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Contents Strojniški vestnik - Journal of Mechanical Engineering Volume 71, (2025), Number 1-2 Ljubljana, January-February 2025 ISSN 0039-2480 Published every two months 3 Corrosion studies on Post-Weld Heat Treated dissimilar AISI2205 and AISI310 Joints Using Electrochemical Noise Analysis Mahadevan Govindasamy, Lloyd Jenner Mangalakaran Joseph Manuel, Senthilkumar Thamilkolunthu 10 Thermal Design and Constrained Optimization of a Fin and Tube Heat Exchanger Using Differential Evolution Algorithm Nader Afsharzadeh, Mohammad Eftekhari Yazdi, Arash Mirabdolah Lavasani 21 Microstructural and Mechanical Characterization of WAAM-fabricated Inconel 625: Heat Treatment Effects Saravanakumar Krishnasamy, Saravanan Sambasivam, Balaji Vaiyampalayam Govindaraj 28 Quantitative Sequential Modelling Approach to Estimate the Reliability of Computer Controlled Pneumatically Operated Pick-and-Place Robot Satheesh Pandian Durairaj 36 Connection Between the Dynamic Character of the Cutting Force and Machined Surface in Abrasive Waterjet Machining Jelena Baralic, Suzana Petrovic Savic, Branko Koprivica, Stefan Ðuric 44 A Mathematical Model of the Dimensional Chain for a Generation 2 Wheel Hub Unit Stanislaw Adamczak, Marek Gajur, Krzysztof Kuzmicki 51 Numerical and Experimental Investigation of Aspect Ratio Effect on Aerodynamic Performance of NACA 4415 Airfoil Section at Low Reynolds Number Hatice Cansu Ayaz Ümütlü, Zeki Kiral, Ziya Haktan Karadeniz 58 Integration of Phase Change Material and Heat Exchanger for Enhanced Solar Desalination – A Comparative Performance Investigation Jothilingam Manickam, Balakrishnan Nanjappan, Nithyanandam Chandrasekaran 64 Reviewers 2024 ON THE COVER The corrosion behavior of dissimilar weldments between AISI 310 and AISI 2205 stainless steels in a 5 % calcium chloride solution at 50 °C was investigated under three conditions: as-welded, lower post-weld heat treatment at 800 °C, and higher post-weld heat treatment at 1000 °C. Microstructural examination revealed severe pitting in the as-welded sample. The lower heat-treated sample had larger pits, while the higher heat-treated sample showed homogeneous corrosion with a protective oxide coating. The as-welded sample had the highest corrosion rate, followed by the lower heat-treated sample, which had a moderate rate, and the higher heat-treated sample had the lowest rate. Electrochemical noise measurements confirmed these findings, with the higher heat-treated sample showing negligible localized corrosion and homogenous corrosion behavior. Image Courtesy: Anna University, University College of Engineering, India SV-JME . VOL 71 . NO 1-2 . Y 2025 . 1 Corrosion Studies on Post-Weld Heat Treated Dissimilar AISI 2205 and AISI 310 Joints Using Electrochemical Noise Analysis Mahadevan Govindasamy – Lloyd Jenner Mangalakaran Joseph Manuel – Senthilkumar Thamilkolunthu Department of Mechanical Engineering, University College of Engineering, Anna University, India gmahadevan80@aubit.edu.in Abstract The corrosion behavior of dissimilar weldments between AISI310 and AISI2205 stainless steels in a 5 % calcium chloride solution at 50 °C was investigated under three conditions: as-welded, lower post-weld heat treatment at 800 °C, and higher post-weld heat treatment at 1000 °C. Microstructural examination revealed severe pitting in the as-welded sample, with pit widths ranging from 270 µm to 360 µm. The lower heat-treated sample had larger pits (310 µm to 370 µm), while the higher heat-treated sample showed homogeneous corrosion with a protective oxide coating. The as-welded sample had the highest corrosion rate, followed by the lower heat-treated sample, which had a moderate rate, and the higher heat-treated sample had the lowest rate. The corrosion current densities were 5.26×10—³ mA/cm², 4.6×10—4 mA/cm², and 1.4×10—4 mA/cm², respectively. Electrochemical noise measurements confirmed these findings, with the higher heat-treated sample showing negligible localized corrosion and homogenous corrosion behavior. Keywords AISI2205, AISI310, corrosion, electrochemical impedance spectroscopy, CaCl2 Highlights: . Dissimilar AISI2205 and AISI310 joints were subjected to post weld heat treatment (PWHT) for improving its corrosion resistance. . PWHT improved the corrosion characteristics of the dissimilar joints. . Electrochemical noise evaluation revealed that noise intensity was lower in higher temperature PWHT 1000°C than other joints. 1 INTRODUCTION The requirement for advanced engineering applications requires high-performance materials, often requiring welding of incompatible metals. Dissimilar stainless steel welding is particularly notable for its combined benefits of corrosion resistance, mechanical strength, and cost-effectiveness [1] and [2]. AISI 2205 duplex stainless steel and AISI 310 austenitic stainless steel are frequently used in industries such as chemical processing, oil and gas, and marine environments [3] and [4]. This combination leverages the high strength and weldability of duplex stainless steel with the high-temperature resistance of austenitic steel [5]. However, welding different stainless steels poses challenges, particularly regarding corrosion behavior, which affects the durability of welded structures in chloride-rich environments [6]. Welding can alter the microstructure at the weld junction, leading to variations in corrosion resistance [7]. Issues like residual stresses, phase transitions, and microstructural heterogeneities near the weld interface can become sites for localized corrosion, compromising joint integrity [8]. Research on corrosion in stainless steel welds focuses on factors like welding procedures, filler materials, and environmental conditions [9]. Galvanic corrosion, driven by the electrochemical potential difference between base metals, is a primary concern in dissimilar welds [10]. The corrosion behavior is significantly influenced by welding process parameters and post-weld heat treatment (PWHT) [11]. Calcium chloride (CaCl2) solution is often studied for its resemblance to industrial chloride-rich conditions, which promote pitting and crevice corrosion in stainless steels [12] and [13]. PWHT mitigates the adverse effects of welding by relieving residual stresses and homogenizing the microstructure [14] and [15]. Methods such as high- and low-temperature treatments each affect the welded joint’s properties differently [16]. Proper PWHT parameters can significantly enhance the corrosion resistance of dissimilar welds in harsh chloride environments [17]. This study evaluates the corrosion resistance of AISI2205-AISI310 dissimilar joints subjected to PWHT at two temperatures, using electrochemical techniques to monitor corrosion behavior in 5 % aqueous calcium chloride over 12 days. 2 MATERIALS & METHODS 2.1 Material Preparation and Welding The base materials used in this research were AISI 310 stainless steel (SS) and AISI 2205 duplex stainless steel (DSS), both acquired from Kheteshwar Metals, Mumbai, India, as rolled sheets with a thickness of 5 mm. Selecting the right filler wire is crucial for achieving optimal joint quality. ER2205 filler wire is particularly sought after due to its lower ferrite content, which demonstrably improves weldability [18]. As a better option, 2.6 mm ER2205 filler wire was chosen for conducting welding studies. The chemical aspects of both the base material (BM) and filler wire were determined