The application aims to determine the thermal and hydraulic performance of externally finned, counterflow, Shell, and Tube Heat Exchangers (STHE). The application refers to the cooling of machine oil flowing in the annular region, including nonspherical cylindrical nanoparticles of Boehmite Alumina. The oil inlet temperature is equal to 80 °C. Sea water is a coolant with an inlet temperature of 20°C. The main parameter in the optimization process is the number of finned tubes used for oil cooling. Another optimization factor is the number of heat exchanger units connected by hairpin. The number of fins per tube is fixed, equal to 34. The oil flow is set and equal to 4.0 kg/s. The inlet water flow varies, with a maximum flow of 5.0 kg/s. The quantities determined for analysis are: the thermal effectiveness, the actual and maximum heat transfer rates, the pressure drops caused in the tubes and by the flow in the annular region and fin system, the thermal and viscous irreversibilities, and the fluid outlet temperatures, and the thermodynamic Bejan number. It was determined that increasing the number of finned tubes from two to six tubes leads to better thermal and hydrodynamic performance. That is, it produces a favorable costbenefit, to the detriment of the high viscous dissipation caused by the oil in the annular region. As an object of analysis, the inclusion of nanoparticles showed a significant improvement in thermal performance and an increase in viscous dissipation, with a slight decline in the Bejan number.
Keywords: Externally finned tube, Second law of thermodynamic, Shell and tube heat exchanger, Theoretical analysis, Thermal effectiveness, Thermal efficiency.
Received: 4 July 2022 / Revised: 17 August 2022 / Accepted: 2 September 2022/ Published: 19 September 2022
The method of thermal efficiency of heat exchangers is a solution procedure that has recently been applied to various types of heat exchangers. When associated with viscous irreversibility and the thermodynamic Bejan number, it enables theoretical optimization analysis that can be helpful in the design and testing phase of heat exchangers. There are few academic works dealing with externally finned tube heat exchangers. The presented procedure is innovative as it includes them together to improve thermal performance and, at the same time, significantly reduce viscous dissipation. The use of nanoparticles amplify innovation.
Finned tubes are widely used to passively improve heat transfer in circular tubes (one of the most used heat transfer surfaces in heat exchangers). Extended surfaces, called fins, are applicable when an additional area is needed to increase heat transfer. As far as the geometry of the fins is concerned, most of them are strips of metal with surfaces positioned longitudinally along the axis of the tube. Many experimental and numerical investigations have been conducted on different types of tubes with internal fins using a variety of fluids (air, water, oil, ethylene, etc.). However, it is observed that literature is scarce regarding investigations in tubes with external fins.
Zafar, et al. [1] numerically investigate finned rings with longitudinal fins of the triangular crosssection. The work aims to obtain optimized configurations where the costbenefit ratio can be as favourable as possible. They use the finite element method and genetic algorithm for configuration optimization. The results obtained provide optimal use of energy together with cost savings. Recommend the use of at least 18 fins.
Muhammad, et al. [2] numerically investigate numerous geometric configurations in a double tube heat exchanger with triangular fins. The use of the DGFEM  Galerkin finite element method to explore the thermal characteristics of the arrangements in the thermal performance of the heat exchanger under analysis. They conclude, among others, that the Nusselt number increases with the values of the solid and fluid thermal conductivity ratio and suggest that the thermal resistance between the media plays a fundamental role in the design of the heat exchanger.
Ghazala, et al. [3] perform a numerical study using finite difference techniques in an externally finned shell and tube heat exchanger. They investigate the influence of variations in fin height, number of fins, and thermal conductivities on thermohydraulic performance and discuss optimal configurations. They make comparisons with results from the literature to validate the developed procedure. They conclude, among other things, that the height and the number of fins are the most effective geometric parameters.
Muhammad., et al. [4] propose an innovative diamondshaped fin profile, which they claim to be the first work of its kind for a double finned tube heat exchanger. The designed profile allows automatic transformation, with changes of some parameters, in triangular and rectangular profiles available in the literature. They use the finite element technique to solve the problem. They present the most recommended shapes for the quantities associated with the fins, introducing variations in the height and width of the fins, both for thermal performance and viscous dissipation. They clarify that the recommendations are valid for the ratio between the radii of the inner and outer tubes, equal to 0.25.
