Thermodynamic and Economic Optimization of Plate Fin Heat Exchangers Using the Bees Algorithm

This study presents the successful application of the bees algorithm (BA) for optimal design of a cross‐flow plate fin heat exchanger by offset strip fins. The ε – NTU method is used to approximate the heat exchanger effectiveness and pressure drop. Two different objective functions including the minimization of total annual cost (sum of investment and operational costs) and total number of entropy generation units for certain heat duty required under given space constraints are considered as targets of optimization separately. Based on the applications, seven design parameters (heat exchanger length at hot and cold sides, fin height, fin frequency, fin thickness, fin‐strip length, and number of hot side layers) are selected as optimization variables. Two examples from the literature are presented to illustrate the efficiency and accuracy of the proposed algorithm. Results showed that the BA can detect an optimum configuration with higher speed (short computational time) and accuracy compared to the imperialist competitive algorithm (ICA) and the genetic algorithm (GA). © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(5): 427–446, 2014; Published online 3 October 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21087     

Thermodynamic optimization of cross flow plate-fin heat exchanger using a particle swarm optimization algorithm

This study explores the use of particle swarm optimization (PSO) algorithm for thermodynamic optimization of a cross flow plate-fin heat exchanger. Minimization of total number of entropy generation units for specific heat duty requirement under given space restrictions, minimization of total volume, and minimization of total annual cost are considered as objective functions and are treated individually. Based on the applications, heat exchanger length, fin frequency, numbers of fin layers, lance length of fin, fin height and fin thickness or different flow length of the heat exchanger are considered for optimization. Heat duty requirement constraint is included in the procedure. Two application examples are also presented to demonstrate the effectiveness and accuracy of the proposed algorithm. The results of optimization using PSO are validated by comparing with those obtained by using genetic algorithm (GA). Parametric analysis is also carried out to demonstrate the effect of heat exchanger dimensions on the optimum solution. The effect of variation of PSO parameters on convergence and optimum value of the objective has also been presented.     

Multiobjective thermo‐economic and thermodynamics optimization of a plate–fin heat exchanger

In the present work, a multiobjective heat transfer search (MOHTS) algorithm is proposed and investigated for thermo‐economic and thermodynamic optimization of a plate–fin heat exchanger (PFHX). Heat exchanger effectiveness and total annual cost (TAC) are considered as thermo‐economic objective functions. Similarly, entropy generation rate and heat exchanger effectiveness are considered as thermodynamic objective functions. Six design variables including flow length of cold and hot streams, no flow length, fin height, fin pitch, and fin offset length are considered as decision variables. Effectiveness and accuracy of the proposed algorithm are evaluated by analyzing application examples of a PFHX. The results obtained using the proposed algorithm for thermo‐economic considerations are compared with the available results of NSGA‐II and TLBO in the literature. Results show that 3.56% to 10.29% reductions in TAC with 0.48% to 0.81% higher effectiveness are observed using the proposed approach compared to TLBO and NSGA‐II approaches. Additionally, the distribution of each design variable in its allowable range is also shown for thermo‐economic consideration to identify the level of conflict on objective functions. The sensitivity analyses of design variables on the objective functions value are also performed in detail.     

应用遗传算法优化设计紧凑式换热器

应用遗传算法对锯齿型板翅式换热器的结构进行了优化设计.以预定的传热量、两侧压降、体积等设计要求为适应度函数,通过对设计变量构成的种群个体进行适应度评估以及选择、交叉、变异等遗传操作,得到符合设计约束的换热器最优结构参数(如翅高、翅长、间距,以及长、宽、高等).此外,对10次计算得到的设计参数进行了统计分析.结果表明:相关结构参数的不确定度很小,应用遗传算法可以快速方便地对紧凑式换热器的几何结构参数作出符合设计要求的选择.     

Thermal-economic multi-objective optimization of plate fin heat exchanger using genetic algorithm

Thermal modeling and optimal design of compact heat exchangers are presented in this paper. ε–NTU$\epsilon ''–''\mathit{NTU}$ method was applied to estimate the heat exchanger pressure drop and effectiveness. Fin pitch, fin height, fin offset length, cold stream flow length, no-flow length and hot stream flow length were considered as six design parameters. Fast and elitist non-dominated sorting genetic-algorithm (NSGA-II) was applied to obtain the maximum effectiveness and the minimum total annual cost (sum of investment and operation costs) as two objective functions. The results of optimal designs were a set of multiple optimum solutions, called ‘Pareto optimal solutions’. The sensitivity analysis of change in optimum effectiveness and total annual cost with change in design parameters of the plate fin heat exchanger was also performed and the results are reported. As a short cut for choosing the system optimal design parameters the correlations between two objectives and six decision variables with acceptable precision were presented using artificial neural network analysis.     

