A simplified two-dimensional (2-D) formulation for FCC risers has been developed. The model approximates the mixture of gasoil, steam, and solid catalyst that flows inside the riser reactor by an equivalent fluid with average properties. The cracking reactions are modeled by a 6-lump kinetic model combined with two energy equations (gas and solid). Due to the adopted simplifications, a fast and simple-to-solve computational code was written; nevertheless, it still is sufficiently precise to be used for the design of new units and for system control and optimization of operating conditions of FCC risers. The validation of the proposed model was performed by direct comparison of the obtained results with available experimental data for a multi-purpose pilot FCC riser unit. The model was then utilized to simulate an actual size industrial FCC riser. The obtained numerical results in this article demonstrate that the model can be used as a powerful and simple tool for design, control, and optimization of FCC units, combining accuracy with low computational time to obtain solutions when simulating actual FCC riser operation. © 2006 American Institute of Chemical Engineers AIChE J, 2006

This paper summarizes a series of works on thermodynamic optimization of heat exchanger area allocation for power and refrigeration plants. It is shown that the thermodynamic optimum is pinpointed by an optimal distribution of the heat exchanger area inventory among the heat exchangers of the installation. Hot-stream-driven power producing devices, solar-driven refrigerators and a combined(1) power and refrigeration systems are discussed. The optimal allocation of heat exchanger area appears as a common result for all the installations.

This paper presents a theoretical, numerical, and experimental study to investigate the possibility of optimizing the configuration (geometry) of underground heat exchangers for maximum heat transfer. The first part of the study identifies a novel fundamental optimization principle for maximizing heat transfer between a tube and its surroundings, which is expected to be present in any buried tube heat exchanger design. The second part presents a practical application of the fundamental principle: a simplified physical model to determine the temperature field inside an electronics shelter that uses an earth-air heat exchanger and the soil as a heat sink. A volume elements methodology is employed to obtain a system of ordinary differential equations with time as the independent variable that combines principles of classical thermodynamics and heat transfer. This allows the computation of the temperature and relative humidity fields at every instant inside the shelter. The numerical results obtained with the proposed model are validated by means of direct comparison with experimental temperature and relative humidity measurements. It is shown that the tube length can be optimized such that the maximum temperature reached inside the shelter is minimal. The results also demonstrate the potential of the utilization of buried tubes for cooling electronic packages. Since accuracy and low computational time are combined, the model is shown to be efficient and could be used as a tool for simulation, design, and optimization of electronic packages cooled by underground heat exchangers.

This paper describes a structured procedure to optimize the internal structure (relative sizes, spacings), single cells thickness, and external shape (aspect ratios) of a polymer electrolyte membrane fuel cell (PEMFC) stack so that net power is maximized. The constructal design starts from the smallest (elemental) level of a fuel cell stack (the single PEMFC), which is modeled as a unidirectional flow system, proceeding to the pressure drops experienced in the headers and gas channels of the single cells in the stack. The polarization curve, total and net power, and efficiencies are obtained as functions of temperature, pressure, geometry and operating parameters. The optimization is subjected to fixed stack total volume. There are two levels of optimization: (i) the internal structure, which accounts for the relative thicknesses of two reaction and diffusion layers and the membrane space, together with the single cells thickness, and (ii) the external shape, which accounts for the external aspect ratios of the PEMFC stack. The flow components are distributed optimally through the available volume so that the PEMFC stack net power is maximized. Numerical results show that the optimized single cells internal structure and stack external shape are “robust” with respect to changes in stoichiometric ratios, membrane water content, and total stack volume. The optimized internal structure and single cells thickness, and the stack external shape are results of an optimal balance between electrical power output and pumping power required to supply fuel and oxidant to the fuel cell through the stack headers and single-cell gas channels. It is shown that the twice maximized stack net power increases monotonically with total volume raised to the power 3/4, similarly to metabolic rate and body size in animal design.