Arvind and Yeshyahou [5] state that the practical use of correlations to determine the thermal performance of finned tube heat exchangers is limited by the large number of parameters that can influence the Nusselt number and the friction factor. In this sense, they conclude, empirical correlations have many limitations in terms of applicability. They describe a methodology to evaluate the thermohydraulic performance of a finned tube heat exchanger with internal and external fins. Initially, they use the usual correlations for smooth tube flow and flat plate flow, which are numerically adjusted through successive substitutions. Then, they use correlations in the literature to prove the procedure performed when applied to simple cases. They observe that adding fins reduces the Nusselt number, but the heat transfer rate increases due to the rise in the total heat exchange area.
Górecki, et al. [6] elaborate on a tubular heat exchanger project composed of individually finned heat tubes and conduct an experimental study and mathematical modeling to develop a thermal model based on empirical correlations obtained from experimental work. Based on the "brute force" method, the global cost optimization process made it possible to determine the most suitable parameters for the heat exchanger under analysis. The mathematical modeling results produced a good agreement with experimental results, with a maximum relative difference equal to 10%.
Prottay, et al. [7] perform a performance study of double tube heat exchangers connected by a clamp (hairpin) for oil cooling. This work aims to obtain geometric parameters that optimize the configuration under analysis for a better costbenefit relationship between heat exchange and pressure drop observed in the heat exchanger since the pressure drop impacts the energy per unit of time generated by the pumping system.
Shiva and Murthy [8] analyze the performance of concentric tube heat exchangers using by passive heat transfer technique. They use different longitudinal profiles of fins: rectangular, parabolic, and triangular. For performance analysis, the mass flows of the internal and external fluids vary, keeping the base and height of the fin constant. They conclude that the fin system allows a higher heat transfer rate concerning the nonfinned tube, with higher rates for the configuration with a rectangular profile fin.
Ayon, et al. [9] designed a compact shell and tube heat exchanger to obtain high thermal efficiency and minimum cost. The heat exchanger under analysis contains inner tubes with axes parallel to the shell to cool oil using seawater. They report that limits were established for the difference in fluid outlet temperatures and total pressure drop as fundamental parameters for minimizing cost and maximizing thermal effectiveness.
Heidar, et al. [10] analyze a radial finned shell and tube heat exchanger, using nine physical parameters as a reference. The main parameters used for analysis are tube diameter, length, number of tubes, and fins. They determine the coefficients related to heat transfer and pressure drop on the hull side using the "modified Delaware" technique. They obtain an optimal compromise between heat transfer rate, ranging from 3517 to 7075 kW, and pipe pressure drop, ranging from 3.8 to 46.7 kPa.
Faraz, et al. [11] use nanoparticles in different volumetric concentrations to numerically analyze the thermal performance of a shell and finned tube heat exchangers. They use Fe2O3 nanoparticles in water as a base fluid at concentrations of 1.0%, 1.5%, and 2.0%. They use ANSYS Fluent software for numerical simulation and comparison with results obtained for pure water. They report that increasing the proportion of nanoparticles causes greater thermal efficiency without significant pressure drop and that a volumetric fraction equal to 2.0 % allows an increase of 19.1% in the heat transfer rate.
Nogueira [12] uses concepts of efficiency and thermal effectiveness in thermal analysis of shell and tube condenser using Freon 134a as refrigerant flowing in the shell. The analysis includes three conditions for the coolant along the hull: superheated steam, saturated steam, and saturated liquid. Each of the three regions contains four tubes, consisting of 12 tubes. Horizontal flow deflectors are included in the superheated steam region. Temperature, efficiency, and effectiveness profiles were obtained for the three regions under analysis, with waterbased aluminum oxide nanoparticles flowing in the tubes. The refrigerant flow rate is fixed, equal to 0.20 kg/s, and the nanofluid flow rate varies from 0.05 kg/s to 0.40 kg/s. It performs a comparative analysis with experimental results obtained in the literature for steam pressure equal to 1.2 Mpa and water flow equal to 0.41 kg/s.
Nogueira [13] applies the second law of thermodynamics through the concepts of efficiency, effectiveness, and thermal irreversibility to analyze shell and tube, heat exchangers. Water flows in the hull with an inlet temperature of 27ºC, and a waterethylene glycol mixture with volume fractions of silver nanoparticles (Ag) or aluminum dioxide (Al2O3) flows in the tube with an inlet temperature of 90ºC. The water flow rate in the shell is kept constant, equal to 0.23 kg/s, and the flow of 50% ethylene glycol varies from 0.01 to 0.50 kg/s. Results were obtained graphically, changing the volume fraction for the nanoparticles. It is shown that the flow regime has a significant effect on the performance of the heat exchanger.
