Design optimization of shell-and-tube heat exchanger using particle swarm optimization technique

Shell-and-tube heat exchangers (STHEs) are the most common type of heat exchangers that find widespread use in numerous industrial applications. Cost minimization of these heat exchangers is a key objective for both designer and users. Heat exchanger design involves complex processes, including selection of geometrical parameters and operating parameters. The traditional design approach for shell-and-tube heat exchangers involves rating a large number of different exchanger geometries to identify those that satisfy a given heat duty and a set of geometric and operational constraints. However, this approach is time-consuming and does not assure an optimal solution. Hence the present study explores the use of a non-traditional optimization technique; called particle swarm optimization (PSO), for design optimization of shell-and-tube heat exchangers from economic view point. Minimization of total annual cost is considered as an objective function. Three design variables such as shell internal diameter, outer tube diameter and baffle spacing are considered for optimization. Two tube layouts viz. triangle and square are also considered for optimization. Four different case studies are presented to demonstrate the effectiveness and accuracy of the proposed algorithm. The results of optimization using PSO technique are compared with those obtained by using genetic algorithm (GA).     

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     

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.     

An imperialist competitive algorithm for optimal design of plate-fin heat exchangers

This paper presents the application of imperialist competitive algorithm (ICA) for optimization of a cross-flow plate fin heat exchanger. Minimization of total weight and total annual cost are considered as objectives. Seven design parameters, namely, 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. A case study from literature is presented to show the effectiveness of the proposed algorithm. The numerical results reveal that ICA can find optimum configuration with higher accuracy in less computational time when compared to conventional genetic algorithm (GA).     

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.     

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.     

Multi-objective optimization of annular fin array with B-spline curve based fin profiles

The design of annular fin array with variable thickness fin profiles defined by B-spline curves is studied as a multi-objective optimization problem for simultaneously maximizing heat transfer rate and minimizing thermal stress. Maximization of surface e?ciency and augmentation factor as well as minimization of fin volume are considered as additional objective functions for further assessment of fin array performance. Evaluating the objective values through hybrid spline difference method, different cases are investigated by solving the optimization model by non-dominated sorting genetic algorithm II. The proposed scheme should aid designers in selecting compromise optimal solutions for practical problems.     

Fin spacing optimization of a fin-tube heat exchanger under frosting conditions

Optimal values of the design parameters for a fin-tube heat exchanger of a household refrigerator under frosting conditions are proposed to improve its thermal performance and extend its operating time. In the optimization procedure, fin spacings of the heat exchanger are selected as the design parameters, and the average heat transfer rate, frost mass, and operating time are considered to be objective functions. The response surface and Taguchi methods are employed to optimize the design parameters. As a result, the average heat transfer rate and operating time of the optimum models increases by up to 6.3% and 12.9% compared to that of the reference model, respectively.     

Multi-objective optimization of shell and tube heat exchangers

The effectiveness and cost are two important parameters in heat exchanger design. The total cost includes the capital investment for equipment (heat exchanger surface area) and operating cost (for energy expenditures related to pumping). Tube arrangement, tube diameter, tube pitch ratio, tube length, tube number, baffle spacing ratio as well as baffle cut ratio were considered as seven design parameters. For optimal design of a shell and tube heat exchanger, it was first thermally modeled using ε–NTU method while Bell–Delaware procedure was applied to estimate its shell side heat transfer coefficient and pressure drop. Fast and elitist non-dominated sorting genetic algorithm (NSGA-II) with continuous and discrete variables were applied to obtain the maximum effectiveness (heat recovery) and the minimum total cost 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 cost with change in design parameters of the shell and tube heat exchanger was also performed and the results are reported.     

Multi‐objective optimization design of plate‐fin vapor generator for supercritical organic Rankine cycle

Supercritical organic Rankine cycle (SORC) is an improved ORC architecture with lower exergy destruction and better heat source utilization when compared with a subcritical one. The accurate design of its vapor generator is of critical importance due to the fact that heat transfer performance significantly affects thermal efficiency, power output, and size of the overall system. This paper aims to develop a mathematical model of the SORC vapor generator using plate‐fin heat exchanger. The finite volume method is applied to deal with the properties' variation problem of the supercritical fluids. Multi‐objective optimization is employed by the nondominated sorting genetic algorithm II to find the optimum geometry design. The objective functions are the number of entropy production units, annual cost, and volume. For a specific SORC system, an optimum vapor generator is designed using the developed model. Parametric studies are conducted to assess the effect of geometry parameters on the vapor generator performance. The off‐design performance of the vapor generator is also evaluated under different mass flow rates and different heat source inlet temperature conditions.     

Multi‐objective genetic algorithm optimization of thermoelectric heat exchanger for waste heat recovery

A model is developed to simulate a cross‐flow heat exchanger, including fins, in the wall of which thermoelectric generators are sandwiched. Such a system could be used for waste heat recovery. The model is used to optimize the device based on several objective functions: total volume, total number of thermoelectric modules, power output, and pumping power. The design variables are the local distribution of modules and of current, the shape of the fins, and the division of the heat exchanger in sub‐channels. Pareto fronts are achieved with a multi‐objective genetic algorithm, and are presented here. The results show that the number of sub‐channels in the heat exchanger has a larger impact on the overall performance than the fin geometry for this particular problem. Also, the net power output is mostly correlated to the number of thermoelectric modules, and less to the heat exchanger volume. Various relations between the different competing objectives are shown and analyzed. Copyright © 2011 John Wiley & Sons, Ltd.     

