Reliable compartmental models for double-pipe heat exchangers: An analytical study

In this work, the analytical properties of the heat exchanger infinite-dimensional dynamic model are discussed. More importantly, those of a 2nd-order lumped-parameter model using the logarithmic mean temperature difference (LMTD) as driving force are derived and shown to agree with those of the former. Three essential aspects are focused: existence and uniqueness of solutions, equilibrium states, and stability properties. The results developed in this work are intended to supply a solid support for the reliability on the use of the kind of simple compartmental model that is treated. This is specially addressed to works where it is not the quantitative solutions but the qualitative behavior that is important, like modelling and simulation of heat exchanger networks and complex industrial processes where heat exchangers are involved.     

Object-oriented modelling and simulation of heat exchangers with finite element methods

The paper describes the derivation of finite-element models of one-dimensional fluid flows with heat transfer in pipes, using the Galerkin/least-squares approach. The models are first derived for one-phase flows, and then extended to homogeneous two-phase flows. The resulting equations have then been embedded in the context of object-oriented system modelling; this allows one to combine the fluid flow model with a model for other phenomena such as heat transfer, as well as with models of other discrete components such as pumps or valves, to obtain complex models of heat exchangers. The models are then validated by simulating a typical heat exchanger plant.     

Synthesis of distillation trains with heat integration by a combined fuzzy and graphical approach

After passing some results of fuzzy synthesis of heat exchanger networks in review the application of this approach to the synthesis of distillation trains for the separation of multicomponent mixtures is demonstrated. The available heuristic rules are transformed into fuzzy implications dependent on different criteria and that competing rule, which is to be applied, is selected by the fuzzy algorithm.The theoretically possible amount of heat recovery within the networks generated in this way is estimated by a graphical method and included in the final cost evaluation. Regarding operating parameters like column pressure and reflux ratio, according to the mathematical effort at least qualitative statements can be made in result of the estimation of possible heat recovery.As already in the case of heat exchanger networks a following learning algorithm can serve to overcome the disadvantages of this sequential approach, representing at the same time the first step of a further evolutionary improvement of the initial distillation train.     

An MINLP retrofit approach for improving the flexibility of heat exchanger networks

A mixed integer nonlinear programming (MINLP) model for the retrofit of heat exchanger networks (HENs) in order to improve their flexibility is presented in this paper. As stream flowrates and inlet temperatures and/or heat transfer coefficients are allowed to vary within either specified ranges or discrete sets, a multiperiod hyperstructure network representation is developed based on critical operating conditions (i.e. periods of operation) that limit the network's flexibility. This multiperiod hyperstructure includes all possible network configurations. Structural modifications, such as new stream matches, exchanger reassignments, splitting and mixing of streams are explicitly modeled either considering one-to-one or one-to-many assignment of heat exchangers to stream matches. Energy recovery and utility consumption are not predetermined but are optimized as part of a total annualized cost along with the structural modification cost in the objective function. Thus, trade-offs between operating and retrofit investment costs to improve the flexibility of a HEN are accounted for. The resulting large scale MINLP is solved with the application of the Generalized Benders Decomposition. The proposed multiperiod retrofit model can be included in a general framework to improve the operability of heat exchanger networks.     

On a proposed model for heat conduction

^** Corresponding author. Email: jcsong{at}hanyang.ac.kr A system of partial differential equation for modelling theconduction of heat was proposed by Ghaleb & El-Deen Mohamedein(1989). According to their theory, the initial-value problemfor the temperature is ill-posed. In this paper, two well-posedproblems for the temperature are introduced and investigated.     

Performance analysis of single stage kanban controlled production systems using parametric decomposition

We present a new approach that permits efficient performance analysis of kanban systems with general demand processes, material arrival processes, and service times. The approach is based on parametric characterization of the traffic processes (arrival and departure) in the network and uses two-moment approximations to estimate performance measures at individual stations. We derive traffic flow constraints that are particular to closed queuing networks with synchronization stations and use these to establish relationships between the parameters characterizing arrival and departure processes at the stations in the network. The resultant set of non-linear equations is solved to estimate network performance measures. Numerical studies show that the approach is not only fast but also reasonably accurate when compared to simulation. These studies also provide insights with respect to the impact of different types of variability on the performance of a kanban system. This work also provides a fundamental building block that can be used in the analysis of multi-stage kanban systems. AMS Subject Classifications 68M20, 60K20, 90B05, 90B30     

