shell & tube heat exchanger thermal design with optimization of ...

Patel et al, International Journal of Advanced Engineering Research and Studies

E-ISSN2249–8974

Research Paper

SHELL & TUBE HEAT EXCHANGER THERMAL DESIGN WITH OPTIMIZATION OF MASS FLOW RATE AND BAFFLE SPACING 1

Sandeep K. Patel, 2Professor Alkesh M. Mavani

Address for Correspondence 1

L.D.R.P –I.T.R, Gandhinagar, Guj., INDIA 2 Professor, L.D.R.P –I.T.R, Gandhinagar, Guj., INDIA ABSTRACT A characteristic of heat exchanger design is the procedure of specifying a design. Heat transfer area and pressure drops and checking whether the assumed design satisfies all requirement or not. The purpose of this paper is how to design the shell and tube heat exchanger which is the majority type of liquid –to- liquid heat exchanger. General design considerations and design procedure are also illustrated in this paper. In design calculation HTRI software is used to verify manually calculated result. KEY WORDS: heat exchanger, mass flow rate, baffle spacing, pressure drop, heat transfer coefficient, LMTD, HTRI.

INTRODUCTION Heat Exchanger is a device which provides a flow of thermal energy between two or more fluids at different temperatures. Heat exchangers are used in a wide variety of engineering applications like power generation, waste heat recovery, manufacturing industry, air-conditioning, refrigeration, space applications, petrochemical industries etc. Heat exchanger may be classified according to the following main criteria. 1. Recuperators and Regenerators. 2. Transfer process: Direct contact and Indirect contact. 3. Geometry of construction: tubes, plates and extended surfaces. 4. Heat transfer mechanisms: single phase and two phase. 5. Flow arrangements: parallel, counter and cross flows. Shell and tube heat exchangers are most versatile type of heat exchanger; they are used in process industries, in conventional and nuclear power station as condenser, in steam generators in pressurized water reactor power plants, in feed water heaters and in some air conditioning refrigeration systems. Shell and tube heat exchanger provide relatively large ratio of heat transfer area to volume and weight and they can be easily cleaned. Shell and tube heat exchanger offer great flexibility to meet almost any service requirement. Shell and tube heat exchanger can be designed for high pressure relative to the environment and high pressure difference between the fluid streams. Basic Components of Shell and Tube Heat Exchanger: Shell and tube heat exchanger are built of round tubes mounted in a cylindrical shell with the tubes parallel to the shell. One fluid flow inside the tubes, while the other fluid flows across and along the axis of the exchanger, the major components of this exchanger are tubes (tube bundles), shell, front end head, rear end head, baffles and tube sheets. Typical parts and their arrangement are show in figure 1. TEMA Standards: The standard of the Tubular Exchanger Manufacturers Association (TEMA) describe various components in detail of shell and tube heat exchanger (STHE). STHE is divided into three parts: the front head, the shell and the rear head. Figure 1 illustrates the TEMA nomenclature for the various construction IJAERS/Vol. II/ Issue I/Oct.-Dec.,2012/130-135

possibilities. Exchangers are described by the letter codes for the three sections. Each part has different construction and specific function. The construction of front and rear head as well as flow patterns in the shell are defined by the TEMA standards- for example, a BFL exchanger has a bonnet cover, a two-pass shell with a longitudinal baffle and a fixed tubesheet rear head. Classification Based on TEMA Construction: There three basic classification based on TEMA based on their end connection and shell type. a. BEM b. CFU c. AES

Figure 1: Construction Parts and Connections

There are various types of STHE, but most of process industries and chemical industries mostly use fixedtube sheet shell and tube type heat exchanger because