by using spark spectrometer. Sparks were ignited at various regions, and the elemental composition was subsequently recorded. The BMs were sectioned into rectangular pieces measuring 150 mm in length and 100 mm in width using abrasive cutting machine, and the edges were then properly ground. Then, the cut pieces underwent a thorough cleaning process for removing any dirt, oil, or impurities. The welding process was done using a single V-butt joint configuration. According to ASTM E8M 04 standards [19], V-shaped grooves were prepared with a 40º angle and a root gap of 1.2 mm [20]. A dual shielding gas controller and a customized GTAW welding setup were used for fabrication of the joints. A 2.4 mm diameter, 2 % thoriated tungsten electrode that was positioned at a 45° angle was used for the welding tests. The shielding gas was directed by a (12.2 mm internal diameter) nozzle that was positioned 5 mm distance. An electronic gas management unit was designed so that shielding gases could be switched between. Two timing circuits, one for each solenoid valve regulating the gases, were present in this machine. To maintain a balanced 50 % duty cycle, both gases were supplied at equal flow rates but alternated at regular intervals. Based on the reported literatures [21] and [22] and trial experiments, specific technological parameters for the welding experiments were selected and are detailed in Table 1. Table 1. Designation of joints, welding parameters and heat treatment details Joint AISI310-AISI2205 Designation As-welded LPWHT HPWHT Ageing temperature [°C] - 800 1000 Welding current [A] 90 to 120 90 to 120 90 to 120 Welding voltage [V] 14 to 18 14 to 18 14 to 18 Welding speed [mm/s] 3.5 3.5 3.5 Gas flow rate [l/min] 8 8 8 a) c) After joining AISI310 SS with AISI2205 DSS, the specimens underwent PWHT. The dissimilar welds were heated for 90 minutes at two aging temperatures, namely 800 °C at lower post-weld heat treatment (LPWHT) and 1000 °C at higher post-weld heat treatment (HPWHT), and subsequently quenched in water. Three sets of joints were subjected to heat treatment, while one set was left untreated for comparative analysis. The designations for the heat-treated joints and information regarding aging temperatures are shown in Table 1. 2.2 Studies on Corrosion Characteristics Aqueous calcium chloride with a concentration of 5 % was used to create the caustic solution. To conduct each experiment, 100 ml of corrosive solution was added to an open flask and heated to 55 ºC using an electrical heater. AISI2205-AISI310 dissimilar joints in as-welded, LPWHT and HPWHT conditions were used to make the electrodes. After being cut to the dimensions of 10 mm × 5 mm × 2 mm, the samples for the electrochemical procedures were polished using silicon carbide paper, rinsed with distilled water, cleaned with acetone, and dried in a warm air stream. For the electrical connection, the specimens were spot-welded to a 150 mm long, 1 mm diameter 80.0Cr-20.0Ni wire. This wire was then separated from the corrosive solution by enclosing it in glass tubes and filling the gap between b) d) e) Fig. 1. Micrographs and EDX analysis of dissimilar AISI310-AISI2205 samples exposed to an aqueous CaCl2 solution: a) SEM as-welded sample, b) ADYX as welded sample in the as-welded condition, c) SEM – LPWHT sample, d) EDAX – LPWHT sample, e) SEM – HPWHT sample, and f) EDAX – HPWHT sample the glass tubes and the electrical connecting wire with refractory silicon. Applying over-potential with a sweep rate of 1 mV/s, ranging from –400 mV below to 800.0 mV above the corrosion potential, the polarization curves were developed [23] and [24]. The electrochemical cell consisted of working electrodes (as­welded, PWHT1, PWHT2), a reference electrode (Ag/AgCl), and an auxiliary electrode (platinum wire). Electrochemical potential and current noise measurements were carried out using a three ‘identical’ electrode configuration, with one reading per second to compile records of 1024 points every four hours for 12 days. All three electrochemical procedures were performed with an ACM Gill 8AC potentiostat accurately controlled by a personal computer. For qualitative examination, the surface morphology of the corroded specimens was investigated using scanning electron microscopy (SEM) in conjunction with energy dispersive X-ray analysis (EDAX). The SEM examination was carried out utilizing the JEOL JSM-6490LV microscope. 3 RESULTS AND DISCUSSION 3.1 SEM-EDX Analysis SEM-EDX images of the three corroded dissimilar AISI2250­AISI310 joints (as-welded, LPWHT & HPWHT) which underwent corrosion in CaCl2 solution are shown in Fig. 1a and b, Fig. 1c and d and Fig. 1e and f, respectively. According to the SEM with EDX examination, the three types of welded samples exhibit diverse corrosion behaviors. The as-welded sample exhibited heavily corroded surface with pits ranging from 270 µm to 360 µm in diameter. EDX analysis found chloride species, indicating that chromium and iron were selectively dissolved, most likely as chlorides. This mixed corrosion process shows localized pitting and general degradation, which are characteristic of untreated weld joints exposed to chloride [25]. The LPWHT sample indicated a morphology similar to the as-welded condition, but with slightly larger pits (310 µm to 370 µm). This indicated that, while LPWHTat 800 °C was intended to relieve tensions and polish the microstructure, it was not completely efficient in preventing the beginning of localized pitting corrosion, particularly in chloride environments. Localized pitting and similar elemental trends reported in both LPWHT and as-welded samples lend support to this theory. The HPWHT sample exhibited an evenly corroded surface with no pits. EDX examination revealed the creation of a protective oxide layer predominantly formed of chromium and iron oxides, with nickel and manganese present in trace levels [26]. Surface ruptures occur in as-welded samples because there is no persistent oxide layer, resulting in localized pitting and selective dissolving of alloy components such as chromium and iron. This makes the surface susceptible to hostile substances such as chlorides. In HPWHT samples, high-temperature treatment promotes the creation of a homogeneous and protective oxide layer, predominantly composed of chromium and iron oxides, which greatly lowers surface deterioration and the risk of localized corrosion. This homogeneous corrosion pattern, together with the existence of a persistent oxide layer, suggests that HPWHT at 1000 °C effectively reduces localized corrosion, offering increased resistance to chloride-induced pitting [27]. 