In this study, an alternative solution to reduce energy consumption in industrial refrigeration systems is proposed and introduced. A typical industrial refrigeration system was conceived, built and modified in the laboratory, receiving a novel power law control system, which utilizes a frequency inverter. The operation and energy consumption of the system operating either with the new control system or with the traditional on–off control were compared to realistically quantify the obtained gains. In this manner, the measured temperature data acquired from several points of both systems and the energy consumption in kWh during a 24h experimental run period are compared. The closed-loop power law controlled system shows a much smaller variation of the cold chamber internal temperature and electrical energy consumption economy of 35.24% in comparison with the traditional on–off system, under the same operating conditions.

This paper presents a three-dimensional numerical and experimental geometric optimization study to maximize the total heat transfer rate between a bundle of finned tubes in a given volume and external flow, for staggered arrangements of circular and elliptic tubes. Experimental results were obtained for circular and elliptic configurations with twelve tubes, starting with an equilateral triangle configuration, which fitted uniformly into the fixed volume with a resulting optimal dimensionless tube-to-tube spacing of S/2b=1.5, where S is the actual spacing and b is the smaller semi-axis of the ellipse. Several experimental configurations were built by reducing the tube-to-tube spacings, identifying the optimal spacing for maximum heat transfer. Similarly, it was possible to investigate the existence of optima with respect to two other geometric degrees of freedom, such as tube eccentricity and fin-to-fin spacing. The results are reported for air as the external fluid in the laminar regime, for ReL=852 and 1065, where L is the swept length of the fixed volume. Circular and elliptic arrangements with the same flow obstruction cross-sectional area were compared on the basis of maximizing the total heat transfer. This criterion allows one to isolate and quantify the heat transfer gain, by studying arrangements with equivalent total pressure drops independently of the tube cross-section shape. This paper continues with three-dimensional numerical optimization results for finned circular and elliptic tubes arrangements, which are validated by direct comparison with experimental measurements. Global optima with respect to tube-to-tube spacing, eccentricity and fin-to-fin spacing (S/2b≅0.5, e≅0.5, φf≅0.06 for ReL=852 and 1065) were found and reported in dimensionless terms. A relative heat transfer gain of up to 19% is observed in the optimal elliptic arrangement, as compared to the optimal circular one. The heat transfer gain, combined with the relative material mass reduction of up to 32% observed in the optimal elliptic arrangement in comparison to the circular, show that the elliptical tubes arrangement has better overall performance and lower cost than the traditional circular tubes geometry.

This work presents a three-dimensional (3-D) numerical and experimental geometric optimization study to maximize the total heat transfer rate between a bundle of finned tubes in a given volume and a given external flow both for circular and elliptic arrangements, for general staggered configurations. The optimization procedure started by recognizing the design limited space availability as a fixed volume constraint. The experimental results were obtained for circular and elliptic configurations with a fixed number of tubes (12), starting with an equilateral triangle configuration, which fitted uniformly into the fixed volume with a resulting maximum dimensionless tube-to-tube spacing S/2b = 1.5, where S is the actual spacing and b is the smaller ellipse semi-axis. Several experimental configurations were built by reducing the tube-to-tube spacings, identifying the optimal spacing for maximum heat transfer. Similarly, it was possible to investigate the existence of optima with respect to other two geometric degrees of freedom, i.e., tube eccentricity and fin-to-fin spacing. The results are reported for air as the external fluid in the laminar regime, for 125 and 100 Re 2b , where 2b is the ellipses smaller axis length. Circular and elliptic arrangements with the same flow obstruction cross-sectional area were compared on the basis of maximum total heat transfer. This criterion allows one to quantify the heat transfer gain in the most isolated way possible, by studying arrangements with equivalent total pressure drops independently of the tube cross section shape. This paper reports three-dimensional (3- D) numerical optimization results for finned circular and elliptic tubes arrangements, which are validated by direct comparison with experimental measurements with good agreement. Global optima with respect to tube-to-tube spacing, eccentricity and fin-tofin spacing ( 0.5 e 0.5, S/2b and 06 . 0 f for 125 and 100 Re 2b , respectively) were found and reported in general dimensionless variables. A relative heat transfer gain of up to 19% is observed in the optimal elliptic arrangement, as compared to the optimal circular one. The heat transfer gain, combined with the relative material mass reduction of up to 32% observed in the optimal elliptic arrangement in comparison to the circular one, show the elliptical arrangement has the potential for a considerably better overall performance and lower cost than the traditional circular geometry.