A fast running numerical model based on the implementation of volume forces for prediction of pressure drop in a fin tube heat exchanger

Numerical based design of geometrical structures is common when studying systems involving heat exchangers, a central component in several fields, such as industrial, vehicle and household systems. The geometrical structure of heat exchangers is generally comprised by closely placed fins and tube bundles. The creation of a mesh grid for a geometrically compact heat exchanger will result in a dense structure, which is not feasible for personal computer usage. Hence, volume forces were created based on Direct Numerical Simulations (DNS) on a Flow Representative Volume (FRV) of a tube fin heat exchanger in an internal duct system of a heat pump tumble dryer. A relation of the volume averaged velocity and the volume averaged force was established in two different FRV models with a finite element simulation in COMSOL. This relation was subsequently used to create flow resistance coefficients based on volume averaged expressions of fluid velocity and volume forces. These flow resistance coefficients were implemented in two respective porous models, which represent the entire heat exchanger except the interior arrangements of fins and tube bundles. Hence, the computation time was reduced thanks to the absence of a dense mesh grid. Experimental results of the entire heat exchanger showed good agreement with the second porous model in terms of pressure drop and volume flow rate.     

Observability and reachability for parallel-flow heat exchanger equations

^** Email: sano{at}cc.kagoshima-u.ac.jp This paper is concerned with the dynamical analysis of parallel-flowheat exchanger equations with observation at the outlet of tube/controlat the inlet of tube. The parallel-flow heat exchanger equationis super-stable under zero boundary condition. The system canbe described by an unbounded operator of lower triangular formthrough a variable transformation. By calculating a C₀-semigroupgenerated by the operator, it is shown that the system is observableif both fluid temperatures are measured at the outlet, and thatthe system is observable with respect to the non-negative coneof the state space if either of them is measured at the outlet.Moreover, it is shown that the system is reachable if both fluidtemperatures are controlled at the inlet, and that the systemis reachable with respect to the non-negative cone of the statespace if either of them is controlled at the inlet.     

Integrated technique assessment based on the pinch analysis approach for the design of production networks

Integrated Process Design aims at a holistic approach to process design, retrofitting, and operations planning. Cost and energy “targets” (i.e. the minimum possible values for these objectives) can be calculated based on pinch technology, which defines the enthalpy at which the hot and cold process streams are separated by the minimum temperature difference in heat exchanger networks. This approach is well established in process engineering and has recently been expanded to mass pinch analysis. The combination of engineering, process integration and Operations Research allows the consideration of a variety of economic and environmental process attributes for an integrated technique assessment, as a case study in the sector of automotive serial coating shows.     

Multi-objective optimization of heat exchangers using a modified teaching-learning-based optimization algorithm

Teaching-learning-based optimization (TLBO) is a recently developed heuristic algorithm based on the natural phenomenon of teaching-learning process. In the present work, a modified version of the TLBO algorithm is introduced and applied for the multi-objective optimization of heat exchangers. Plate-fin heat exchanger and shell and tube heat exchanger are considered for the optimization. Maximization of heat exchanger effectiveness and minimization of total cost of the exchanger are considered as the objective functions. Two examples are presented to demonstrate the effectiveness and accuracy of the proposed algorithm. The results of optimization using the modified TLBO are validated by comparing with those obtained by using the genetic algorithm (GA).     

Numerical study of melting in an enclosure with discrete protruding heat sources

In order to explore the capability of a solid–liquid phase change material (PCM) for cooling electronic or heat storage applications, melting of a PCM in a vertical rectangular enclosure was studied. Three protruding generating heat sources are attached on one of the vertical walls of the enclosure, and generating heat at a constant and uniform volumetric rate. The horizontal walls are adiabatic. The power generated in heat sources is dissipated in PCM (n-eicosane with the melting temperature, T_m = 36 °C) that filled the rectangular enclosure. The advantage of using PCM is that it is able to absorb high amount of heat generated by heat sources due to its relatively high energy density. To investigate the thermal behaviour and thermal performance of the proposed system, a mathematical model based on the mass, momentum and energy conservation equations was developed. The governing equations are next discretised using a control volume approach in a staggered mesh and a pressure correction equation method is employed for the pressure–velocity coupling. The PCM energy equation is solved using the enthalpy method. The solid regions (wall and heat sources) are treated as fluid regions with infinite viscosity and the thermal coupling between solid and fluid regions is taken into account using the harmonic mean of the thermal conductivity method. The dimensionless independent parameters that govern the thermal behaviour of the system were next identified. After validating the proposed mathematical model against experimental data, a numerical investigation was next conducted in order to examine the thermal behaviour of the system by analyzing the flow structure and the heat transfer during the melting process, for a given values of governing parameters.     