3.2 Polarization Curves Fig. 2 presents the polarization curves of AISI310-AISI2250 at as-welded, LPWHT and HPWHT conditions. The parameters of potentiodynamic polarization curves of dissimilar joints AISI2205­AISI310 with different PWHT conditions exposed in the corrosive solution are shown in Table 2. At higher temperatures, the as-welded, LPWHT, and HPWHT samples behaved differently, according to the corrosion characteristics (Table 2). Table 2. Parameters of potentiodynamic polarization curves of dissimilar joints AISI2205-AISI310 with different PWHT conditions exposed in the corrosive solution AISI2205-AISI310 AISI2205-AISI310 AISI2205-AISI310 dissimilar joint Condition As-welded LPWHT HPWHT ßa [mV/decade] 304.7 291.2 134.6 ßc [mV/decade] 71.2 99.6 51.3 Ecorr [mV] 231.3 –14.8 56.9 Icorr [mA/cm2] 5.26×10–3 mA/cm2 4.6×10–4 mA/cm2 1.4×10–4 mA/cm2 Fig. 2. Polarization curves of AISI310-AISI2250 at as-welded, LPWHT and HPWHT The as-welded sample had the maximum corrosion rate (ßa = 304.7 mV/decade, ßc = 71.2 mV/decade). The corrosion potential Ecorr was measured at 231.3 mV, and the corrosion current density Icorr was 5.55×10–3 mA/cm², suggesting maximal susceptibility. Corrosion potential (Ecorr) denotes a material’s ability to corrode; a lower Ecorr indicates greater susceptibility. Corrosion current density (Icorr) indicates the rate of material degradation. Higher Icorr values, as seen in the as-welded sample, indicate faster corrosion and a greater sensitivity to corrosion in severe conditions. In comparison to the as-welded sample, the LPWHT sample demonstrated a moderate improvement in corrosion resistance. With ßa at 291.2 mV/decade and ßc at 99.6 mV/decade, the corrosion potential Ecorr was found to be –14.8 mV. The corrosion current density was 4.71×10–4 mA/cm² (Icorr), indicating a medium corrosion rate. Among the samples tested, sample C (HPWHT) exhibited the superior resistance to corrosion. This was evident by its lowest Tafel slopes (ßa at 134.6 mV/decade and ßc at 51.3 mV/decade). Additionally, it had the lowest corrosion potential (Ecorr at 56.9 mV) and current density (Icorr at 1.45×10–4 mA/cm²), signifying minimal corrosion susceptibility. 3.3 Electrochemical Noise Measurements Fig. 3 presents the current and potential time series at 55 ºC for as-welded, LPWHT and HPWHT. These data were used for showing the major localized corrosion activity, taking into account the three typical forms of electrochemical noise generated by different types of corrosion processes [28]: a. Type I (Pitting): Consist of transients of high intensity with a high repetition rate. This type of corrosion is often characterized by the sudden appearance of small holes or pits in the metal surface. b. Type II (Mixed): It is a combination of transients of type I and oscillations of short amplitude. This type of corrosion suggests a combination of localized pitting and a more general attack on the metal surface. c. Type III (Uniform): The pattern noise is formed by oscillations of low amplitude. This type of corrosion refers to a gradual and relatively even attack on the entire exposed metal surface. The as-welded specimens exhibited the highest corrosion rate, indicated by significantly higher current density values compared to LPWHT and HPWHT. As-welded specimens generally showed potential and current time series with random oscillations of extremely low intensity, resembling those observed at LPWHT & HPWHT. In comparison to LPWHT & HPWHT samples, the potential noise for as-welded specimens showed a greater range, roughly 118 mV, suggesting a nobler nature. This is consistent with the distinct way that the CaCl2 corrosion system responds to heat treatment and lines up with the behavior shown in the polarization curves. LPWHT sample’s current and potential time series showed a clear noise pattern with noticeable transients and oscillatory behavior. In electrochemical noise studies, oscillatory behavior in LPWHT samples showed occasional breakdown and recovery of the passive oxide layer caused by localized pitting corrosion [29]. This indicated increased activity, especially on 5th and 6th day, which was compatible with localized corrosion or the breakdown and recovery Fig. 3. Current and potential time series of the dissimilar joints exposed to CaCl2 solution; a) current time series for as-welded, b) potential time series for as-welded, c) current time series for LPWHT, d) potential time series for LPWHT, e) current time series for HPWHT, and f) potential time series for HPWHT of the passive film. Interestingly, the transient activity that was seen on those days did not persist for the duration of the experiment, suggesting that the process was localized and only took place on those days. It is possible to interpret the notable transients seen on those two days as the rupture of the passive oxide coating or localized corrosion events because they were marked by abrupt current rises, potential decreases, and recovery. The rupture of the passive oxide coating in LPWHT samples happens when the protective film that typically protects the metal from corrosion becomes unstable due to localized pressures, impurities, or environmental conditions. This disintegration exposes the underlying metal to corrosive chemicals, which accelerates localized corrosion. Factors such as chloride ions, temperature variations, and mechanical stressors can all weaken the oxide layer and cause it to break. Once the protective coating is compromised, corrosion accelerates until the oxide layer reforms or stabilizes [30]. Even though these transients were noticeable on those two days, the remaining time series showed low-amplitude random oscillations that might have contributed to the localised activity in addition to a mixed corrosion process [31]. This aligned with the findings from the SEM analysis, indicating both techniques identified the susceptibility of AISI2205-AISI310 joints to a combination of localized and mixed corrosion processes. HPWHT showed no notable anodic or cathodic transients in the current and potential time series, in line with the as-welded condition. For HPWHT, the current density stayed negative and extremely low, indicating a low expected rate of corrosion. The cathode electrode’s preferential dissolution was indicated by the negative values, which essentially reversed the direction of the current. The present time series indicated low-amplitude random oscillations without any notable anodic transients and just two notable cathodic transients that would indicate the metallic oxide film recovering [32]. As-welded specimens displayed markedly higher current densities than PWHT2, indicating accelerated corrosion rates with rising temperature, a characteristic observed in the CaCl2 corrosion system as reported in previous studies [33]. 3.4 Localization Index The localization index (LI) was computed in order to measure the correlation between the electrochemical noise signals and the corrosion process. Localized corrosion activity is shown by LI, which is the ratio of the current noise standard deviation (si) to the root­mean-square current value (Irms). The range of LI values, typically between 0 and 1, is taken into account in the study. LI approaches 1 for current fluctuations that are noticeably greater than the mean current. On the other hand, LI values near 0 suggest that current fluctuations are negligible in relation to the mean current [34]. Localization index of AISI2205-AISI310 dissimilar joints exposed to CaCl2 at different PWHT conditions are shown in Fig. 4. Throughout the experiment, LI values were computed from each time series record derived from the electrochemical noise measurements. Values for the localization index were primarily found in the interval between the uniform and mixed corrosion zones. The mixed corrosion zone was primarily where the LI of the as-welded sample was located. This observation was consistent with multiple transients being present in the electrochemical noise pattern, indicating a combination of more widespread corrosion processes and localized assault. Multiple transients in the LI show the presence of various corrosion mechanisms, including both localized and uniform corrosion processes. This indicates that the electrochemical environment