This paper introduces a model and a structured procedure to optimize the internal structure (relative sizes, spacings) and external shape (aspect ratios) of a unit PEM fuel cell so that net power is maximized. The optimization of flow geometry is conducted for the smallest (elemental) level of a fuel cell stack, i.e., the unit PEM fuel cell, which is modeled as a unidirectional flow system. The polarization curve, total and net power, and efficiency are obtained as functions of temperature, pressure, geometry and operating parameters. The optimization is subjected to fixed total volume. There are two levels of optimization: (i) the internal structure, which basically accounts for the relative thicknesses of two reaction and diffusion layers and the membrane space, and (ii) the external shape, which accounts for the external aspect ratios of a square section plate that contains all unit PEM fuel cell components. The available volume is distributed optimally through the system so that the net power is maximized. Temperature and pressure gradients play important role, especially as the fuel and oxidant flow paths increase. Numerical results show that the optimized internal structure is “robust” with respect to changes in external shape. The optimized internal structure and external shape are a result of an optimal balance between electrical power output and pumping power required to supply fuel and oxidant to the fuel cell through the gas channels. Directions for future improvements at the PEM fuel cell stack level in flow architecture (constructal design) are discussed.

This paper shows that the internal structure (relative sizes, spacings) of a fuel cell can be optimized so that performance is maximized at the global level. The optimization of flow geometry begins at the smallest (elemental) level, where the fuel cell is modelled as a unidirectional flow system. The polarization curve, power and efficiency are obtained as functions of temperature, pressure, geometry and operating parameters. Although the model is illustrated for an alkaline fuel cell, it may be applied to other fuel cell types by changing the reaction equations and accounting for the appropriate energy interactions. The optimization of the internal structure is subjected to fixed total volume. There are four degrees of freedom in the optimization, which account for the relative thicknesses of the two (anode and cathode) diffusion layers, two reaction layers and the space occupied by the electrolyte solution. The available volume is distributed optimally through the system so that the total power is maximized. Numerical results show that the optima are sharp, and must be identified accurately. Temperature and pressure gradients play important roles, especially as the fuel and oxidant flow paths increase. The optimized internal structure is reported in dimensionless form. Directions for future improvements in flow architecture (constructal design) are discussed. Copyright © 2004 John Wiley & Sons, Ltd.

Heat transfer from a surface in motion relative to either a stationary or moving fluid occurs in many materials processing applications such as hot rolling, extrusion, drawing, and drying. In this study, an analysis has been carried out to predict the convective transport occurring between air and a continuous inclined surface which moves with an assisting or opposing flow with respect to the free stream in the presence of gravity. The steady flow of air is assumed laminar and is modeled by using a two dimensional (2-D) complete set of conservation equations, subject to the appropriate boundary conditions. The equations were solved numerically by employing the finite element method. Predictions for the local dimensionless skin friction and heat transfer are made for different configurations of the relative position of the surface and the free stream. The numerical results of the present study for the buoyancy-assisting and opposing flows on vertical surfaces are validated by direct comparison with the available published data. New results are presented for inclined surfaces with the buoyancy-assisting and opposing flows. The buoyancy-assisting results are then correlated for wide ranges of inclination angles and moving sheet relative velocities.

The authors believe that reducing the size of solar-driven refrigerators and air conditioning systems will make them more attractive to potential users. This paper presents a contribution to understanding the behaviour of such systems with a view to determining the manner in which refrigeration rate, mass flows and heat transfer areas are related. The intention is to make possible the identification of preliminary design rules. The basic thermodynamic problem of how to obtain maximum exergy input rate in a solar-driven refrigerator is considered. The existence of an optimal refrigerant flow rate for maximum refrigeration is investigated. The analysis proceeds by relating the entropy generation rate, the physical and operating parameters, and the constraints of the system, through well-established heat transfer relationships. Finally, a thermodynamic analysis determines the optimal characteristics that lead to minimum entropy generation. The second law efficiency is identified as the appropriate figure of merit for the thermodynamic optimum. Copyright (C) 2001 John Wiley & Sons, Ltd.