Graphical Explanation in Belief Networks

Abstract

Belief networks provide an important bridge between statistical modeling and expert systems. This article presents methods for visualizing probabilistic “evidence flows” in belief networks, thereby enabling belief networks to explain their behavior. Building on earlier research on explanation in expert systems, we present a hierarchy of explanations, ranging from simple colorings to detailed displays. Our approach complements parallel work on textual explanations in belief networks. Graphical-Belief, Mathsoft Inc.'s belief network software, implements the methods.     

On blow-up solutions for systems of semilinear heat equations with quadratic nonlinearities

This article deals with blow-up solutions of the Cauchy–Dirichlet problem for system of semilinear heat equations with quadratic non-linearities. Sufficient conditions for the existence of blow-up solutions are established. Sets of initial values for these solutions as well as upper bounds for corresponding blow-up time are determined. Furthermore, an application to the Lotka-Volterra system with diffusion is also discussed. The result of this article may be considered as a continuation and a generalization of the results obtained in (Baris, J., Baris, P. and Ruchlewicz, B., 2006, On blow-up solutions of nonautonomous quadratic differential systems. Differential Equations, 42, 320–326; Baris, J., Baris, P. and Wawiórko, E., 2006, Asymptotic behaviour of solutions of Lotka-Volterra systems. Nonlinear Analysis: Real World Applications, 7, 610–618; Baris, J., Baris, P. and Ruchlewicz, B., 2006, On blow-up solutions of quadratic systems of differential equations. Sovremennaya Matematika. Fundamentalnye Napravleniya, 15, 29–35 (in Russian); Baris, J. and Wawiórko, E., On blow-up solutions of polynomial Kolmogorov systems. Nonlinear Analysis: Real World Applications, to appear).     

Modelling and simulation of heat exchange and moisture content in a cereal storage silo

ABSTRACT

In this paper, a mathematical model is developed based on the heat transfer of stored grains aerated in a cylindrical silo. This work is a part of study that aims to model the whole process of cereal storage system including a dehumidifier. The use of dehumidifier is intended to remove excess moisture from the airflow injected by the ventilator system in the silo filled with wheat, and to keep hygroscopic properties of grain in safe level during the storage period. Temperature and humidity are the two important variables coupled to control the process and to preserve grain quality. The laboratory device permitted us to achieve several tests for different conditions of grain stored in silo without aeration. A simulation of the airflow through the thermal space of the silo and grain parameters has been carried out. The results are reasonably in agreement with experiments and other published data. The system performance is evaluated at critical conditions of storage boundaries.     

Flexible Energy Management and Heat Exchanger Network Design

The design of heat exchanger networks (HEN) is a well-studied problem in process synthesis and an ideal test base to benchmark methods and techniques in the field. Despite a significant number of relevant publications, networks are still designed under assumptions of fixed operating conditions. Significant variations in supply and demand, alongside a need for efficient management in energy markets (energy grids, deregulated markets), impose limitations to this practice. Networks, designed with thermodynamic and economic efficiency under nominal operation, are known to have their efficiency dissipated and wasted in a context of similar though different conditions and demands. In a process plant, operational changes are common but designers still favor the staged approach of Pinch Technology (i.e., targeting-network development) where flexibility is not addressed properly and systematically. Alternatively, superstructure methods offer formulations with complexities hard to address by conventional algorithms. In this work, flexibility is addressed in a context amenable to targeting and network development stages, offering opportunities to visualise solutions and review options. For targeting, a dual approach is proposed that follows the framework of Hypertargets by Briones and Kokossis (1999a, 1999b, 1999c). The conceptual screening involves (i) the selection of cost-effective (primal) matches, and (ii) a model-based approach to assess the flexibility of the design options. Models and procedures are employed to assess trade-offs between operating cost (energy), capital cost (area), and the options' ability to handle variations (flexibility). Primal matches are automatically developed into network configurations with the use of mathematical models. A rigorous, superstructure-based approach is next applied to ensure the development of networks capable of handling operational variations without a need to consider exhaustive combinations of scenarios. The iterative approach incrementally augments the mathematical formulation by constraints and vertex conditions that guarantee consistency. The procedure is illustrated with two industrial problems and reports important improvements over conventional techniques.     