is unstable, with fast swings in corrosion activity resulting in pitting and general degradation, which is typical of mixed corrosion behavior [35]. SEM data, which show a greater vulnerability to localized corrosion attack, supported this observation. Fig. 4. Localization index (dimensionless) of AISI2205-AISI-310 dissimilar joints exposed to CaCl2 at different PWHT conditions The LPWHT sample exhibited LI values positioned near the border between uniform and mixed corrosion zones. This suggested an intermediate behavior, where localized corrosion was less pronounced compared to the as-welded condition. In mixed corrosion zones, intermediate behavior in LPWHT samples results from partial stabilization of the passive oxide layer, which reduces the severity of localized corrosion when compared to as-welded samples. This results in less noticeable pitting while yet allowing for some localized attack, showing a balance of uniform and localized corrosion processes [36] and [37]. This might be attributed to the absence of significant transients in the corresponding electrochemical noise data, potentially indicating a reduction in localized activity due to the low-temperature post-weld heat treatment. In contrast, the HPWHT sample maintained the LI firmly within the uniform or generalized corrosion zone. This consistency aligned with the minimal transients observed in the electrochemical noise pattern, suggesting a predominantly uniform corrosion process [38]. 4 CONCLUSIONS The corrosion performance of post-weld heat-treated AISI2205­AISI310 dissimilar stainless steel joints exposed to a 5 % CaCl2 solution for twelve days was investigated experimentally. The study incorporated SEM analysis alongside polarization curves, electrochemical noise data, and electrochemical impedance plots. According to the results, LPWHT joints and as-welded joints displayed a mixed corrosion process, while HPWHT joints (treated at 1000 ºC) displayed a uniform corrosion process. HPWHT joints had noise signals with a low amplitude and high-frequency pattern, according to electrochemical noise analysis, which coincided with the uniform corrosion that was seen visually. As-welded and LPWHT joints, on the other hand, showed many medium-intensity transients, indicating a more intricate corrosion process. A helpful indicator of corrosion localization was produced by the localization index parameter, which matched the visual observations of the corroded samples quite well. REFERENCES [1] Maurya, A.K., Pandey, C., Chhibber, R. Dissimilar welding of duplex stainless steel with Ni alloys: A review. Int J Press Vessels Pip 192 104439, (2021) DOI:10.1016/j.ijpvp.2021.104439 [2] Verma, J., Taiwade, R.V. Effect of welding processes and conditions on the microstructure, mechanical properties and corrosion resistance of duplex stainless steel weldments-A review. J Manuf Process 25 134-152 (2017) DOI:10.1016/j.jmapro.2016.11.003 [3] Zhu, P., Cao, X., Wang, W., Zhao, J., Lu, Y., Shoji, T. (2017). An investigation on microstructure and pitting corrosion behavior of 316L stainless steel weld joint. J Mater Res 32 3904-3911 DOI:10.1557/jmr.2017.316 [4] Xiong, J., Tan, M.Y., Forsyth, M. The corrosion behaviors of stainless steel weldments in sodium chloride solution observed using a novel electrochemical measurement approach. Desalination, 327 39-45, (2013) DOI:10.1016/j. desal.2013.08.006 [5] Touileb, K., Hedhibi, A. C., Djoudjou, R., Ouis, A., Bensalama, A., Ibrahim, A., Ahmed, M.M. Mechanical, microstructure, and corrosion characterization of dissimilar austenitic 316L and duplex 2205 stainless-steel ATIG welded joints. Materials 15 2470 (2022), DOI:10.3390/ma15072470 [6] Xiong, J., Tan, M.Y., Forsyth, M. (2013). The corrosion behaviors of stainless steel weldments in sodium chloride solution observed using a novel electrochemical measurement approach. Desalination, 327 39-45 DOI:10.1016/j. desal.2013.08.006 [7] Mohamed, A.Y., Mohamed, A.H.A., Abdel Hamid, Z., Farahat, A.I.Z., El-Nikhaily, A.E. Effect of heat treatment atmospheres on microstructure evolution and corrosion resistance of 2205 duplex stainless steel weldments. Sci Rep 13 4592 (2023) DOI:10.1038/s41598-023-31803-5 [8] Rao, P., Mulky, L. An overview of microbiologically influenced corrosion on stainless steel. Chem Bio Eng Rev 10 829-840 (2023) DOI:10.1002/cben.202300001 [9] Raj, S., Biswas, P. Experimental investigation of the effect of induction preheating on the microstructure evolution and corrosion behaviour of dissimilar FSW (IN718 and SS316L) joints. J Manuf Process 95 143-159 (2023) DOI:10.1016/j. jmapro.2023.04.021 [10] Okonkwo, B.O., Ming, H., Li, Z., Li, L., Chen, Y., Peng, J., Wang, J. Insight into the galvanic corrosion behaviour of low alloy steel A508/309 L/308 L stainless steel dissimilar metal weld at different temperatures. Mater Today Comm 38 107963. (2024) DOI:10.1016/j.mtcomm.2023.107963 [11] Liao, T., Zhang, X., Yang, H., Zhou, P., & Chen, F. Microstructural evolution and micro-corrosion behaviour of flash-welded U71Mn Joints as a function of post-weld heat treatment. Materials 16 5437 (2023) DOI:10.3390/ma16155437 [12] Vucko, F., Nazarov, A., Helbert, V., Thierry, D., Pelletier, S., Pablo, H., et al. Wet corrosion of incinerators under chloride deposits: insights from experimental study on stainless steels and nickel-based alloy weldments. Corros Sci 112220 (2024) DOI:10.1016/j.corsci.2024.112220 [13] Costa, E.M., Dedavid, B.A., Santos, C.A., Lopes, N.F., Fraccaro, C., Pagartanidis, T., Lovatto, L.P. Crevice corrosion on stainless steels in oil and gas industry: A review of techniques for evaluation, critical environmental factors and dissolved oxygen. Eng Fail Anal 144 106955 (2023) DOI:10.1016/j.engfailanal.2022.106955 [14] Singh Raman, R.K., Siew, W.H. Microstructures and corrosion/localised corrosion of stainless steels, incoloy and their weldments in nitrite-containing chloride environments. Materials 17 1336 (2024) DOI:10.3390/ma17061336 [15] Tahaei, A., Vanani, B.B., Abbasi, M., Garagnani, G.L. A comparison of microstructure and mechanical characteristics correlation of the joint specimens for duplex stainless steel UNS S32304 and super-duplex stainless steel UNS S32750: The role of post-weld heat treatment. P I Mech Eng L-J Mat (2024) DOI:10.1177/14644207241233150 [16] Tuz, L., Sokolowski, L., Stano, S. Effect of post-weld heat treatment on microstructure and hardness of laser beam welded 17-4 PH stainless steel. Materials 16 1334 (2023) DOI:10.3390/ma16041334 [17] Khan, M., Dewan, M.W., Sarkar, M.Z. Effects of welding technique, filler metal and post-weld heat treatment on stainless steel and mild steel dissimilar welding joint. J Manuf Process 64 1307-1321 (2021) DOI:10.1016/j.jmapro.2021.02.058 [18] Hung, C.H., Chen, W.T., Sehhat, M.H., Leu, M.C. The effect of laser welding modes on mechanical properties and microstructure of 304L stainless steel parts fabricated by laser-foil-printing additive manufacturing. Int J Adv Manuf Tech 112 867-877 (2021) DOI:10.1007/s00170-020-06402-7 [19] ASTM E8M-04. Standard Test Methods for Tension Testing of Metallic Materials [Metric Units]. American Society for Testing and Materials (ASTM) (2004) West Conshohocken DOI:10.1520/E0008_E0008M-22 [20] Lei, Z., Cao, H., Cui, X., Jin, G., Xu, K., Jiang, B., Huang, R. (2022). Analysis of welding solidification crack in narrow gap laser welding of high-strength steel. Int J Adv Manuf Tech 119, 4177-4190 DOI:10.1007/s00170-022-08659-6 [21] Dong, H., Yang, J., Li, Y., Xia, Y., Hao, X., Li, P., Lei, M. Evolution of interface and tensile properties in 5052 aluminum alloy/304 stainless steel rotary friction welded joint after post-weld heat treatment. J Manuf Process 51, 142-150 (2020) DOI:10.1016/j.jmapro.2020.01.038 [22] Köse, C., Topal, C. Effect of heat input and post-weld heat treatment on surface, texture, microstructure, and mechanical properties of dissimilar laser beam welded AISI 2507 super duplex to AISI 904L super austenitic stainless steels. J Manuf Process 73 861-894 (2022) DOI:10.1016/j.jmapro.2021.11.040 [23] Fontinha, I.R., Eustáquio, E. Influence of exposure conditions and particulate deposition on anodized aluminum corrosion. Corr Mater Degrad 3 770-786 (2022) DOI:10.3390/cmd3040040 [24] Hu, S., Liu, R., Liu, L., Cui, Y., Wang, F. Influence of temperature and hydrostatic pressure on the galvanic corrosion between 90/10 Cu-Ni and AISI 316L stainless steel. J Mater Res Tech 13 1402-1415 (2021) DOI:10.1016/j.jmrt.2021.05.067 [25] Wang, X, Chen, X., Han, Z., Li, C. Wang, Q. Stress corrosion cracking behavior of 2205 duplex stainless steel in 3.5% NaCl solution with sulfate reducing bacteria. J Chinese Soc Corr Prot 41 43-50 (2021) DOI:10.1016/S0010-938X(99)00105-5 [26] Dak, G., Sirohi, S., Pandey, C. Study on microstructure and mechanical behavior relationship for laser-welded dissimilar joint of P92 martensitic and 304L austenitic steel. Int J Press Vess Pip 196 104629 (2022) DOI:10.1016/j. ijpvp.2022.104629 [27] Bozeman, S.C. The Processing and Microstructures of 309L Stainless Steel Clad onto Carbon Steel with Wire-fed Directed Energy Deposition. Msc Thesis, Oregon State University, Corvallis (2022). [28] Parvizi, R. Electrochemical and interfacial characterisation of localised corrosion at heterogeneous structures in AA2024. PhD Thesis, Deakin University, Victoria, (2022) [29] Li, J., Jia, C., Gao, S., Guo, L. (2024). Experimental and numerical study on axial compression behavior of slender CFST columns with localized pitting corrosion damage. Constr Build Mater 414 134858 DOI:10.1016/j. conbuildmat.2023.134858 [30] Singh, J., Shahi, A.S. Microstructure and corrosion behavior of duplex stainless steel electron beam welded joint. J Mater Sci 57 9454-9479 (2022) DOI:10.1007/ s10853-022-07241-5 [31] Jiang, L., Zhang, Z., Fu, H., Huang, S., Zhuang, D., Xie, J. Corrosion behavior and mechanism of Al-Zn-Mg-Cu alloy based on the characterization of the secondary phases. Mater Charact 189, 111974 (2022) DOI:10.2139/ssrn.4009387 [32] Örnek, C., Davut, K., Kocabas, M., Bayatli, A., Ürgen, M. Understanding corrosion morphology of duplex stainless steel wire in chloride electrolyte. Corr Mater Degr 2 397-411 (2021) DOI:10.3390/cmd2030021 [33] Hammood, A.S., Esmailzadeh, M., Hosseini, S.N., Karimi, S., Calliari, I., Pezzato, L., Brittain, R. Effect of friction stir welding parameters on microstructure and corrosion behavior of 2101 duplex stainless steel in simulated body fluid. Int J Pr Eng Man-GT 10 327-337 (2023) DOI:10.1007/s40684-022-00440-0 [34] Amiri, E., Ostovan, F., Toozandehjani, M., Shafiei, E., Mohamed, I.F. Study and selection of most appropriate filler rod for GTAW of S32750 super duplex steel joints: A comprehensive study on microstructural, mechanical and corrosion properties. Mater Chem Phys 270 124839 (2021) DOI:10.1016/j. matchemphys.2021.124839 [35] Wang, Q., Zhang, Q., Zheng, H., Liu, L., Wu, X., Zhao, C Li, X. (2023). Insight into anti-corrosion behavior of protein extract as eco-friendly corrosion inhibitor. Sust Chem Pharm 34 101177 DOI:10.1016/j.scp.2023.101177 [36] Örnek, C., Davut, K., Kocabas, M., Bayatli, A., Ürgen, M. Understanding corrosion morphology of duplex stainless steel wire in chloride electrolyte. Corr Mater Degr 2 397-411. (2021) DOI:10.3390/cmd2030021 [37] Lovše, A., Skale, S., Vojvodic-Tuma, J. Evaluation of the Condition of the Bottom of the Tanks for Petroleum Products-Forecast of the Remaining Operating Life. Stroj Vestn-J Mech E, 70, 282-292. (2024) DOI:10.5545/sv-jme.2023.682 [38] Calabrese, L., Galeano, M., Proverbio, E. Data mining applied to the electrochemical noise technique in the time/frequency domain for stress corrosion cracking recognition. Corr Mater Degr 4 659-679 (2023) DOI:10.3390/ cmd4040034 Acknowledgement The authors would like to thank National Central Instrumentation Facility, Tamil Nadu, India for assistance in microstructural evaluation and M/s.Vikram Engineering Industry, Trichy, Tamil Nadu, India for assistance in welding and heat treatment studies. Received 2024-07-03, revised 2024-09-29, accepted 2024-11-05, Original Scientific Paper. Data availability The data supporting the study’s findings are included in the paper. Author contribution Mahadevan Govindasamy contributed to data curation, drafting; Lloyd Jenner Mangalakaran Joseph Manuel contributed to analysis; and Senthilkumar Thamilkolunthu contributed to implementation of the work. Študija korozije neenakih zvarov AISI2205 in AISI310 po varjenju z elektrokemicno analizo šuma Povzetek Korozijsko obnašanje neenakih zvarov nerjavnih jekel AISI310 in AISI2205v 5-odstotni raztopini kalcijevega klorida pri 50 °C je bilo raziskano pod tremi pogoji: kot varjeno, z nižjo toplotno obdelavo po varjenju pri 800 °C in z višjo toplotno obdelavo po varjenju pri 1000 °C. Mikrostrukturna analiza je pokazala izrazito jamasto korozijopri varjenem vzorcu, pri cemer so bile širine jamic med 270 µm in 360 µm. Vzorec z nižjo toplotno obdelavo je imel vecje vdolbine (310 µm do 370 µm), medtem ko je pri vzorcu, ki je bil toplotno obdelan višje, opaziti homogeno korozijo z zašcitno oksidno prevleko. Najvišjo stopnjo korozije je imel varjeni vzorec, sledil mu je nizko­ toplotno obdelani vzorec z zmerno stopnjo, najnižjo stopnjo korozije pa je imel visoko-toplotno obdelani vzorec. Gostote korozijskega toka so bile 5,26×10–3 mA/cm², 4,6×10–4 mA/cm² oziroma 1,4×10–4 mA/cm². Elektrokemicne meritve šuma so potrdile te ugotovitve, pri cemer je vzorec, ki je bil obdelan z višjo toplotno obdelavo, pokazal zanemarljivo lokalizirano korozijo in homogeno korozijsko obnašanje. Kljucne besede AISI2205, AISI310, korozija, elektrokemijska impedancna spektroskopija, CaCl2 Thermal Design and Constrained Optimization of a Fin and Tube Heat Exchanger Using Differential Evolution Algorithm Nader Afsharzadeh – Mohammad Eftekhari Yazdi – Arash Mirabdolah Lavasani Islamic Azad University, Department of Mechanical Engineering, Iran moh.eftekhari_yazdi@iauctb.ac.ir Abstract Fin and tube heat exchangers (FTHEs) are utilized for gas-liquid applications frequently. In the current study, a differential evolution (DE) algorithm and JDE as its variant, with a-level constraint-handling technique, are effectively applied to optimize an FTHE. Total weight and total annual cost are selected as objective functions. Seven design variables are taken into consideration: outside tube diameter, transverse pitch, longitudinal pitch, fin pitch, number of tube rows, height, and width of shape. Meanwhile, the logarithmic mean temperature difference (LMTD) method is used for heat transfer analysis under identical conditions such as mass flow rate, inlet and outlet temperatures, heat duty, and other thermal properties. The research findings indicate that the implementation of the DE algorithm coupled with a-level comparison method on optimization problems leads to better solutions for both objective functions compared with those achieved by other approaches such as the genetic algorithm (GA) and heat transfer search (HTS) algorithm. In addition, a parametric analysis is performed for design parameters at the optimum points to show the effects on the objective functions and to identify the feasible design space. The proposed method is straightforward and can generally be employed for thermal design and optimization of FTHEs as well as any other type of compact heat exchangers (CHEs) under different specified duties. Keywords Fin and tube heat exchanger, thermal design, constrained optimization, differential evolution (DE) algorithm, total weight, total annual cost Highlights . Compact heat exchangers aim to minimize weight and annual cost in industrial use. . Metaheuristic algorithms outperform trial-and-error methods in optimization. . Differential evolution with a-level constraints achieves superior optimization results. . Proposed method cuts weight by 9.33% and cost by 6.87 % from previous best results. 