Diffusion coefficient calculated by time-lag using the film-roll method

A method for determining the diffusion coefficient by time-lag using the film-roll method for the sublimation diffusion of disperse dye was proposed. A polyethylene terephthalate film-roll coated with dye paste was treated at 170–190°C for various times. A solution consisting of the sum of a steady-state solution and a transient solution was obtained by the homogeneous boundary value problem from a trigonometrical series. The boundary conditions of the steady-state first layer and the steady-state first layer amount of dye were determined from the steady-state concentration distribution. For various diffusion times, the steady-state first layer-passed total amounts of dye that passed through the first layer in the steady-state condition were obtained by subtracting the steady-state first layer amounts from the total amounts. The time-lag was calculated from the linear regression line for the plot of the steady-state first layer-passed total number(X) of positive values against time. The diffusion coefficient was calculated by the boundary conditions of the steady-state first layer and the time-lag. For diffusion at 170°C, 180°C, and 190°C, the correlations of the steady-state first layer-passed total amounts with respect to time were very linear and the reliability of the diffusion coefficients obtained by the time-lag was proved by the good linearity of the Arrhenius plot. The activation energy obtained was 36.8 kcal[Formula: see text]mol−1.

PREDICTOR-CORRECTOR QUASI-STATIC METHOD FOR TIGHTLY-COUPLED REACTOR MULTIPHYSICS TRANSIENT CALCULATIONS

Several methods have recently been developed to solve multiphysics transients using the Improved Quasi-Static method and its derivatives. In order to address some perceived drawbacks of these methods, we have developed a new method for solving multiphysics transient calculations using the Predictor-Corrector Quasi-Static method. Our method involves computing reactivity feedback parameters during each transport timestep in order to enable reactivity feedback on the small timescale used by the point kinetics phase of the calculation. The advantage of this approach is that the transport solver does not need to store local flux information between time steps, potentially making it more appropriate for use with a Monte Carlo solver. We have demonstrated the accuracy of our method by solving a simple model problem that exhibits difficult multiphysics behavior. Additionally, we have compared our results against another recently published multiphysics coupling scheme, confirming that our approach does not negatively affect the accuracy of the transient solution.

Single Degree of Freedom Forced Vibration System

This chapter concerns the study of forced vibration of a single degree of freedom system, treating undamped and damped system under harmonic, periodic, and arbitrary loading with different cases and examples. Passing by all components of the general solution of an undamped forced system, which are a transient solution, depends only on initial conditions, transient solution due to the load at the end the stationary solution. In this chapter, a study of the dynamic influence factor depends on the ration between load frequency and structure one is presented.

PREDICTION OF EQUILIBRIUM SCOUR HOLES USING OPTIMIZATION PROCEDURES

This paper presents an optimization procedure that finds the equilibrium scour depth under a pipeline. Even though much knowledge on scour is available for the most typical marine structures such as a vertical circular monopile of a horizontal pipelines the calculation of the scour depth complex and time-consuming as the transient solution is often modelled as well. In this paper we present a optimization procedure that combined with a computational fluid dynamics, and a model of the bed load finds the equilibrium shape of a scour hole. This can potentially speed up the calculation of the shape of the equilibrium scour hole with a factor of 100. However, it comes with a coast as we will not model the transition and the time scale of the scour hole development.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/LpKq9Twj7zo

Transient Solution of 𝑀𝑋/𝑀/𝐶 Queueing Model for Homogenous Servers, with Catastrophes, Balking & Vacation

In this paper we analyze 𝑴𝑿/𝑴/𝑪 Queueing model of homogenous service rate with catastrophes, balking and vacation. Here we consider the customers, where arrival follow a poisson and the service follows an exponential distribution. Based on the above considerations, under catastrophes, balking and vacation by using probability generating function along with the Bessel properties we obtain the transient solution of the model in a simple way.

Study of Droplet Diffusion in Hydrothermal-Assisted Transient Jet Fusion of Ceramics

Hydrothermal-assisted transient jet fusion (HTJF) is a powder-based additive manufacturing (AM) method of ceramics, which utilizes a water-mediated hydrothermal mechanism to fuse particles together, eliminating the use of organic binders in forming green bodies and thereby contributing to high green-density parts (>90%) advantageous for fabricating functional materials with high performance. In the HTJF process, a transient solution such as water is selectively deposited into a powder bed in a layer-by-layer fashion followed by a hydrothermal fusion process. Upon the ejection and deposition of a droplet of the transient solution on the surface of the powder bed, the diffusion behavior of the liquid significantly influences the particle fusion and the fabrication accuracy of the HTJF process. Precise control of the liquid diffusion in the powder bed is critical for the fabrication of ceramic structures with both high density and accuracy. In this paper, the dependence of transient solution diffusion on different process parameters (i.e., powder packing density, droplet size, pressure, etc.) in the HTJF process were studied. Both numerical modeling and experimental methods were used to quantify the relationships between processing parameters and diffusion profiles of transient solution droplets (e.g., diffusion width/depth). Optimum processing conditions were identified to mitigate the undesired diffusion of transient solution droplets in the powder bed.

Transient analysis of a single server queueing system with infinite buffer

As a typical single server queueing system, computer integrated manufacturing system (CIMS) has been widely used in the field of intelligent manufacturing. Howerve, how to derive its instantaneous index is still an imporant issue. This paper investigates the transient behavior of the CIMS with spectral method. By constructing an asymptotic system and analyzing the spectral distribution, we derive the explicit transient solution of the asymptotic system. Trottter-Kato theorem is used to prove that the transient solution of the CIMS is just the limitation of explicit transient solution of the asymptotic system. At the end of the paper, numerical examples are shown to illustrate the effectiveness of the proposed approximation.