Reliability-based design optimization (RBDO) problems have been intensively studied for many decades. Since Hasofer and Lind [1974, “Exact and Invariant Second-Moment Code Format,” J. Engrg. Mech. Div., 100 (EM1), pp. 111–121] defined a measure of the second-moment reliability index, many RBDO methods utilizing the concept of reliability index have been introduced as the reliability index approach (RIA). In the RIA, reliability analysis problems are formulated to find the reliability indices for each performance constraint and the solutions are used to evaluate the failure probability. However, the traditional RIA suffers from inefficiency and convergence problems. In this paper, we revisited the definition of the reliability index and revealed the convergence problem in the traditional RIA. Furthermore, a new definition of the reliability index is proposed to correct this problem and a modified reliability index approach is developed based on this definition. The strategies to solve RBDO problems with non-normally distributed design variables by the modified RIA are also investigated. Numerical examples using both the traditional and modified RIAs are compared and discussed.

There has been an explosive growth in the development of new materials and processing techniques in recent years to meet the challenges posed by new applications arising in electronics, telecommunications, aerospace, transportation, and other new and traditional areas. Semiconductor and optical materials, composites, ceramics, biomaterials, advanced polymers, and specialized alloys are some of the materials that have seen intense interest and research activity over the last two decades. New approaches have been developed to improve product quality, reduce cost, and achieve essentially custom-made material properties. Current trends indicate continued research effort in materials processing as demand for specialized materials continues to increase. Fluid flow that arises in many materials processing applications is critical in the determination of the quality and characteristics of the final product and in the control, operation, and optimization of the system. This review is focused on the fluid flow phenomena underlying a wide variety of materials processing operations such as optical fiber manufacture, crystal growth for semiconductor fabrication, casting, thin film manufacture, and polymer processing. The review outlines the main aspects that must be considered in materials processing, the basic considerations that are common across fluid flow phenomena involved in different areas, the present state of the art in analytical, experimental and numerical techniques that may be employed to study the flow, and the effect of fluid flow on the process and the product. The main issues that distinguish flow in materials processing from that in other fields, as well as the similar aspects, are outlined. The complexities that are inherent in materials processing, such as large material property changes, complicated domains, multiple regions, combined mechanisms, and complex boundary conditions are discussed. The governing equations and boundary conditions for typical processes, along with important parameters, common simplifications and specialized methods employed to study these processes are outlined. The field is vast and it is not possible to consider all the different techniques employed for materials processing. Among the processes discussed in some detail are polymer extrusion, optical fiber drawing, casting, continuous processing, and chemical vapor deposition for the fabrication of thin films. Besides indicating the effect of fluid flow on the final product, these results illustrate the nature of the basic problems, solution strategies, and issues involved in the area. The review also discusses present trends in materials processing and suggests future research needs. Of particular importance are well-controlled and well-designed experiments that would provide inputs for model validation and for increased understanding of the underlying fluid flow mechanisms. Also, accurate material property data are very much needed to obtain accurate and repeatable results that can form the basis for design and optimization. There is need for the development of innovative numerical and experimental approaches to study the complex flows that commonly arise in materials processing. Materials processing techniques that are in particular need of further detailed work are listed. Finally, it is stessed that it is critical to understand the basic mechanisms that determine changes in the material, in addition to the fluid flow aspects, in order to impact on the overall field of materials processing.

Two-dimensional natural-convection heat transfer to air from multiple identical protruding heat sources, which simulate electronic components, located in a horizontal channel which is open on both sides, has been studied numerically. Of particular interest is the accurate simulation of realistic boundary conditions in such a channel. The effects of source temperatures, channel dimensions, openings, boundary conditions, and source locations on the heat transfer from and flow above the protruding sources are investigated, and the onset of instability is studied. The results indicate that the channel dimensions and the presence of openings have significant effects on the fluid flow. However, their effects on heat transfer are found to be relatively small. The increase in channel height is seen to lead to a less stable flow and, consequently, a decrease in the critical Grashof number. Numerical simulation of the flow at the openings is investigated and found to be crucial to an accurate modeling of the transport.

Cooling of electronic chips has become a critical aspect in the development of electronic devices. Overheating may cause the malfunction or damage of electronics. The time needed for heat removal is particularly important in a wide range of electronic systems, such as switching circuits. Thus, it is important to characterize the transient behavior of the system and determine the response. Most studies in the literature have focused on steady-state circumstances and the transient effects have not been considered in the detail needed. In this article, an experimental system and a numerical model were developed to test the effects of different parameters and their influence on the transient electronic chip cooling by liquid flow in microchannel heat sinks. The temperature change with time of the system for different heat fluxes at different flow rates was determined, from which the response time is obtained. Three different configurations of multi-microchannel heat sinks were tested during the experiment. Numerical models were then developed to simulate the transient cooling for two of these configurations. A good agreement between the experimental data and numerical results showed that single-channel models are capable of simulating the thermal behavior of the entire heat sink by applying appropriate assumptions and boundary conditions. The experimental results can then be used to improve the numerical models and vice versa.