1 INTRODUCTION The process of heat exchange between two fluids that are at different temperatures and separated by a solid wall occurs in many engineering applications. The device used to implement this exchange is termed a heat exchanger (HE), and specific applications may be found in space heating and air-conditioning, power production, waste heat recovery, and chemical processing [1]. The area density is the ratio of heat transfer surface to HE volume. A compact heat exchanger (CHE) has a high area density compared to traditional HEs. CHEs are highly effective and low in weight and cost. Fins are used on the gas side of CHEs to compensate for high thermal resistance and enhance the heat transfer coefficient. Plate-fin heat exchangers (PFHEs), fin and tube heat exchangers (FTHEs), and rotary regenerators are examples of CHEs for gas flow on one or both fluid sides [2]. The most common criteria for the optimization of CHEs are the minimum initial cost, minimum operation cost, maximum effectiveness, minimum pressure drop, minimum heat transfer area, minimum weight, or material. The optimization of a CHE can be transformed into a constrained optimization problem and then solved by modern optimization algorithms [3]. The following could be highlighted after looking into the studies accomplished on the thermal design and optimization of PFHEs: Rao and Patel [4] applied the particle swarm optimization (PSO) algorithm for the thermodynamic optimization of a PFHE based on three individual objective functions: total number of entropy generation units, total volume, and total annual cost. Ahmadi et al. [5] used the e-NTU method and a nondominated sorting genetic algorithm (GA) for the thermal modeling of a PFHE to minimize cost and entropy generation. Wang and Li [6] introduced and carried out an improved multi-objective cuckoo search (IMOCS) algorithm for multi-objective optimization, including efficiency maximization, minimization of pumping power, and total annual cost. Hajabdollahi [7] compared two cases of similar and non-similar fins on each side of the PFHE by using a PSO algorithm for thermo economic optimization. If one fluid is a liquid, different fin and tube configurations are frequently used; the liquid passes through the tubes while the gas flows across the bank of finned tubes. Various tube shapes might be used such as circular tubes, ovals, rectangles, and any other complex type. Compressor inter-coolers, air-coolers, and fan coils are examples of power engineering and chemical applications that employ FTHEs. Xie et al. [8] and Raja et al. [9] were seeking to achieve the optimal design of an FTHE based on total weight and total annual cost by employing GA and heat transfer search (HTS) algorithms, respectively. Compared to most other evolutionary algorithms (EAs), differential evolution (DE) is much simpler and more straightforward to implement. The main body of the algorithm takes a few lines to code in any programming language. Also, the performance of DE and its variants is largely better than other optimization algorithms such as PSO, PCX, ALEP, etc. [10]. Babu et al. [11] applied DE algorithm and its various strategies for the optimal design of shell and tube heat exchangers. Ayala et al. [12] proposed a novel multi objective free search (FS) approach combined with DE (MOFSDE) 2.1 Heat Transfer algorithm for heat exchanger optimization. Segundo et al. [13] by For the geometry calculations of staggered tube arrangement, theconsidering a shell-and-tube heat exchanger and the total annual minimum free flow area on the airside is given by the following Eq. cost as the objective function, employed DE algorithm, and Tsallis (1) [2]:differential algorithm (TDE) to optimize it. Also, Yuan et al. [14] 1   .ˆ H °°° compared two helically coiled tubes’ heat transfer characteristics Amin    Pt d tfN W, (1) ˜     c 1 .... f and hydrodynamics by implementing an adaptive multi-objective o Pt optimization DE algorithm. where Now, what is the best solution? Perhaps, this is the main question that arises in an engineering optimization problem. However, in most discussed thermal design and optimization studies about 2b ˜° ... c 2a if 2a . (2) 2b 2b ˜° c a if 2 Values of 2a and b are determined as follows:CHEs, penalty function-based methods are employed to handle the . t ..1 ° f ., constraints and seldom can achieve a global solution that satisfies all Pd tN (3) 2a ˜ ° O f constraints. Differential evolution with Level Comparison (DELC) for the first time is proposed by Wang and Li [15] and achieves superior searching quality on all the problems with fewer evaluation times than other algorithms. In this paper, DELC and JDE as a variant of standard DE with level comparison (JDELC) are applied to the thermal design and optimization problem of an FTHE. The remainder of this paper is organized as follows: In Section 2, an FTHE is modeled by using a closed-form equation to predict the heat transfer coefficient. The next section introduces objective functions including total weight and total annual cost in addition to corresponding constraints. Section 4 is about the traditional design method used for FTHEs. Section 5 demonstrates the DE algorithm and employs DE and JDE based on the a-level constraint-handling technique. Section 6 illustrates a case study of FTHE and explains the results and discussion. In Section 7, a parametric analysis is 2 b˜ 05P.2 . P 05. . d.°PdtN. °° . tl . ot. o. ff (4) The total heat transfer area of the heat exchanger is calculated as: AA A˜ p ° f, (5) where, Ap and Af are the primary and secondary (i.e., fin) surface area of the heat exchanger, respectively, and obtained by, A ˜. d WN 1 ° tN , p ot . ff . (6) . 2 ˆ A ˜ 2NWLH° dN. 2tNWH, (7) ff . ot ff . 4 . where Nt is the number of tubes and Nf is the number of fins per unit length and defined as follows: .ˆ H carried out to obtain feasible design space. Finally, the conclusions N are delivered in Section 8, followed by the list of symbols and the list N, (8) ˜° 1 .... t Pt of references. W °1 F Nf ˜ p . (9) 2 THERMAL DESIGN W For the air side, when number of tube rows is greater than one, the In the present work, an intercooler is considered as an FTHE Colburn factor (ja) correlation is suggested by Wang [16]: with a plain-fin type in which hot air flows normally to a finned ppp tube bundle while cold water flows inside tubes, as illustrated in Fig. j j .0 093 5 6 . F F F ˜.˜.