of its low cost, simple construction and low maintenance cost. From industrial point of view it is necessary to operate shell and tube heat exchanger at optimal condition thus it reduce an operating and maintenance cost. Mass velocity strongly influences the heat-transfer coefficient. For turbulent flow, the tube side heattransfer coefficient varies to the 0.8 power of tube side mass velocity, whereas tube side pressure drop varies to the square of mass velocity. Thus, with increasing mass velocity, pressure drop increases more rapidly than does the heat-transfer coefficient. Consequently, there will be an optimum mass velocity above which it will be wasteful to increase mass velocity further. The construction geometry and thermal parameters such as mass flow rate, heat transfer coefficient etc are strongly influenced by each other. A detail study of research of design procedures, effect and variation of thermal parameters under different conditions and optimization methods implemented for STHE has been carried out in literature review. BAFFLE Baffles serve two important functions. They support the tubes during assembly and operation and help prevent vibration from flow induced eddies and direct the shell side fluid back and forth across the tube bundle to provide effective velocity and Heat Transfer rates. The diameter of the baffle must be slightly less than the shell inside diameter to allow assembly, but must be close enough to avoid the substantial performance penalty caused by fluid bypass around the baffles. Shell roundness is important to achieve effective sealing against excessive bypass. Baffles can be made from a variety of materials compatible with the shell side fluid. They can be punched or machined. Some baffles are made by a punch which provides a lip around the tube hole to provide more surfaces against the tube and eliminate tube wall cutting from the baffle edge. The tube holes must be precise enough to allow easy assembly and field tube replacement, yet minimize the chance of fluid flowing between the tube wall and baffle hole, resulting in reduced thermal performance and increased potential for tube wall cutting from vibration. Baffles do not extend edge to edge, but have a cut that allows shell side fluid to flow to the next baffled chamber. For most liquid applications, the cuts areas represent 20-25% of the shell diameter. For gases, where a lower pressure drop is desirable, baffle cuts of 40-45% is common. Baffles must overlap at least one tube row in order to provide adequate tube support. They are spaced throughout the tube bundle somewhat evenly to provide even fluid velocity and pressure drop at each baffled tube section. Single-segmental baffles force the fluid or gas across the entire tube count, where is changes direction as dictated by the baffle cut and spacing. This can result in excessive pressure loss in high velocity gases. In order to affect Heat Transfer, yet reduce the pressure drop, double-segmental baffles can be used. This approach retains the structural effectiveness of the tube bundle, yet allows the gas to flow between alternating sections of tube in a straighter overall direction, thereby reducing the effect of numerous changes of direction. IJAERS/Vol. II/ Issue I/Oct.-Dec.,2012/130-135

E-ISSN2249–8974

Figure:2

Type of baffles: Baffles are used to support tubes, enable a desirable velocity to be maintained for the shell side fluid, and prevent failure of tubes due to flow-induced vibration. There are two types of baffles: plate and rod. Plate baffles may be singlesegmental, double-segmental, or triple-segmental as shown in Figure 2. Baffle spacing: Baffle spacing is the centerline-tocenterline distance between adjacent baffles. It is the most vital parameter in STHE design. The TEMA standards specify the minimum baffle spacing as onefifth of the shell inside diameter or 2 in., whichever is greater. Closer spacing will result in poor bundle penetration by the shell side fluid and difficulty in mechanically cleaning the outsides of the tubes. Furthermore, a low baffle spacing results in a poor stream distribution as will be explained later.

Figure:3. Types of Baffles

The maximum baffle spacing is the shell inside diameter. Higher baffle spacing will lead to predominantly longitudinal flow, which is less efficient than cross-flow, and large unsupported tube spans, which will make the exchanger prone to tube failure due to flow-induced vibration. Optimum baffles pacing. For turbulent flow on the shell side (Re > 1,000), the heat-transfer coefficient varies to the 0.6–0.7 power of velocity; however, pressure drop varies to the 1.7–2.0 power. For laminar flow (Re < 100), the exponents are 0.33 for the heattransfer coefficient and 1.0 for pressure drop. Thus, as baffle spacing is reduced, pressure drop increases at a much faster rate than does the heat-transfer coefficient. This means that there will be an optimum ratio of baffle spacing to shell inside diameter that will result in the highest efficiency of conversion of pressure drop to heat transfer. This optimum ratio is normally between 0.3 and 0.6. PRESSURE DROP IN STHE PRELIMINARY CALCULATION A selected shell and tube heat exchanger must satisfy the process requirements with the allowable pressure drops until the next scheduled cleaning of plant. The methodology to evaluate thermal parameters is


explained with suitable assumptions. The following are the major assumptions made for the pressure drop analysis; 1. Flow is steady and isothermal, and fluid properties are independents of time. 2. Fluid density is dependent on the local temperature only or is treated as constant. 3. The pressure at a point in the fluid is independent of direction. 4. Body force is caused only by gravity. 5. There are no energy sink or sources along streamline; flow stream mechanical energy dissipation is idealized as zero. 6. The friction factor is considered as constant with passage flow length. Heat transfer or the size of heat transfer exchanger can be obtained from equation, Q = UoAo∆Tm (1) The overall heat transfer coefficient Uo based on the O.D. of tubes can be estimated from the estimated values of individual heat transfer coefficients, the wall and fouling resistance and the overall surface efficiency using equation

(2) For the single tube pass, purely countercurrent heat exchanger, F= 1.00. For preliminary design shell with any even number of tube side passes, F may be estimated as 0.9 Heat load can be estimated from the heat balance as:

E-ISSN2249–8974

taking the shell circle and dividing it by the projected area of the tube layout (fig 4) pertaining to a single tube A1.