It analyzes configurations of heat exchangers with finned inner tubes, as shown in Figure 1. Figure 2 shows shell and tube heat exchangers connected through a clamp. This type of configuration, called hairpin in the literature, is used to optimize the space where heat exchangers will be installed.
Table 1 presents the properties of the oil, water, and Alumina. For performance analysis, the nonspherical cylindrical Alumina nanoparticles, with a volume fraction equal to 5.0%, will be associated with the oil.
ρ kg/m^{3} 
k W/ (m K) 
Cp J/(kg K) 
µ kg/(m s) 
ν m^{2}/s 
α m^{2}/s 
Pr 

Oil (hot) 
885.27 
0.1442 
1902 
7.5 10^{2} 
8.47 10^{5} 
8.56 10^{8} 
989 
Water (cold) 
1013.4 
0.639 
4004 
9.61 10^{4} 
9.48 10^{7} 
1.57 10^{7} 
6.02 
B. Alumina 
3050 
30.0 
618.3 
 
 
 
 
a – 2 finned tubes; b – 4 finned tubes; c – 6 finned tubes.
The formulation, with the data necessary to determine the quantities of interest in the analysis, is described below.
For the compound oil + Boehmite Alumina Nanoparticles, we have Monfared, et al. [14]:
are constants associated with cylindrical nonspherical nanoparticles [14].
Equation 72 represented by is the Bejan thermodynamic number [16].
The application refers to the cooling of machine oil flowing in the annular region, including nonspherical cylindrical nanoparticles of Boehmite Alumina. The oil inlet temperature is equal to 80 °C. Sea water is a coolant with an inlet temperature of 20°C. The main parameter in the optimization process is the number of finned tubes used for oil cooling. Another optimization factor is the number of heat exchanger units connected by hairpin. The number of fins per tube is fixed, equal to 34. The oil flow is fixed and equal to 4.0 kg/s. The inlet water flow varies, with a maximum flow of 5.0 kg/s.
Figures 3  5 present thermal effectiveness for three typical situations under analysis: 2, 4, and 6 finned tubes. The number of heat exchangers connected per clamp also varies, from 1 heat exchanger to 4 heat exchangers. The thermal effectiveness increases with the mass flow of water in the tubes, represented by the Reynolds number (Rec), with the number of finned tubes and the number of heat exchangers connected to each other.
The thermal effectiveness increases as the heat exchange area increase with the number of finned tubes. The effectiveness reaches maximum values of approximately 0.6, 0.8, and 0.9 for 2.4 and 6 finned tubes, respectively Figures 3  5, when the number of connected heat exchangers equals 4. The Reynolds number for the refrigerant decreases with the number of finned tubes, because the total flow of water entering the heat exchanger is divided between the tubes. The thermal effectiveness is influenced by the volume fraction of the nonspherical cylindrical alumina nanoparticles, presenting higher values than those obtained for pure oil.
As the thermal effectiveness reflects the heat transfer rate value, the ratio between the actual heat transfer rate and the maximum heat transfer rate, the conclusions regarding the thermal effectiveness observed for 2, 4, and 6 finned tubes Figures 34, are valid for heat transfer rates Figures 6  8. Therefore, the predominant factor for presenting these data is that the absolute numerical energy values per unit of time transferred between the fluids can be measured.
The principal thermal quantity to measure the heat exchanger's actual thermal performance is, of course, the outlet temperature of the fluid to be cooled, a parameter presented in Figures 9 and 10.
Figure 9 shows the oil outlet temperature for some finned tubes equal to 2, 4, and 6, and two (NHE=2) clampconnected heat exchangers. Again, one can observe the influence of nonspherical cylindrical alumina nanoparticles. For Nt = 2, the minimum temperature observed for pure oil is close to 62 ºC; for oil, with a volume fraction of nanoparticles equal to 5.0%, the minimum temperature is close to 57 ºC. In this last situation, using nanoparticles, there is a maximum gain of approximately 8.0% for thermal performance within the flow rate under analysis. For Nt = 4, the minimum temperature observed for pure oil is close to 50 ºC; for oil with a volume fraction of nanoparticles equal to 5.0%, the minimum temperature is close to 45 ºC. In this last situation, using nanoparticles, there is a maximum gain of approximately 10.0% for thermal performance within the flow rate under analysis. For Nt = 6, the minimum temperature observed for pure oil is close to 46 ºC. For oil with a volume fraction of nanoparticles equal to 5.0%, the minimum temperature is close to 41 ºC. In this last situation, using nanoparticles, there is a maximum gain of approximately 11.0% for thermal performance within the flow rate under analysis.