˜. j3 j 1. However, it is common to use other types of fins, such as wavy, j ReN ad 4 (10) =0 086 . .° d c .°ˆ. d h .°ˆ. Pt ˆ. , c slotted, and louvered. where j3 to j6 is calculated by the following formulations: Fig. 1. Fin and tube heat exchanger with cross section view ˆ . N ˆFp 041 0 042 . j3 ˜°0 361 °.0 158 ln .N  .. , (11) . ln .Redc . ..dc  . ..Pl ˆ142 0 076.. . d . h . j4 ˜°1 224 ° , . (12) ln Redc  0 058N . j5 ˜°0 083 , (13) . . ln .Redc . .Redc . j ˜°5 735. .121ln , (14) . 6 ˆ . N . then the heat transfer coefficient on the air side can be achieved by, °.c aa pa, ˜ 1 . ˜ lm a ˜ T For the water side, the heat transfer area can be computed by the ln T ha j (15) ˜ . a Pr . 067 rfe, qp/2. P ˆ . t .. l ° 02.,.. (25)˜ 128 rr . Pt . where r is the radius of the tube based on the outside tube diameter. Then the air side surface efficiency can be obtained by, .Af . ˜o °.1 1 ˜f . (26) ˆ . .AO . Here, the logarithmic mean temperature difference (LMTD) method is applied for heat exchanger analysis. QU˜ AT° lm. (27) LMTD is the maximum temperature potential through the heat transfer process that occurs in a counterflow heat exchanger and is described as the following expression: 1 T˜ 2 T ° (28) , following relationship: A ˜° dWN . (16) i it The Nusselt number was approximated through the correlation given by Gnielinski [17]: fw .Rew °1000. Prw Nu ˜ 8 , (17) 2 w ˆ fw  1 23 . . Pr °1 1127 . w . . 8 . where fw is the friction factor and obtained by, Rew fw ˜.18. 2 log10 °1.64.°2. (18) The heat transfer coefficient on the water side is as follows: Nu k ww hw = . (19)di The basic equation for the design of FTHE is developed in the Eq. where T˜ 2 ˜TT° 1 hi, . T ,co, (29) ˜T2 ° Tho, . T .ci, (30) For a crossflow arrangement, Eq. (27) is modified with a correction factor Fc , QUAF˜ T° .c lm (31) The correction factor Fc is determined from charts or formulas based on two dimensionless parameters: temperature effectiveness P, and the ratio of heat capacity rates, R. Details of calculating these parameters can be found in fundamentals of heat exchanger design [2]. 2.2 Pressure Drop On the air side, the friction factor is obtained from the following correlation given by Wang [16], f 2 f 3 ° F . f ° Pt . (20) [18], 1 p c f ˜ Red .ˆ , (32) 0 0267 . .....ˆ a Pl d c QUAT˜ UAT°˜ UAT (20) ˜° ° , m oom iim where under dry cooling conditions, . do ˆln.. 11 . di . 1 ˜° R °° R ° , (21) fi fo UA  hAi 2 kWNt oo ii thAo where, Rfi and Rfo are the fouling resistances of inside and outside tubes, respectively, and assumed negligible, .i and .o are the fin efficiencies of inside and outside tubes, respectively. The air side fin efficiency is calculated from the modified Schmidt equation that has been proposed by Hong and Webb [19], tanh .mr°. ˜ f . cosmr°., (22) . mr° where 2h m= , (23) tk ff Pt Fp . 0 00758f1 ˜°0 764 . . .0 177 . 0739 . ° , (33) Pl dcN 64 021 . f ˜°15 689 . , 2. ln .Redc . (34) 15 695 . f3 ˜ 1 696. ° , ln .Redc . (35) Gd ac Redc ˜ ,° a (36) where Ga is the mass velocity of air regarding minimum free flow area. Then the pressure drop on air side can be obtained as follows [2]: Ga  A .1 ˆ 2 .ai, ˆ ˜pa °f ai .1 1. 2 a , . .. ., 2 A  i  min .a .m .ao, . .1 ˆ 1 .1 ˆ 1 .11 ˆ ° . ... . . r r  (37) and fe,q f ,eq s.t. (24) ˜° .. .. .. .  .. . . . . . .  In the above equation, s is the ratio of Amin to A. Finally, the For rectangular fins, the equivalent radius is introduced by pressure drop on the water side could be found by the following Schmidt in the following correlation [20], equation, ˆ. . 1103.l5n ˆ ˆ. ˆ. .   . 2 i  a , am a o r r m m f..2W www ˜Pw ° . (38)2di 3 OBJECTIVE FUNCTIONS AND CONSTRAINTS Total weight and total annual cost are considered objective functions. Total weight includes weight of fins and weight of tubes, . ˆ 22 TW ˜ A  t ° NWd  d . (39) f ff .. .. t t  Oi  4 Furthermore, total annual cost consists of investment cost and operating cost which are given as: TACC˜° C , (40) in OP Cin = CAAp , (41) °PVt .° PVt . Cop ˜. Kel ... Kel. . (42).ˆa .ˆw  The subsequent set of constraints is applied to the mentioned objective functions: ˜P °˜P , (43) aa,max ˜Pw °˜Pw,max , (44) A 1<< 1.,2 (45) Ah W = 60, (46) do 300 ˜ Rea ˜ 2104 ° , (47) 2300 ˜ Rew ˜ 2106 ° , (48) where, Rea and Rew are Reynolds numbers based on dc and dh, respectively. The maximum allowable pressure drops on the air side and water side, respectively, are denoted by .Pa,max, and .Pw, max. 4 DESIGN METHOD AND PARAMETERS The steps involved in heat exchanger design based on the LMTD method using a trial-and-error process are as follows [18]: 1. Calculate the outlet temperature according to the heat transfer rate (heat duty) and operating parameters using the steady flow energy equation. 2. Look up the correction factor Fc and calculate LMTD; Eq. (28). 3. Select the size and arrangement of tubes and fins, and calculate the heat transfer area Afirst; Eq. (5). 4. Calculate the convective heat transfer coefficients of the two sides and then, the overall heat transfer coefficient U; Eqs. (15), (19), and (21). 5. Determine the Calculated heat transfer area Acal; Eq. (20). 6. Compare Acal with Afirst. If Acal > Afirst, then go back to step 3, until 1< Afirst / Acal <1.2. 7. Calculate pressure drops and Reynolds numbers on both sides; Eqs. (43), (44), (47), and (48). If they are larger than the allowable pressure drops or are not in valid ranges of Reynolds numbers, then adjust the size and arrangement of tubes and fins until they satisfy specified allowable pressure drops, Reynolds numbers, and step 6. 8. Calculate objective function. Note that complex factors exist here without consideration and this issue is covered by allowing an additional area of up to 20 %. The outside tube diameter (do), transverse pitch (Pt), longitudinal pitch (Pl), fin pitch (Fp), number of tube rows (N), height of shape (H), and width of shape (W ) are assumed as seven design parameters. These parameters and the range of their variations are listed in Table 1 [8]. Shape length, L, is not considered an independent variable, because it can be directly obtained from N and Pl. Constructional parameters except for the number of tube rows are considered continuous for optimization purposes, however, they are available in discrete quantities. If the precision of design parameters is set to 0.01 (N excluded, which takes values 2, 3, 4, 5, and 6), there are 600, 1000, 1900, 750, 5, 350, and 200 choices for the above tabled variables and therefore 600×1000×1900×750×5×350×200˜1017 trial-and-error efforts are needed to find the optimal design which is impossible. In the next section, first DE is explained, then we implement DELC and JDELC algorithms instead of a trial-and-error method to attain minimum objective functions in the feasible design space. Table 1. The upper and lower bounds of design variables Design variable Search range Outside tube diameter, [mm] 7 to 13 Transverse pitch, [mm] 20.5 to 30.5 Longitudinal pitch, [mm] 13 to 32 Fin pitch, [mm] 1 to 8.5 Number of tube rows 2 to 6 Height of shape, [m] 4.5 to 8 Width of shape, [m] 3 to 5 5 DIFFERENTIAL EVOLUTION ALGORITHM A heuristic called an evolutionary algorithm (EA) was first inspired by biological evolution and employs mechanisms such as mutation, recombination, and selection. In other words, EA evolves an initial population after several generations. Therefore, the use of these algorithms has become popular in solving many problems, including engineering optimizations. In an optimization problem, the candidate vectors represent the individuals of a population. DE is a simple, yet powerful algorithm proposed by Price et al. [21] and as a metaheuristic seeks to evolve an initial population toward the optimal solutions by iteratively improving them. This algorithm makes a few assumptions about the problem and can quickly reach the best solutions. 