Weak solutions to a stationary heat equation with nonlocal radiation boundary condition and right‐hand side in Lp (p⩾1)

Accurate modelling of heat transfer in high‐temperature situations requires accounting for the effect of heat radiation. In complex industrial applications involving dissipative heating, we hardly can expect from the mathematical theory that the heat sources will be in a better space than L¹. In this paper, we focus on a stationary heat equation with nonlocal boundary conditions and L^p right‐hand side, with p?1 being arbitrary. Thanks to new coercivity results, we are able to produce energy estimates that involve only the L^p norm of the heat sources and to prove the existence of weak solutions. Copyright © 2008 John Wiley & Sons, Ltd.     

Computing availability for redundant flow systems

There are many papers in the literature about computing reliability for binary redundant systems. However in the real world there are many systems, whose economics depend on average availability of flow throughout the life span of the system rather than reliability on one particular threshold level only. Such systems exist in oil and gas redundant flow networks. To best of this author’s knowledge no attempt has been made yet to compute availability of such systems. Computing availability of flow is of utmost importance for the economical planning and design of any industrial flow networks. In this paper an approach is proposed to compute availability of flow in redundant flow systems. The proposed approach is compared with the approach used in the weighted $k$ -out-of- $n$ systems for computing reliability. The results show the better performance of the proposed approach in terms of computational time if the system bears heavier weights. Furthermore proposed scheme has additional advantage of being capable of handling fractional weights.     

Tractable stochastic analysis in high dimensions via robust optimization

Modern probability theory, whose foundation is based on the axioms set forth by Kolmogorov, is currently the major tool for performance analysis in stochastic systems. While it offers insights in understanding such systems, probability theory, in contrast to optimization, has not been developed with computational tractability as an objective when the dimension increases. Correspondingly, some of its major areas of application remain unsolved when the underlying systems become multidimensional: Queueing networks, auction design in multi-item, multi-bidder auctions, network information theory, pricing multi-dimensional options, among others. We propose a new approach to analyze stochastic systems based on robust optimization. The key idea is to replace the Kolmogorov axioms and the concept of random variables as primitives of probability theory, with uncertainty sets that are derived from some of the asymptotic implications of probability theory like the central limit theorem. In addition, we observe that several desired system properties such as incentive compatibility and individual rationality in auction design are naturally expressed in the language of robust optimization. In this way, the performance analysis questions become highly structured optimization problems (linear, semidefinite, mixed integer) for which there exist efficient, practical algorithms that are capable of solving problems in high dimensions. We demonstrate that the proposed approach achieves computationally tractable methods for (a) analyzing queueing networks, (b) designing multi-item, multi-bidder auctions with budget constraints, and (c) pricing multi-dimensional options.     

MULTIQ: A Queueing Model for FMSs with Several Pallet Types

Analytical modelling of the work flow through flexible manufacturing systems (FMSs), based on closed queueing network models, has been successfully applied to the early stages of design and analysis of FMSs. This paper describes the advantages of using multiple job-class closed queueing networks for modelling realistic situations occurring in FMSs. The general modelling of FMSs by closed queueing networks is first reviewed. The way Solberg's CAN-Q—a single job-class queueing-based package—deals with several part types is clarified. A new model called MULTIQ, allowing multiple pallet types, each of which is used by several part types, is proposed. Results are derived using the data from an existing FMS. The use of the MULTIQ model for optimization purposes is suggested by some examples.     

Rough hypoellipticity for the heat equation in Dirichlet spaces

This paper aims at proving the local boundedness and continuity of solutions of the heat equation in the context of Dirichlet spaces under some rather weak additional assumptions. We consider symmetric local regular Dirichlet forms, which satisfy mild assumptions concerning (1) the existence of cut-off functions, (2) a local ultracontractivity hypothesis, and (3) a weak off-diagonal upper bound. In this setting, local weak solutions of the heat equation, and their time derivatives, are shown to be locally bounded; they are further locally continuous, if the semigroup admits a locally continuous density function. Applications of the results are provided including discussions on the existence of locally bounded heat kernel; $L^{\infty }$ structure results for ancient (local weak) solutions of the heat equation.