Optimal design of plate-fin heat exchangers by a hybrid evolutionary algorithm

This study explores the first application of a Genetic Algorithm hybrid with Particle Swarm Optimization (GAHPSO) for design optimization of a plate-fin heat exchanger. A total number of seven design parameters are considered as the optimization variables and the constraints are handled by penalty function method. The effectiveness and accuracy of the proposed algorithm is demonstrated through an illustrative example. Comparing the results with the corresponding results using GA and PSO reveals that the GAHPSO can converge to optimum solution with higher accuracy.     

The application of field synergy number in shell-and-tube heat exchanger optimization design

In the present work the field synergy principle is applied to the optimization design of the shell-and-tube heat exchanger with segmental baffles. The field synergy number which is defined as the indicator of the synergy between the velocity field and the heat flow is taken as the objective function. The genetic algorithm is employed to solve the heat exchanger optimization problems with multiple design variables. The field synergy number maximization approach for heat exchanger optimization design is thus formulated. In comparison with the initial design, the optimal design leads to a significant cost cut on the one hand and an improvement of the heat exchanger performance on the other hand. The comparison with the traditional heat exchanger optimization design approach with the total cost as the objective function shows that the field synergy number maximization approach is more advantageous.     

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.     

Design and optimization of a downhole coaxial heat exchanger for an enhanced geothermal system (EGS)

The present study considers the design, performance analysis and optimization of a downhole coaxial heat exchanger for an enhanced geothermal system (EGS). The optimum mass flow rate of the geothermal fluid for minimum pumping power and maximum extracted heat energy was determined. In addition, the coaxial pipes of the downhole heat exchanger were sized based on the optimum geothermal mass flow rate and steady-state operation. Transient effect or time-dependent cooling of the Earth underground, and the optimum amount and size of perforations at the inner pipe entrance region to regulate the flow of the geothermal fluid were disregarded to simplify the analysis. The paper consists of an analytical and numerical thermodynamic optimization of a downhole coaxial heat exchanger used to extract the maximum possible energy from the Earth's deep underground (2 km and deeper below the surface) for direct usage, and subject to a nearly linear increase in geothermal gradient with depth. The thermodynamic optimization process and entropy generation minimization (EGM) analysis were performed to minimize heat transfer and fluid friction irreversibilities. An optimum diameter ratio of the coaxial pipes for minimum pressure drop in both limits of the fully turbulent and laminar fully-developed flow regime was determined and observed to be nearly the same irrespective of the flow regime. Furthermore, an optimum geothermal mass flow rate and an optimum geometry of the downhole coaxial heat exchanger were determined for maximum net power output. Conducting an energetic and exergetic analysis to evaluate the performance of binary power cycle, higher Earth's temperature gradient and lower geofluid rejection temperatures were observed to yield maximum first- and second-law efficiencies.     

Analysis and optimization of electrokinetic microchannel heat sink

A mixed (electroosmotic and pressure-driven) flow microchannel heat sink has been studied and optimized with the help of three-dimensional numerical analysis, surrogate methods, and the multi-objective evolutionary algorithm. Two design variables; the ratio of the microchannel width-to-depth and the ratio of fin width-to-depth of the microchannel are selected as the design variables while design points are selected through a four-level full factorial design. The single-objective optimization is performed taking overall thermal resistance as the objective function and Radial Basis Neural Network as the surrogate model while for multi-objective optimization pumping power is considered as the objective function along with the thermal resistance. It is observed that the optimum design shifted towards the lower values of the ratio of the channel width-to-depth and the higher values of the ratio of fin width-to-depth of channel with increase of the driving source. The trade-off between the two conflicting objectives has been found and discussed in detail in light of the distribution of Pareto-optimal solutions in the design space. The ratio of channel width-to-depth is found to be higher Pareto-sensitive (sensitivity along the Pareto-optimal front) than the ratio of fin width-to-depth of the channel.     

Performance analysis and optimization of straight taper fins with variable heat transfer coefficient

In the present paper, the thermal analysis and optimization of straight taper fins has been addressed. With the help of the Frobenius expanding series the temperature profiles of longitudinal fin, spine and annular fin have been determined analytically through a unified approach. Simplifying assumptions like length of arc idealization and insulated fin tip condition have been relaxed and a linear variation of the convective heat transfer coefficient along the fin surface has been taken into account. The thermal performance of all the three types of fin has been studied over a wide range of thermo-geometric parameters. It has been observed that the variable heat transfer coefficient has a strong influence over the fin efficiency. Finally, a generalized methodology has been pointed out for the optimum design of straight taper fins. A graphical representation of optimal fin parameters as a function of heat duty has also been provided.     

Power optimization of an endoreversible closed intercooled regenerated Brayton cycle

In this paper, power is optimized for an endoreversible closed intercooled regenerated Brayton cycle coupled to constant-temperature heat reservoirs in the viewpoint of finite-time thermodynamics (FTT) or entropy generation minimization (EGM). The effects of some design parameters, including the cycle heat reservoir temperature ratio and total heat exchanger inventory, on the maximum power and the corresponding efficiency are analyzed by numerical examples. The analysis shows that the cycle dimensionless power can be optimized by searching the optimum heat conductance distributions among the hot- and cold-side heat exchangers, the regenerator and the intercooler for fixed total heat exchanger inventory, and by searching the optimum intercooling pressure ratio. When the optimization is performed with respect to the total pressure ratio of the cycle, the maximum dimensionless power can be maximized again.     

Second law based optimisation of crossflow plate-fin heat exchanger design using genetic algorithm

A genetic algorithm based optimisation technique has been developed for crossflow plate-fin heat exchangers using offset-strip fins. The algorithm takes care of large number of continuous as well as discrete variables in the presence of given constraints. The optimisation program aims at minimising the number of entropy generation units for a specified heat duty under given space restrictions. The results have also been obtained and validated through graphical contours of the objective function in the feasible design space. The effect of variation of heat exchanger dimensions on the optimum solution has also been presented.     

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.