Figure 10 shows the oil outlet temperature for a few finned tubes equal to 2,4, and 6 for four (NHE=4) clampconnected heat exchangers. Again, one can observe the influence of nonspherical cylindrical alumina nanoparticles. For Nt = 2, the minimum temperature observed for pure oil is close to 54 ºC; for oil with a volume fraction of nanoparticles equal to 5.0%, the minimum temperature is close to 48 ºC. In this last situation, using nanoparticles, there is an approximate maximum gain of 11.1% for thermal performance within the flow rate under analysis. For Nt = 4, the minimum temperature observed for pure oil is close to 40 ºC; for oil, with a volume fraction of nanoparticles equal to 5.0%, the minimum temperature is close to 34 ºC. In this last situation, using nanoparticles, there is a maximum gain of approximately 15.0% for thermal performance within the flow rate under analysis. For Nt = 6, the minimum temperature observed for pure oil is close to 34 ºC, and for oil with a volume fraction of nanoparticles equal to 5.0%, the minimum temperature is close to 29 ºC. In this last situation, using nanoparticles, there is a maximum gain of approximately 15.0% for thermal performance within the flow rate under analysis.
The numbers demonstrate that the doubling of finned tubes brings a significant gain in thermal performance. When added by doubling the number of heat exchangers, the thermal performance is increased to approximately 24% when pure oil. And 29% with the introduction of nanoparticles. However, the gain with doubling the heat exchangers is significantly more significant than including nanoparticles with a 5.0% volume fraction for the same number of finned tubes.
Thermal irreversibility, Figures 11  13, are relevant factors for analyzing the global, systemic performance of the heat exchanger. Thermal irreversibility is, by nature, associated with thermal effectiveness and heat transfer rate since it represents the relative increase in the total entropy rate in thermal energy generation. As the objective when designing a heat exchanger is to obtain the best possible heat transfer between the fluids, despite the viscous irreversibility, the increase in thermal irreversibility tends to improve the performance of the heat exchanger in general. In this case, when observing the results presented in Figures 11  13, it is evident that the increase in the number of finned tubes points to an improvement in the overall performance of the heat exchanger. Analyzing the thermal performance with NHE ranging from 1 to 4, a gain of 50% is observed for Nt=2, 37% for Nt=4, and 32% for Nt=6.0.
To analyze the overall performance of the heat exchanger, Figure 14 shows the total pressure drop in the annular region, where the fins are located. The pressure drop in the annular region is prevalent against the pressure drop in the tubes. The analysis encompasses the number of heat exchangers, the number of finned tubes, and alumina nanoparticles' influence. The pressure drop grows with the increasing number of heat exchangers and nanoparticle volume fraction. The most relevant is that the pressure drop decreases significantly when the number of finned tubes increases. This decrease is related to the relative increase in area for oil flow. This result is highly relevant to the system's overall performance under analysis regarding costbenefit.
Figures 15  17 present results for viscous irreversibility for finned tube numbers equal to 2, 4 and 6, respectively.
Viscous irreversibility follows the trend of pressure drop since it is influenced by it. It is observed that the viscous irreversibility increases with the number of heat exchangers and decreases with the number of tubes since the expansion of finned tubes increases the oil passage area.
Figures 18 and 19 show the results obtained for the thermodynamic Bejan number for a few finned tubes equal to 2, 4, and 6, respectively. The Bejan number is the ratio between thermal irreversibility and total irreversibility (thermal + viscous). The values presented are significantly low, with great relevance to the viscous irreversibility. As already observed, more excellent performance can be marked with an increase in the number of finned tubes, with and without nanoparticles.
Since what leads to better thermal performance influences and contributes to more significant viscous loss, the need to cool the oil to a specific temperature is a price. However, it should be noted that the expansion of finned tubes can lead to costeffectiveness improvement over time of use of the considered configuration.