An optimization study on the finned tube heat exchanger used in hydride hydrogen storage system – analytical method and numerical simulation

Metal hydrides show great potential for hydrogen storage. However, for efficient hydrogen storage, thermal management is the technical barrier. Among the different heat exchangers proposed in the literature, finned tube heat exchangers are of great technological interest due to their adaptability to wide range of practical applications, high compactness and high heat transfer efficiency. In the present paper, the optimization of finned heat exchanger considering both enhanced heat transfer and vessel volume efficiency is conducted. A semi-analytical expression of heat transfer rate from a single fin is derived. The effects of fin dimension (fin thickness and radius) on the heat exchanger performance are studied. It was shown that the thermal resistance of the whole heat exchanger can be reduced by increasing the fin radius and decreasing the fin thickness, while the fin volume is kept fixed. In the second part of the study, a 2-D numerical simulation was performed in order to validate the results of the analytical study. The effects of two parameters (cooling tube diameter, the fin length) on the hydrogen charging time were highlighted. The increasing in the tube diameter from 2.5 mm to 5 mm results to 25% reduction of the charging time, which is very noticeable. On the other hand, given a reactor radius, increasing the length of fin reduces the overall thermal resistance of the reactor-heat exchanger. The results showed that the decreasing of the thermal resistance of 13% leads to a decreasing in charging time of 42%. Finally, it was found that the results of the numerical simulation agreed qualitatively with those of analytical study. Therefore, the analytical solution presented can be used for a quick assessment of the finned tube heat exchanger design without significant errors.     

Optimizing heat exchanger networks with genetic algorithms for designing each heat exchanger including condensers

This paper presents a procedure for the design of the components of a heat exchanger network (HEN). The procedure first uses pinch analysis to maximize heat recovery for a given minimum temperature difference. Using a genetic algorithm (GA), each exchanger of the network is designed in order to minimize its total annual cost. Eleven design variables related to the exchanger geometry are considered. For exchanger involving hot or cold utilities, mass flow rate of the utility fluid is also considered as a design variable. Partial or complete condensation of hot utility fluid (i.e., water vapor) is allowed. Purchase cost and operational cost are considered in the optimization of each exchanger. Combining every exchanger minimized cost with the cost of hot utility and cold utility gives the total cost of the HEN for a particular ΔT_min. The minimum temperature difference yielding the more economical heat exchanger network is chosen as the optimal solution. Two test cases are studied, for which we show the minimized total cost as a function of the minimum temperature difference. A comparison is also made between the optimal solution with the cost of utilities and without it.     

Applying multiple decomposition methods and optimization techniques for achieving optimal cost in mixed materials heat exchanger networks

The optimization of the total annual cost in heat exchanger networks has been one of the overarching goals when synthesizing these networks. Several methodologies and techniques have been developed to achieve optimal costs in mixed material heat exchanger networks. This paper demonstrates the application of two decomposition methodologies (total decomposition and partial decomposition) for typical cost rules. The objective function was defined as the optimization and minimization of the total annual cost in mixed materials heat exchanger network. Three optimization algorithms, hybrid genetic‐particle swarm optimization (GA‐PSO), shuffled frog leaping algorithm (SFLA) techniques, and ant colony optimization (ACO), were used to further optimize the total cost in mixed materials heat exchanger network. The results indicate that the total annual cost in partial decomposition method was smaller than that in full integration method and total decomposition method. The reduction of the total annual cost was about 27% for GA‐PSO algorithm, 24% for SFLA and 10% for ACO relative to the results reported in this work. In partial decomposition method, at least one mixed material of heat exchanger was used to reduce the hot and cold utility for decreasing the total annual cost. Partial decomposition method resulted in the highest reduction of the total annual cost compared with other methods. Percentage of difference of the total annual cost were 0.36%, 1.92%, and 5.05% for full integration, total decomposition, and partial decomposition methods, respectively, in comparison with the previous studies. Results have been compared with the results of other studies to demonstrate the accuracy of the applied algorithms.     