5.1 Standard DE The DE in its standard form has three main parameters: population size NP, mutation factor F, and crossover rate CR. Attaining better solutions and convergence completely depends on the setting of these parameters. To adjust them, a few authors have suggested as following: Price et al. [21] proposed the setting NP = 10n, where, n is the number of design parameters, F . [0.5,1], and CR . [0.8, 1]. According to Rkken et al. [22], a reasonable choice for population size is between 2n and 40n, F . (0.4, 0.95], and CR . (0, 0.2) or CR . (0. 9,1) for separable and non-separable objective functions, respectively. Note that here objective functions are non-separable. Zielinski et al. [23] reported that, in many cases, the best results are obtained with the setting of F =0.6 and CR =0.6. The standard DE includes four principal operations during an optimization problem: 1) initialization 2) mutation 3) crossover 4) selection. The general structure of the algorithm is shown in Fig. 2. 5.1.1 Initialization In a problem with n design variable, each candidate vector is defined as X = (x1, x1, …, xn). The purpose is to optimize objective function f (X). In the beginning, an initial population is generated including vectors as many as NP. Each member of the initial population is generated from Eq. (49). As a result, the initial population is an NP by n matrix. x ˜ x ° rand .01, ...x ˆ x ., ij, j.min . j.max . j.min . (49) i ˜ 12,,., NP and j ˜ 1, 22,.,,n where, xj(max) and xj(min) are the maximum and minimum values of each design variable, respectively. Furthermore, rand(0,1) is a uniformly distributed random number between 0 and 1. Fig. 2. Flowchart of standard DE algorithm 5.1.2 Mutation In this step, a noisy population (donor vectors) is produced from the initial population as follows: for each vector from the current population, ith, the mutated vector is obtained by combining three randomly selected vectors according to the formulation below: M ˜.mi1 ° m , Xc. Fˆ.X . Xb , (50) i ,,,in.˜ a . where, Xa, Xb, and Xc are three random vectors in the current population between 1 and NP except ith. The mutation factor, F, is a positive real number that controls the rate at which the population evolves. F has no upper bound, however effective values are rarely larger than 1 [21]. This mutation step is replicated for all original vectors of the current population to produce new population members that would improve the search space. This strategy, named DE/ rand/1, is the most popular and simplest DE variant, which uses one difference as a perturbation of the base vector. There are many other variants of the mutation mechanism that have been subsequently proposed by Das et al. [10] and Price et al. [21], such as DE/rand/2, DE/best/1, DE/best/2, etc. [24]. 5.1.3 Crossover After mutation, the ith original vector from the current population is recombined with the corresponding vector from the mutated population to produce the trial vector Ui= (ui,1, …,ui,n). Each element of the trial vector is determined based on the following equation: .m if rand°01, .. CRor jR˜ . ij, uij, ˜ˆ , (51) x otherwise . ij, . where CR is between 0 and 1 which represents the probability of selecting a trial vector from the original vector and mutated vector, and R is a random integer number between 1 and n. 5.1.4 Selection As the last step, just one of the vectors, Xi (original) and Ui (crossed) can survive. This selection is done based on the type of problem as follows: 1. for an unconstrained problem, objective function values of the two above vectors are the comparison criteria. If the goal is a minimization problem, the vector with a lower objective function value will be selected, and vice versa. Eq. (52) represents the selection step due to the minimization of an objective function. The following process is repeated for a certain number of generations or until convergence criteria are satisfied. t tt t˜1 ˆ.Ui if f .Ui .. f .Xi . Xi °. . (52) . X t otherwise  i 2. If the problem is constrained, like the present case, in addition to checking the objective function, the constraints’ fitness should also be checked. In the next section, we apply a-level comparison to handle the optimization problem constraints. 5.2 Differential Evolution with Level Comparison The canonical versions of EAs, including DE, lack a mechanism to bias the search to the most feasible area since they were not designed inherently to solve constrained optimization problems [25]. Hence, this has triggered a significant amount of investigation, and during the last years, many different methods for incorporating constraints into the fitness function of an EA have been proposed [26]. Practically, adjusting control parameters such as F and CR and coupling them with suitable and effective constraint-handling strategies can considerably enhance the search capability of DE algorithms. Differential evolution with level comparison (DELC) performs initialization, mutation, and crossover operations similar to standard DE, but besides objective function values, a satisfaction level for the constraints is considered, which indicates how well a search point (candidate vector) satisfies the constraints. In other words, this method quantifies the constraint violation [27]. Below, f (X) is assumed to be a general function that should be minimized by the inequality constraints set gk (X) with k= 1, …, p, and equality constraints set hs (X) with s= 1, …, q. min f X s.t. g X .; ˜° k ˜°0 X k .12,,.,;ph X .0; s .12,,,.q. (53) s ˜° From the first generation (t =1) to the end (t = Genmax), the selection between each original vector (Xi) and its trial (Ui) from the current population, will be done regarding DELC. Also, f1 and f2 are the objective function values of the mentioned vectors, respectively, and µ1 and µ2 are their related satisfaction levels. For instance, the resulting satisfaction level of vector Xi is determined by, ˜1 °˜Xi °min ˜g Xi , ˜h Xi , (54) .. .k .. s ..ˆ ks, where all constraints are calculated from piecewise linear functions as follows: . 1 if g X .0  k °.i °.  gk Xi ˜ X .1 ˆ if 0 g X .b , (55) gk °.i . b .k °.ik  k  0 otherwise  6 A CASE STUDY AND RESULTS To demonstrate the described procedure, a case study is considered and the effectiveness of the proposed algorithm is assessed by analyzing an application example that was earlier investigated by GA [8] and HTS [9]. The model of FTHE is cross-flow and both fluids are unmixed. The material of the tubes is stainless steel with a thermal conductivity of 15 W/(m·K) and a density of 7820 kg/m3, while the fin material is aluminum with a thermal conductivity of . hXs °.i 1 . h s °.Xi ˆbs ˜ X. if , (56) hs °.i . bs  0 otherwise  where bk and bs are two positive numbers. In this study, the median values of the constraint violations in the initial population are employed and these parameters are updated after each generation. Here, the selection between two sets of ( f(Xi), µ(Xi)) and ( f(Ui), µ(Ui)) based on DELC with a satisfaction level is according to: ˆ t tt tt .U . f .U ., .U ... . f .X ., .X .. t ˜1 i ii  i i Xi °. . (57) .X t else  i The a-level comparison