(7) Where CTP is the tube count calculation constant that accounts for the incomplete coverage of the shell diameter by the tubes. Based on fixed tube sheet the following values are suggested: One tube pass: CTP = 0.93 Two tube pass: CTP = 0.90 Three tube pass: CTP = 0.85 A1 = (CL) (PT)2 (3.8) Where CL is the tube layout constant: CL = 1.0 for 90 and 45 CL = 0.87 for 30 and 60 Equation (3.7) can be written as:

(8) Where PR is the Tube Pitch Ratio (PR = PT/do).The shell diameter in terms of main construction diameter can be obtained as from equations (3.6) and (3.9),

(9) TUBE SIDE PRESSURE DROP The tube side pressure drop can be calculated by knowing the number of tube passes (Np) and length (L) oh heat exchanger; the pressure drop for the tube side fluid is given by equation

(3) If one stream changes phases: Q = mhfg (4) LMTD (Log Mean Temperature Difference Method) calculation: If three temperatures are known, the fourth one can be found from the heat balance,

(5) Heat transfer area can be calculated from equation (3.1). Number of tubes of diameter (do), shell diameter (Ds) to accommodate the number of tubes (Nt), with given tube length (L) can be estimated,

(10)

(11) The change of direction in the passes introduction in the passes introduction an additional pressure drop due to sudden expansions and contractions that the tube fluid experiences during a return that is accounted for allowing four velocity head per pass

(12) (6) One can find the shell diameter (Ds), which would contain the right number of tubes (Nt), of diameter (dt).

Figure 4: Square and Triangular Pitch Tube Layout The total number of tubes can be predicted in fair approximation as function of the shell diameter by IJAERS/Vol. II/ Issue I/Oct.-Dec.,2012/130-135

The total pressure drop of the side becomes:

(13) SHELL SIDE PRESSURE DROP The shell side pressure drop depends on the number of tubes, the number of times the fluid passes the tube bundle between the baffles and the length of each crossing. The pressure drop on the shell side is calculated by the following expression:


(14) Where, фs = (µb+ µs) 0.14 Nb = Number of baffles (Nb + 1) = Number of times fluid passes to the tube bundle Friction factor (f) calculated from:

(15) Where,

(16) The correlation has been tested based on data obtained on actual exchangers. The friction coefficient also takes entrance and exit losses into account. LITERATURE REVIEW The subject of shell and tube heat exchanger (STHE) has a wide variety of process and phenomena. A vast amount of the material is published regarding STHE which depicts various factors affecting the thermal efficiency of the STHE. On the basis of that a brief summary is reviewed as follows: LITERATURE REVIEW RELATED TO DESIGN OF STHE Su Thet Mon Than, Khin Aung Lin, Mi Sandar Mon:[1] In this paper data is evaluated for heat transfer area and pressure drop and checking whether the assumed design satisfies all requirement or not. The primary aim of this design is to obtain a high heat transfer rate without exceeding the allowable pressure drop.

Figure 5: Reynolds Number on Number of Baffles and Length of Tube [1]

Figure 6: Heat Transfer Coefficient on Number of Baffles and Length of Tube [1] IJAERS/Vol. II/ Issue I/Oct.-Dec.,2012/130-135