Exergetic Optimization of Shell-and-Tube Heat Exchangers Using NSGA-II

In this article, a multi-objective exergy-based optimization through a genetic algorithm method is conducted to study and improve the performance of shell-and-tube type heat recovery heat exchangers, by considering two key parameters, such as exergy efficiency and cost. The total cost includes the capital investment for equipment (heat exchanger surface area) and operating cost (energy expenditures related to pumping). The design parameters of this study are chosen as tube arrangement, tube diameters, tube pitch ratio, tube length, tube number, baffle spacing ratio, and baffle cut ratio. In addition, for optimal design of a shell-and-tube heat exchanger, the method and Bell–Delaware procedure are followed to estimate its pressure drop and heat transfer coefficient. A fast and elitist nondominated sorting genetic algorithm (NSGA-II) with continuous and discrete variables is applied to obtain maximum exergy efficiency with minimum exergy destruction and minimum total cost as two objective functions. The results of optimal designs are a set of multiple optimum solutions, called “Pareto optimal solutions.” The results clearly reveal the conflict between two objective functions and also any geometrical changes that increase the exergy efficiency (decrease the exergy destruction) lead to an increase in the total cost and vice versa. In addition, optimization of the heat exchanger based on exergy analysis revealed that irreversibility like pressure drop and high temperature differences between the hot and cold stream play a key role in exergy destruction. Therefore, increasing the component efficiency of a shell-and-tube heat exchanger increases the cost of heat exchanger. Finally, the sensitivity analysis of change in optimum exergy efficiency, exergy destruction, and total cost with change in decision variables of the shell-and-tube heat exchanger is also performed.     

A method to reduce the flow depth of a plate heat exchanger without a loss of heat transfer performance

With the aim of improving heat exchanger compactness, this study investigates how the optimum configuration of an air–liquid plate heat exchanger changes as the heat exchanger depth decreases. In this respect, optimization of an air–liquid plate heat exchanger with a given frontal area and a given depth is achieved. The optimum fin pitch and plate pitch are obtained to maximize the heat transfer rate based on heat transfer and pressure loss correlations in finned channels. Then, the focus of this study is placed on how the optimum channel configuration changes when the heat exchanger depth decreases for compactness. The results illustrate that the heat transfer performance can remain unchanged if the geometric parameters, such as the plate thickness, the plate pitch, the fin thickness, and the fin pitch, are reduced proportionally to the square root of the flow depth reduction given that the flow remains laminar. This finding is arranged into a simple scaling rule to obtain the configuration of a more compact heat exchanger from an existing configuration. In addition, the scaling arguments are extended to practical situations where the fin thickness and the plate thickness are not properly reduced following the scaling rule due to limitations on available material thicknesses.     

Heat transfer and pressure loss characteristics of a heat exchanger for recovering latent heat (effects of straight fin length and fin pitch on the heat transfer and pressure loss characteristics)

In recent years, the requirement for the reduction of energy consumption has been increasing to solve the problems of global warming and the shortage of petroleum resources. A latent heat recovery type heat exchanger is one of the effective methods for improving thermal efficiency by recovering latent heat. This paper describes the heat transfer and pressure loss characteristics of a latent heat recovery type heat exchanger having straight fins (fin length: 65 mm or 100 mm, fin pitch: 2.5 mm or 4 mm). These were clarified by measuring the exchange heat quantity, the pressure loss of the heat exchanger, and the heat transfer coefficient between the outer fin surface and gas. The effects of fin length and fin pitch on heat transfer and pressure loss characteristics were clarified. Furthermore, equations for predicting the heat transfer coefficient and pressure loss which are necessary for heat exchanger design were proposed. ©2007 Wiley Periodicals, Inc. Heat Trans Asian Res, 36(4): 230– 247, 2007; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20153 Copyright © 2004 Wiley Periodicals, Inc.     

Design and economic optimization of shell and tube heat exchangers using Artificial Bee Colony (ABC) algorithm

In this study, a new shell and tube heat exchanger optimization design approach is developed. Artificial Bee Colony (ABC) has been applied to minimize the total cost of the equipment including capital investment and the sum of discounted annual energy expenditures related to pumping of shell and tube heat exchanger by varying various design variables such as tube length, tube outer diameter, pitch size, baffle spacing, etc. Finally, the results are compared to those obtained by literature approaches. The obtained results indicate that Artificial Bee Colony (ABC) algorithm can be successfully applied for optimal design of shell and tube heat exchangers.     