This paper considers the fundamental problem of optimizing the geometry of the interface between two conductive bodies, with the objective of minimizing the thermal resistance. The interface geometry is free to change. For simplicity, the geometry is assumed to be two-dimensional with equidistant tooth-shaped features. The tooth shape varies from triangles, to trapezoids and rectangles. The aspect ratio (height/width) of the tooth also varies. The third degree of freedom of the interface architecture is the volume fraction of the higher-conductivity tooth material that is present in the interface region. It is shown that the interface geometry can be optimized with respect to tooth shape. The global thermal resistance minimized with respect to tooth shape varies monotonically with the tooth aspect ratio and volume fraction. The optimized geometry and performance are reported graphically as functions of the physical properties and geometric parameters of the interface region.

This paper introduces a general computational model for electronic packages, e.g., cabinets that contain electronic equipment. A simplified physical model, which combines principles of classical thermodynamics and heat transfer, is developed and the resulting three-dimensional differential equations are discretized in space using a three-dimensional cell centered finite volume scheme. Therefore, the combination of the proposed simplified physical model with the adopted finite volume scheme for the numerical discretization of the differential equations is called a volume element model (VEM). A typical cabinet was built in the laboratory, and two different experimental conditions were tested, measuring the temperatures at forty-six internal points. The proposed model was utilized to simulate numerically the behavior of the cabinet operating under the same experimental conditions. Mesh refinements were conducted to ensure the convergence of the numerical results. The converged mesh was relatively coarse (504 cells), therefore the solutions were obtained with low computational time. The model temperature results were directly compared to the steady-state experimental measurements of the forty-six internal points, with good quantitative and qualitative agreement. Since accuracy and low computational time are combined, the model is shown to be efficient and could be used as a tool for simulation, design, and optimization of electronic packages.

This paper documents the process of determining the internal geometric configuration of a component by optimizing the global performance of the installation that uses the component. The example chosen is the crossflow heat exchanger used in the environmental control system of a modern aircraft. The optimization of global performance is achieved by minimizing the total entropy generation rate of the installation. There are three degrees of freedom in the heat exchanger configuration (the length-to-width and height-to-width aspect ratios, and the separator plate spacing ratio), which is subjected to two global constraints: total component volume, and total wall material volume (or weight/density) of wall material. Numerical results show how the optimal configuration responds to changes in specified external parameters such as volume, weight, Mach number, diffuser inlet cross-sectional area, and the pressure at which the cabin air is initially bled from the engine compressor. It is shown that the optimal configuration is robust and that major features such as the ratios of channel spacings and flow lengths are relatively insensitive to changes in some of the external parameters. It is also shown that the optimal heat exchanger geometry is insensitive to the thermodynamic irreversibility caused by discharging the used ram air into the ambient.

In this paper we propose to optimize the geometric configuration of a component by maximizing the global thermodynamic performance of the much larger system that contains the component. This "integrative" approach departs from current thermodynamic optimization practice in which the configuration of a component (e.g., heat exchanger) is optimized by itself, in isolation. In the present example the larger system is an aircraft and the component is its environmental control system (ECS). We show that the configuration of the ECS impacts the performance (exergy destruction, fuel consumption) of the aircraft in two ways, not one: through its own irreversibility, and its weight-related contribution to the power required to sustain the flight. By minimizing the thermodynamic losses at the aircraft level, we deduce all the geometric details of the cross-flow heat exchanger that dominates the weight and structure of the ECS. The optimized geometry is robust with respect to changes in some of the operating parameters that have to be specified. The integrative method illustrated in this paper is generally applicable to the optimization of architecture in other systems where all the functions are driven by the exergy of the fuel installed onboard.