E-ISSN2249–8974

The decreasing pattern of curves of Reynolds Number and heat transfer coefficient shown in figure 5 and figure 6 shows that the Re and h are gradually decreases corresponding as high as tube effective length. Gradual decrease in Reynolds Number means there is significant decrease in pressure drop respectively. ; explains the basics of exchanger thermal design, covering such topics as: STHE components; classification of STHEs according to construction and according to service; data needed for thermal design; tube side design; shell side design, including tube layout, baffling, and shell side pressure drop; and mean temperature difference. The basic equations for tube side and shell side heat transfer and pressure drop. Correlations for optimal condition are also focused and explained with some tabulated data. This paper gives overall idea to design optimal shell and tube heat exchanger. The optimized thermal design can be done by sophisticated computer software however a good understanding of the underlying principles of exchanger designs needed to use this software effectively. Studied that, increased fluid velocities result in larger heat transfer coefficients and, consequently, less heat-transfer area and exchanger cost for given rate of heat transfer. On the other hand, the increased fluid velocities cause an increase in pressure drop and greater pumping power cost. The optimum economic design occurs at the condition where the total cost is a minimum. The basic problem, therefore, is to minimize the sum of the variable annual costs for the exchanger and its operation. The main objective of this paper is to reduce the operating cost of shell and tube heat exchanger. Yusuf Ali Kara, Ozbilen Guraras:[4] Prepared a computer based design model for preliminary design of shell and tube heat exchangers with single phase fluid flow both on shell and tube side. The program determines the overall dimensions of the shell, the tube bundle, and optimum heat transfer surface area required to meet the specified heat transfer duty by calculating minimum or allowable shell side pressure drop. He concluded that circulating cold fluid in shell-side has some advantages on hot fluid as shell stream since the former causes lower shell-side pressure drop and requires smaller heat transfer area than the latter and thus it is better to put the stream with lower mass flow rate on the shell side because of the baffled space. M.Serna and A.Jimenez:[5] They have presented a compact formulation to relate the shell-side pressure drop with the exchanger area and the film coefficient based on the full Bell–Delaware method. In addition to the derivation of the shell side compact expression, they have developed a compact pressure drop equation for the tube-side stream, which accounts for both straight pressure drops and return losses. They have shown how the compact formulations can be used within an efficient design algorithm. They have found a satisfactory performance of the proposed algorithms over the entire geometry range of single phase, shell and tube heat exchangers.


Andre L.H. Costa, Eduardo M. Queiroz:[6] Studied that techniques were employed according to distinct problem formulations in relation to: (i) heat transfer area or total annualized costs, (ii) constraints: heat transfer and fluid flow equations, pressure drop and velocity bound; and (iii) decision variable: selection of different search variables and its characterization as integer or continuous. This paper approaches the optimization of the design of shell and tube heat exchangers. The formulation of the problem seeks the minimization of the thermal surfaces of the equipment, for certain minimum excess area and maximum pressure drops, considering discrete decision variables. Important additional constraints, usually ignored in previous optimization schemes, are included in order to approximate the solution to the design practice. describes to consider suitable baffle spacing in the design process, a computer program has been developed which enables designers to determine the optimum baffle spacing for segmentally baffled shell and tube condensers. Throughout the current research, a wide range of design input data specification for E and J types shell and tube condensers have been considered and their corresponding optimum designs for different values of W1 have been evaluated. This evaluation has been led to some correlation for determining the optimum baffle spacing. M. M. El-Fawal, A. A. Fahmy and B. M. Taher:[8] In this paper a computer program for economical design of shell and tube heat exchanger using specified pressure drop is established to minimize the cost of the equipment. The design procedure depends on using the acceptable pressure drops in order to minimize the thermal surface area for a certain service, involving discrete decision variables. Also the proposed method takes into account several geometric and operational constraints typically recommended by design codes, and provides global optimum solutions as opposed to local optimum solutions that are typically obtained with many other optimization methods. LITERATURE REVIEW RELATED TO EXPERIMENTAL AND METHOD FOR EVALUATING SHELL SIDE HEAT TRANSFER COEFFICIENT Zahid H. Ayub:[9] A new chart method is presented to calculate single-phase shell side heat transfer coefficient in a typical TEMA style single segmental shell and tube heat exchanger. A case study of rating water-to-water exchanger is shown to indicate the result from this method with the more established procedures and softwares available in the market. The results show that this new method is reliable and comparable to the most widely known HTRI software. R. Hosseini, A. Hosseini-Ghaffar, M. Soltani:[10] experimentally obtained the heat transfer coefficient and pressure drop on the shell side of a shell-and-tube heat exchanger for three different types of copper tubes (smooth, corrugated and with micro-fins). Also, experimental data has been compared with theoretical data available. Experimental work shows higher Nusselt number and pressure drops with respect to theoretical correlation based on Bell’s method. The IJAERS/Vol. II/ Issue I/Oct.-Dec.,2012/130-135