Numerical computation for parallel plate thermoacoustic heat exchangers in standing wave oscillatory flow

A simplified computational method for studying the heat transfer characteristics of parallel plate thermoacoustic heat exchangers is presented. The model integrates the thermoacoustic equations of the standard linear theory into an energy balance-based numerical calculus scheme. Details of the time-averaged temperature and heat flux density distributions within a representative domain of the heat exchangers and adjoining stack are given. The effect of operation conditions and geometrical parameters on the heat exchanger performance is investigated and main conclusions relevant for HX design are drawn as far as fin length, fin spacing, blockage ratio, gas and secondary fluid-side heat transfer coefficients are concerned. Most relevant is that the fin length and spacing affect in conjunction the heat exchanger behavior and have to be simultaneously optimized to minimize thermal losses localized at the HX-stack junctions. Model predictions fit experimental data found in literature within 36% and 49% respectively at moderate and high acoustic Reynolds numbers.     

Optimum design of a longitudinal fin array with convection and radiation heat transfer using a genetic algorithm

In the present work, the optimization of a longitudinal fin array is investigated. Heat is transferred by conduction along the fins and dissipated from the fin surface via natural convection to the ambient and radiation to other fin surfaces and surrounding. The aim of the optimization is to find the optimum geometry and the number of fins in such a way that the rate of heat transfer from the array is maximized. A modified genetic algorithm is used to maximize the objective function which is defined as the net heat rate from the fin surface for a given length. The fin profile is represented by B-spline curves, where the shape of fin is determined by the positions of a set of control points. The effects of the base temperature, the fin length and the height of array on the optimum geometry and on the number of fins are investigated by comparing the results obtained for several test cases. In addition, the contributions of convective heat transfer and radiative heat transfer in net heat transfer are studied for these cases. The enhancement of heat transfer due to the optimum fin geometry is examined by comparing the results obtained for the optimum fin profile with those with conventional profiles.     

The heat transfer and pressure loss characteristics of a heat exchanger for recovering latent heat (the heat transfer and pressure loss characteristics of the heat exchanger with wing fin)

In recent years the requirement for reduction of energy consumption has been increasing to solve the problems of global warming and the shortage of petroleum resources. A latent heat recovery type heat exchanger is one of the effective methods of improving thermal efficiency by recovering latent heat. This paper described the heat transfer and pressure loss characteristics of a latent heat recovery type heat exchanger having a wing fin (fin pitch: 4 mm, fin length: 65 mm). These were clarified by measuring the exchange heat quantity, the pressure loss of heat exchanger, and the heat transfer coefficient between outer fin surface and gas. The effects of condensate behavior in the fins on heat transfer and pressure loss characteristics were clarified. Furthermore, the equations for predicting the heat transfer coefficient and pressure loss which are necessary in the design of the heat exchanger were proposed. ©2007 Wiley Periodicals, Inc. Heat Trans Asian Res, 36(4): 215–229, 2007; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20154     

Heat transfer and pressure drop characteristics of peripheral-finned tube heat exchangers

The peripheral-finned tube is a new geometry aimed at avoiding moisture-condensate blockage hindering of the air-side heat transfer, by allowing for robust air flow pathways. It consists of a porous structure formed by periodic, radial-hexagonal fin arrangements of different radial extents mounted with a 30° offset from its neighboring level. Here, the air-side pressure drop and the heat transfer characteristics of five different heat exchanger prototypes with different geometric characteristics, such as the radial fin length, fin distribution, and heat exchanger length, were evaluated experimentally in an open-loop wind-tunnel calorimeter. The results demonstrate the effective performance, i.e., the pressure drop and heat transfer characteristics, of this new heat exchanger. A one-dimensional theoretical model based on the porous media treatment was also developed to predict the thermal-hydraulic behavior of the heat exchanger. The model incorporates the actual fin geometry into the calculation of the air-side porosity. The air-side permeability is calculated according to the Kozeny–Carman model and the particle-diameter based analysis. The model predicts the experimental data within a few percent RMS, depending on the correlations used for the friction coefficient and interstitial Nusselt number.     

