as well as just above the liquid withdrawal point. They found that in all instances of countercurrent flow, including conditions along the flooding curve, the time-averaged wall shear stress was directed upward indicating that the velocity near the wall was downward. They also measured the instantaneous film thickness from two conductance probes located 0.053 m apart. Cross-correlation of these signals showed a well-defined peak at a measurable time delay even under flooding conditions. Zabaras and Dukler, therefore, concluded that waves were travelling downward even under flooding conditions and that they did not reverse direction at the flooding point. They explained the photographic observation of upward-travelling waves by McQuillan et al.3 as a transient phenomenon generated by the small depressurization used by McQuillan et al. to induce flooding. Thus, Zabaras and Dukler argued that the process of flooding was controlled by conditions that existed at the or just below the feed rather than at the liquid exit. Jayanti et al.6 attributed the existence of different mechanisms of flooding to the effect of tube diameter. In small diameter tubes, a coherent, ring-like wave could be formed around the inside wall of the tube which could then be transported upward by the gas. A flooding model, based on the formation of a large standing wave at the flooding point was developed by Shearer and Davidson.7 Jayanti et al. argued that such a wave would be very unstable in large diameter tubes and, hence, could not travel upward for long distances. Vijayan et al.8 conducted flooding experiments in tubes of 25, 67 and 99 mm inner dia. and confirmed visually the existence of upward travelling waves in the 25 mm dia. tube under flooding conditions. In the larger diameter tubes, the waves were observed to move only a short distance before collapsing. Similar behavior was also observed by Biage et al.9 in a duct of rectangular cross-section and by Watson and Hewitt10 in a tube of 82 mm internal dia. While there is, thus, a convergent view on the flooding mechanism, the careful experimental results of Zabaras and Dukler5 remain unexplained. Specifically, their observations that the wall shear stress always indicated a downward moving flow and that the film thickness measurements recorded no upward-moving waves need to be explained in a manner consistent with the recent visual observations of flooding mechanisms. Toward this end, film thickness measurements have been conducted under conditions in which different flooding mechanisms prevailed. The details of these studies and the results obtained are reported here.

A.R. Balakrishnan

Papers

Layout optimization of passive micro mixers with cylindrical obstacles

Effect of tube diameter on elongated bubble length in mini channels

On axial coherence of interfacial waves in countercurrent flow

On Axial Coherence of Interfacial Waves in Countercurrent Flow (R&D Note)