E-ISSN2249–8974

optimum condition for flow rate (for the lowest increase of pressure drop) in replacing the existing smooth tube with similar micro-finned tube bundle was obtained for the oil cooler of the transformer under investigation. LITERATURE REVIEW RELATED TO DIFFERENT OPTIMIZATION TECHNIQUES Resat Selbas, Onder Kızılkan, Marcus Reppich:[11] Applied genetic algorithms (GA) for the optimal design of shell-and-tube heat exchanger by varying the design variables: outer tube diameter, tube layout, number of tube passes, outer shell diameter, baffle spacing and baffle cut. From this study it was concluded that the combinatorial algorithms such as GA provide significant improvement in the optimal designs compared to the traditional designs. GA application for determining the global minimum heat exchanger cost is significantly faster and has an advantage over other methods in obtaining multiple solutions of same quality. G.N. Xie, Q.W. Wang , M. Zeng, L.Q. Luo:[12] carried out an experimental system for investigation on performance of shell-and-tube heat exchangers, and limited experimental data is obtained. The ANN is applied to predict temperature differences and heat transfer rate for heat exchangers. BP algorithm is used to train and test the network. It is shown that the predicted results are close to experimental data by ANN approach. Comparison with correlation for prediction heat transfer rate shows ANN is superior to correlation, indicating that ANN technique is a suitable tool for use in the prediction of heat transfer rates than empirical correlations. It is recommended that ANNs can be applied to simulate thermal systems, especially for engineers to model the complicated heat exchangers in engineering applications. B.V. Babu, S.A. Munawarb:[13] in the present study for the first time DE, an improved version of genetic algorithms (GAs), has been successfully applied with different strategies for 1,61,280 design configurations using Bell’s method to find the heat transfer area. In the application of DE, 9680 combinations of the key parameters are considered. For comparison, GAs are also applied for the same case study with 1080 combinations of its parameters. For this optimal design problem, it is found that DE, an exceptionally simple evolution strategy, is significantly faster compared to GA and yields the global optimum for a wide range of the key parameters. José M. Ponce-Ortega et al.:[14] presented an approach based on genetic algorithms for optimum design of shell and tube heat exchanger and for optimization major geometric parameters such as the number of tube-passes, standard internal and external tube diameters, tube layout and pitch, type of head, fluids allocation, number of sealing strips, inlet and outlet baffle spacing, and shell side and tube-side pressure drops were selected. Genetic algorithms provide better expectations to detect global optimum solutions than gradient methods, in addition to being more robust for the solution of non-convex problems. M. Fesanghary et al.:[15] explores the use of global sensitivity analysis (GSA) and harmony search algorithm (HSA) for design optimization of shell and


tube heat exchangers (STHXs) from the economic viewpoint. Comparing the HSA results with those obtained using genetic algorithm (GA) reveals that the HSA can converge to optimum solution with higher accuracy. Jiangfeng Guo et al.:[16] took some geometrical parameters of the shell-and-tube heat exchanger as the design variables and the genetic algorithm is applied to solve the associated optimization problem. It is shown that for the case that the heat duty is given, not only can the optimization design increase the heat exchanger effectiveness significantly, but also decrease the pumping power dramatically. Sepehr Sanaye, Hassan Hajabdollahi:[17] considered seven design parameters namely tube arrangement, tube diameter, tube pitch ratio, tube length, tube number, baffle spacing ratio as well as baffle cut ratio. Fast and elitist non-dominated sorting genetic algorithm with continuous and discrete variables were applied to obtain the maximum effectiveness (heat recovery) and the minimum total cost as two objective functions. V.K. Patel, R.V. Rao:[18] explores the use of a nontraditional 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. The presented PSO technique's ability is demonstrated using different literature case studies and the performance results are compared with those obtained by the previous researchers. PSO converges to optimum value of the objective function within quite few generations and this feature signifies the importance of PSO for heat exchanger optimization. studied that the optimum ratio of baffle spacing to shell diameter is determined by applying the thermo economic analysis method. Although there is no precise criterion to determine baffle spacing in the literature, it is obvious that thermo economic analysis, as defined in this paper, is a powerful tool for determining of the optimum baffle spacing. The results obtained, corresponding to the different objective functions, are also discussed. The results of these methods are then used to demonstrate how the optimum baffle spacing ratio is affected by the varying values of the heat exchanger geometrical parameters. CONCLUSION From literature review it can be concluded that, • There is increase in pressure drop with increase in fluid flow rate in shell and tube heat exchanger which increases pumping power. • Genetic algorithm provide significant improvement in the optimal designs compared to the traditional designs. Genetic algorithm application for determining the global minimum heat exchanger cost is significantly faster and has an advantage over other methods in obtaining multiple solutions of same quality. Thus, providing more flexibility to the designer. IJAERS/Vol. II/ Issue I/Oct.-Dec.,2012/130-135

