Application of the cross-entropy method to the buffer allocation problem in a simulation-based environment

The buffer allocation problem (BAP) is a well-known difficult problem in the design of production lines. We present a stochastic algorithm for solving the BAP, based on the cross-entropy method, a new paradigm for stochastic optimization. The algorithm involves the following iterative steps: (a) the generation of buffer allocations according to a certain random mechanism, followed by (b) the modification of this mechanism on the basis of cross-entropy minimization. Through various numerical experiments we demonstrate the efficiency of the proposed algorithm and show that the method can quickly generate (near-)optimal buffer allocations for fairly large production lines.

Effects of temperature-dependent viscosity variation on entropy generation, heat and fluid flow through a porous-saturated duct of rectangular cross-section

Effect of temperature-dependent viscosity on fully developed forced convection in a duct of rectangular cross-section occupied by a fluid-saturated porous medium is investigated analytically. The Darcy flow model is applied and the viscosity-temperature relation is assumed to be an inverse-linear one. The case of uniform heat flux on the walls, i.e. the H boundary condition in the terminology of Kays and Crawford, is treated. For the case of a fluid whose viscosity decreases with temperature, it is found that the effect of the variation is to increase the Nusselt number for heated walls. Having found the velocity and the temperature distribution, the second law of thermodynamics is invoked to find the local and average entropy generation rate. Expressions for the entropy generation rate, the Bejan number, the heat transfer irreversibility, and the fluid flow irreversibility are presented in terms of the Brinkman number, the Péclet number, the viscosity variation number, the dimensionless wall heat flux, and the aspect ratio (width to height ratio). These expressions let a parametric study of the problem based on which it is observed that the entropy generated due to flow in a duct of square cross-section is more than those of rectangular counterparts while increasing the aspect ratio decreases the entropy generation rate similar to what previously reported for the clear flow case.

Heat transfer and entropy generation optimization of forced convection in a porous-saturated duct of rectangular cross-section

We investigate analytically the first and the second law characteristics of fully developed forced convection inside a porous-saturated duct of rectangular cross-section. The Darcy-Brinkman flow model is employed. Three different types of thermal boundary conditions are examined. Expressions for the Nusselt number, the Bejan number, and the dimensionless entropy generation rate are presented in terms of the system parameters. The conclusions of this analytical study will make it possible to compare, evaluate, and optimize alternative rectangular duct design options in terms of heat transfer, pressure drop, and entropy generation. (c) 2006 Elsevier Ltd. All rights reserved.

Entropy generation for forced convection in a porous saturated circular tube with uniform wall temperature

A numerical study is reported to investigate both the First and the Second Law of Thermodynamics for thermally developing forced convection in a circular tube filled by a saturated porous medium, with uniform wall temperature, and with the effects of viscous dissipation included. A theoretical analysis is also presented to study the problem for the asymptotic region applying the perturbation solution of the Brinkman momentum equation reported by Hooman and Kani [1]. Expressions are reported for the temperature profile, the Nusselt number, the Bejan number, and the dimensionless entropy generation rate in the asymptotic region. Numerical results are found to be in good agreement with theoretical counterparts.

A fast cross-entropy method for estimating buffer overflows in queuing networks

In this paper, we propose a fast adaptive importance sampling method for the efficient simulation of buffer overflow probabilities in queueing networks. The method comprises three stages. First, we estimate the minimum cross-entropy tilting parameter for a small buffer level; next, we use this as a starting value for the estimation of the optimal tilting parameter for the actual (large) buffer level. Finally, the tilting parameter just found is used to estimate the overflow probability of interest. We study various properties of the method in more detail for the M/M/1 queue and conjecture that similar properties also hold for quite general queueing networks. Numerical results support this conjecture and demonstrate the high efficiency of the proposed algorithm.

Analysis of heat transfer and entropy generation for a thermally developing Brinkman–Brinkman forced convection problem in a rectangular duct with isoflux walls

Heat transfer and entropy generation analysis of the thermally developing forced convection in a porous-saturated duct of rectangular cross-section, with walls maintained at a constant and uniform heat flux, is investigated based on the Brinkman flow model. The classical Galerkin method is used to obtain the fully developed velocity distribution. To solve the thermal energy equation, with the effects of viscous dissipation being included, the Extended Weighted Residuals Method (EWRM) is applied. The local (three dimensional) temperature field is solved by utilizing the Green’s function solution based on the EWRM where symbolic algebra is being used for convenience in presentation. Following the computation of the temperature field, expressions are presented for the local Nusselt number and the bulk temperature as a function of the dimensionless longitudinal coordinate, the aspect ratio, the Darcy number, the viscosity ratio, and the Brinkman number. With the velocity and temperature field being determined, the Second Law (of Thermodynamics) aspect of the problem is also investigated. Approximate closed form solutions are also presented for two limiting cases of MDa values. It is observed that decreasing the aspect ratio and MDa values increases the entropy generation rate.

Alkyl halides, super hydrogen production and the pathogenesis of pneumatosis cystoides coli

Background and aims-The colons of patients with pneumatosis cystoides coli produce excessive H-2. Exposure to alkyl halides could explain this. Six consecutive patients who had pneumatosis cystoides coli while taking chloral hydrate (1-5+ g/day) are reported. Patients 2 and 3 were investigated after they had ceased chloral hydrate treatment. One produced methane, the other did not. (Pneumatosis cystoides coli patients are non-methanogenic according to the literature.) Both had overnight fasting breath H-2 of less than 10 ppm. A literature review disclosed just one patient who was using chloral at the time of diagnosed pneumatosis cystoides coli, but an epidemic of the disease in workers exposed to trichloroethylene. Methods-(i) In vitro experiments with human faeces: chloral or closely related alkyl halides were added to anaerobic faecal cultures derived from four methane-producing and three non-methanogenic human subjects. H-2 and CH4 gases were measured. (ii) In vivo animal experiment: chloral hydrate was added to drinking water of four Wistar rats, and faecal HI compared with control rats. Results-Alkyl halides increased H-2 up to 900 times in methanogenic and 10 times in non-methanogenic faecal cultures. The K-i of chloral was 0.2 mM. Methanogenesis was inhibited in concert with the increase in net H-2. In the rat experiment, chloral hydrate increased H-2 10 times, but did not cause pneumatosis. Conclusions-Chloral and trichloroethylene are alkyl halides chemically similar to chloroform, a potent inhibitor of H-2 consumption by methanogens and acetogens. These bacteria are the most important H-2-consuming species in the colon. It is postulated that exposure to these alkyl halides increases net H-2 production, which sets the scene for counterperfusion supersaturation and the formation of gas cysts. In recent times, very low prescribing rates for chloral have caused primary pneumatosis cystoides to become extremely rare. As with primary pneumatosis, secondary pneumatosis cystoides, which occurs if there is small bowel bacterial overgrowth distal to a proximally located gut obstruction, is predicted by counterperfusion supersaturation. Inherent unsaturation due to metabolism of O-2 is a safety factor, which could explain why gas bubbles do not form more often in tissue with high H-2 tension.