In this study, a two-dimensional (2-D) heat transfer analysis was performed in circular and elliptic tube heat exchangers. The finite element method was used to discretize the fluid flow and heat transfer governing equations and a 2-D isoparametric, four-noded, linear element was implemented for the finite element analysis program, FEAP (O.C. Zienkiewicz, R.L. Taylor, The Finite Element Method, vol. 1, McGraw-Hill, London, 1989, Chapter 15). The numerical results for the equilateral triangle staggering configuration, obtained with the new element were then validated qualitatively by means of direct comparison to previously published experimental results for circular tubes heat exchangers (G. Stanescu, A.J. Fowler, A. Bejan, Int. J. Heat Mass Transfer 39 (2) (1996) 311-317). Next, a numerical geometric optimization was conducted to maximize the total heat transfer rate between the given volume and the given external flow both for circular and elliptic arrangements, for general staggering configurations. The results are reported for air in the range 300 less than or equal to Re-L less than or equal to 800, where L is the swept length of the fixed volume. Circular and elliptical arrangements with the same flow obstruction cross-sectional area were compared on the basis of maximum total heat transfer. The effect of ellipses eccentricity was also investigated. A relative heat transfer gain of up to 13% is observed in the optimal elliptical arrangement, as compared to the optimal circular one. The heat transfer gain, combined with the relative pressure drop reduction of up to 25% observed in previous studies (H. Brauer, Chem. Process Eng., August (1964) 451-460; S.N. Bordalo, F.E.M. Saboya, Determinacao experimental dos coeficientes de perda de carga em trocadores de calor de tubos circulares e elipticos aletados, in: Proceedings of the 13th COBEM, Congresso Brasileiro de Engenharia Mecanica (in Portuguese), Belo Horizonte, Brasil, 1995) show that the elliptical arrangement has the potential for a considerably better overall performance than the traditional circular one. (C) 2001 Published by Elsevier Science Ltd.

This paper considers the basic thermodynamic optimization problem of extracting the most power from a stream of hot exhaust when the contact heat transfer area is fixed. It shows that when the receiving (cold) stream boils in the counterflow heat exchanger, the thermodynamic optimization consists of locating the optimal capacity rate of the cold stream. At the optimum, the cold side of the heat transfer surface divides itself into three sections: liquid preheating, boiling and vapor superheating. Numerical results are developed for a range of design parameters of applications with either water or toluene on the cold side. It is shown that the optimal design is robust, because several of the design parameters have only a weak effect on the optimal design.

The optimum thermodynamic match between two streams at different temperatures is determined by maximizing the power generation (or minimizing the entropy generation) associated solely with the stream-to-stream interaction. Each stream experiences a change of phase. It is shown that the optimum is marked by an optimal ratio between the stream mass flow rates, and an optimal ratio between the two heat exchanger sizes when the total heat transfer area is fixed. The sensitivity of the optimum relative to the various physical parameters of the two-stream arrangement is documented systematically. The study shows that the optimum is “robust” relative to changes in several parameters such as the distribution of heat transfer coefficient along the hot-end heat exchanger, and the model used for the thermodynamic behavior of steam.

The present work introduces a transient endoreversible model of a heat-driven refrigeration plant, which is driven by a fuel-burning heater The model consists of a combustion chamber with negligible heat loss to the ambient, a refrigerator with three finite-size heat exchangers, namely, the evaporator between the refrigeration load and refrigerant, the condenser between the refrigerant and the ambient, and the generator between the combustion chamber and the refrigerant, and finally the refrigerated space. The total thermal conductance of the three heat exchangers is fixed. A thermodynamic optimization of the absorption cycle is then performed, reporting the operating conditions for minimum time to reach a prescribed cold-space temperature, thus maximum refrigeration rate, specifically the optimal mass fuel flow rate and the optimal way of allocating the thermal conductance inventory. Half of the total supply of thermal conductance has to be divided equally between the generator and evaporator and the other half allocated to the condenser for optimal operation. A narrow range of fuel flow rates lead to the minimum time to achieve a prescribed cold-space temperature, thus stressing the importance of the transient analysis. Appropriate dimensionless groups were identified and the generalized results are reported in dimensionless charts.

This is a theoretical and experimental study of the time-optimisation of condensation on a vertical wall when the film is removed periodically by a mechanical device. The objective is to fine-tune the periodic process so that the production of condensate and the heat transfer rate are maximal. The first part of the paper develops the scales of the periodic condensation process, and predicts the existence of an optimal condensation time interval. The analysis also predicts that the augmentation of condensation increases as the mechanical cleaning time decreases. These design optimisation opportunities are confirmed in the second part of the paper, which reports measurements of steam condensation on a vertical surface scraped periodically. (c) Elsevier, Paris. (C)Elsevier, Paris.