E-ISSN2249–8974

• It also reveals that the harmony search algorithm can converge to optimum solution with higher accuracy in comparison with genetic algorithm. • Tube pitch ratio, tube length, tube layout as well as baffle spacing ratio were found to be important design parameters which has a direct effect on pressure drop and causes a conflict between the effectiveness and total cost. In brief, it is necessary to evaluate optimal thermal design for shell and tube heat exchanger to run at minimal cost in industries. REFERENCES 1. 2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

Sadik kakac, “Heat Exchangers Selection, Rating and Thermal Design”, 2002. Ramesh K shah and Dusan P. Sekulic, “Fundamental of heat exchanger design”, Rochester Institute of Technology, Rochester New York, 2003. Rajeev Mukharji, “Effective design of shell and tube heat exchanger”, American Institute of Chemical Engineering, 1988. Yusuf Ali Kara, Ozbilen Guraras, “A computer program for designing of Shell and tube heat exchanger”, Applied Thermal Engineering 24(2004) 1797–1805. M.Serna and A.Jimenez, “A compact formulation of the Bell Delaware method for Heat Exchanger design and optimization”, Chemical Engineering Research and Design, 83(A5): 539–550. Andre L.H. Costa, Eduardo M. Queiroz, “Design optimization of shell-and-tube heat exchangers”, Applied Thermal Engineering 28 (2008) 1798–1805. Su Thet Mon Than, Khin Aung Lin, Mi Sandar Mon, “Heat Exchanger design", World Academy of Science, Engineering and Technology 46 2008. M. M. El-Fawal, A. A. Fahmy and B. M. Taher, “Modelling of Economical Design of Shell and tube heat exchanger Using Specified Pressure Drop”, Journal of American Science. Zahid H. Ayub, “A new chart method for evaluating singlephase shell side heat transfer coefficient in a single segmental Shell and tube heat exchanger”, Applied Thermal Engineering 25 (2005) 2412–2420. R. Hosseini, A. Hosseini-Ghaffar, M. Soltani, “Experimental determination of shell side heat transfer coefficient and pressure drop for an oil cooler shell and tube heat exchanger with three different tube bundles”, Applied Thermal Engineering 27 (2007) 1001–1008. Resat Selbas, Onder Kızılkan, Marcus Reppich, “A new design approach for shell and tube heat exchanger using genetic algorithms from economic point of view”, Chemical Engineering and Processing 45 (2006) 268–275. G.N. Xie, Q.W. Wang , M. Zeng, L.Q. Luo, “Heat transfer analysis for shell and tube heat exchanger with experimental data by artificial neural networks approach”, Applied Thermal Engineering 27 (2007) 1096–1104. B.V. Babu, S.A. Munawarb, “Differential evolution strategies for optimal design of shell and tube heat exchanger”, Chemical Engineering Science 62 (2007) 3720 – 3739. José M. Ponce-Ortega, Medardo Serna-González, Arturo Jiménez-Gutiérrez, “Use of genetic algorithms for the optimal design of shell and tube heat exchanger”, Applied Thermal Engineering 29 (2009) 203–209. M. Fesanghary, E. Damangir, I. Soleimani, “Design optimization of shell and tube heat exchanger using global sensitivity analysis and harmony search algorithm”, Applied Thermal Engineering 29 (2009) 1026–1031. Jiangfeng Guo, Lin Cheng, Mingtian Xu, “Optimization design of shell and tube heat exchanger by entropy generation minimization and genetic algorithm”, Applied Thermal Engineering 29 (2009) 2954–2960. Sepehr Sanaye, Hassan Hajabdollahi, “Multi-objective optimization of shell and tube heat exchanger”, Applied Thermal Engineering 30 (2010) 1937-1945. V.K. Patel, R.V. Rao, “Design optimization of shell and tube heat exchanger using particle swarm optimization technique”, Applied Thermal Engineering 30 (2010) 14171425.