Parametric and design optimization investigation of a wavy fin and tube air heat exchanger using the T-G technique

The focus of this paper is to optimize the air-side performance of a wavy fin and tube heat exchanger at different design parameters on an individual target response using the Taguchi method. However, a statistical concept, gray relational analysis, is also studied for combined optimization, considering all target responses at a time. Based on the heat exchanger requirement, parametric study for the air-side is regarded as a more significant heat transfer and lower frictional factor. Experimental correlations were available and used for the 27 orthogonal runs. Investigation revealed the highest 47.06% fin pitch, 37.24% fin pitch, 25.46% air velocity, and 23.9% fin thickness contribution ratio for the target response of friction factor (TPF), heat transfer coefficient, and Colburn factor, respectively, with the application of the Taguchi method in a heat exchanger. GRG gives an optimum set of design parameters, A3B3C2D1E3F2G1, for wavy fin and tube of fin pitch of 6 mm, tube row number of 6, waffle height 1.8 mm, fin thickness 0.12 mm, and air velocity 5 m/s. Also, longitudinal tube pitch is 27.5 mm, and transverse tube pitch of 24.8 mm, at which TPF is maximum while the friction factor is minimal. The Colburn factor is the most significant, minor friction factor, and the heat transfer coefficient and TPF are the most considerable in GRG. Hence, an improved heat transfer performance design of a wavy fin and tube heat exchanger is achieved using the above techniques.     

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In this study, fully developed laminar flow and convective heat transfer in an internally finned tube heat exchanger are investigated numerically. The flow is assumed to be both hydrodynamically and thermally developed with uniform outside wall temperature. Parameters of the thickness, length, and number of fins and thermal conductivity ratio between fin and working fluid are varied to obtain the friction factor as well as Nusselt number. The results show that the heat transfer improves significantly if more fins are used; however, the pressure drop turns out to be large in this heat exchanger. In addition, it is found that the emergence of closed-loop isotherms between the areas of two neighboring fins leads to heat transfer enhancement in the internally finned tube. When the fin number is smaller than 14, there appears a maximum Nusselt number at about 0.8 of the dimensionless fin length. Finally, an experiment is conducted to verify the numerical results.     

Performance evaluation of flat finned tube fin heat exchanger with different fin surfaces

When an extended surface is needed on only one fluid side (such as in a gas-to-liquid exchanger) or when the operating pressure needs to be contained on one fluid side, a tube-fin exchanger may be selected, with the tubes being round, flat, or elliptical in shape. The paper is concerned with the performance evaluation of flat tube fin heat exchangers (TFHE), having different fin configurations and flat tubes. The thermal performance of each configuration is based on the ε-NTU method. The extensive experimental research data of Kays and London available in the form of graphs are translated into algebraic relations for developing computational models. From the present work, a generalized heat transfer correlations is proposed based on geometrical parameters for the effectiveness of the heat exchanger. The generalization is with respect to the different fin surface geometry and not with the different combination of hot and cold fluids. The correlation is limited in its applicability to gas to water heat exchangers only. Further, guidelines are proposed for an easy way of designing a TFHE using correlations based on geometrical parameters and the same is compared with traditional ε-NTU method.     

Optimal design analysis of a tubular heat exchanger network with extended surfaces using multi-objective constructal optimization

The present work aims to investigate the influence of extended surfaces (fins) on the multi-objective optimization of a tubular heat exchanger network (THEN). An increase in the heat transfer area using various extended surfaces (fins) to enhance the performance of the heat exchanger was used while considering the effectiveness and total heat transfer area as two objective functions. In addition to the simulation of simple fins, a new set of fins, called constructal fins, was designed based on the constructal theory. Tubular heat exchanger network design parameters were chosen as optimization variables, and optimization results were achieved in such a way as to enhance the effectiveness and decrease the total heat transfer area. The results show the importance of constructal fins in improving the objective functions of heat exchangers. For instance, the simple fins case enhances the effectiveness by up to 5.3% compared to that without fins (usual heat exchanger) while using constructal fins, in addition to the 7% increment of effectiveness, reduces the total heat transfer area by 9.47%. In order to optimize the heat exchanger, the heat transfer rate and cold fluid temperature must increase, and at the same time, the hot exiting fluid temperature should decrease at the same constant total heat transfer area, which is higher in the constructal fins case. Finally, optimized design variables were studied for different cases, and the effects of various fins were reported.