The presented methodology makes it possible to increase the number of finned tubes and digits of heat exchangers automatically, paying attention to the internal diameter of the annular region, whose area must surpass the space occupied by the finned tubes. Therefore, the increase in the number of tubes is expected to improve the thermal performance versus viscous dissipation relationship.
The application refers to the cooling of machine oil flowing in the annular region, including nonspherical cylindrical nanoparticles of Boehmite Alumina. The main parameter in the optimization process is the number of finned tubes used for oil cooling. Another optimization factor is the number of heat exchanger units connected by hairpin.
The numbers show that the expansion of finned tubes brings a significant gain in thermal performance when added to the increase in the number of heat exchangers.
The thermal effectiveness reaches a maximum value approximately equal to 0.6 for two finned tubes and 0.9 for six finned tubes, within the flow range under analysis.
The pressure drop grows with the increase in heat exchangers and the inclusion of nanoparticles. However, it decreases significantly when the number of finned tubes is increased. This decrease is related to the relative increase in the area for oil flow and is highly relevant to the system's overall performance under analysis. Viscous irreversibility increases with the number of heat exchangers and decreases with the number of tubes.
Since what leads to better thermal performance influences and contributes to more significant viscous loss, the need to cool the oil to a specific temperature is a price. However, it should be noted that the expansion of finned tubes can lead to costeffectiveness improvement over time of use of the considered configuration.
The increase in the number of finned tubes is expected further to improve the thermal performance versus viscous dissipation relationship.
Funding: This study received no specific financial support. 
Competing Interests: The author declares that there are no conflicts of interests regarding the publication of this paper. 
[1] I. Zafar, S. S. Khalid, and I. Muhammad, "Optimum configurations of annulus with triangular fins for laminar convection," Thermal Science, vol. 21, pp. 161173, 2017.
[2] I. Muhammad, K. S. Syed, Z. Iqbal, and A. Hassan, "A conjugate heat transfer analysis of a triangular finned annulus based on DGFEM," Mathematical Problems in Engineering, pp. 118, 2018.Available at: https://doi.org/10.1155/2018/6947565.
[3] A. Ghazala, K. S. Syed, and M. Ishaq, "Finite difference solution of conjugate heat transfer in double pipe with trapezoidal fins," Numerical Modeling and Computer Simulation, 2019.Available at: https://doi.org/10.5772/intechopen.82555.
[4] I. Muhammad., A. Ali, M. Amjad, K. S. Syed, and Z. Iqbal, "Diamondshaped extended fins for heat transfer enhancement in a doublepipe heat exchanger: An innovative design," Applied Sciences, vol. 11, pp. 121, 2021.Available at: https://doi.org/10.3390/app11135954.
[5] R. G. Arvind and L. Yeshyahou, "A semiempirical methodology for performance estimation of a double pipe finned heat exchanger," in Proceedings of the 9th Biennial ASME Conference on Engineering Systems Design and Analysis, July 79, 2008, Haifa, Israel, 2008.
[6] G. Górecki, M. Łęcki, A. N. Gutkowski, D. Andrzejewski, B. Warwas, M. Kowalczyk, and A. Romaniak, "Experimental and numerical study of heat pipe heat exchanger with individually finned heat pipes," Energies, vol. 14, pp. 126, 2021.Available at: https://doi.org/10.3390/en14175317.
[7] M. Prottay, R. J. Ishan, M. Sumit, and M. M. Ali, "Oil cooler: Finnedtube doublepipe heat exchanger." A ME 310 Project. Department of Mechanical Engineering Bangladesh University of Engineering and Technology. Supervisor: Dr. A. K. M. Monjur Morshed & Dr. Md. Ashiqur Rahman," 2020.
[8] K. V. K. K. Shiva and K. Murthy, "Numerical study of heat transfer in a finned double pipe heat exchanger," World Journal of Modelling and Simulation, vol. 11, pp. 4354, 2015.
[9] M. Ayon, M. L. Khalid, T. Md Mahbub, and A. Md Younus, "Design of a shell and tube heat exchanger: Oil cooler for marine applications," Bangladesh University of Engineering & Technology Technical Report2020.
[10] S. Heidar, M. Aliehyaei, and M. A. Rosen, "Optimization of a finned shell and tube heat exchanger using a multiobjective optimization genetic algorithm," Sustainability, vol. 7, pp. 1167911695, 2015.
[11] A. Faraz, A. Sözen, A. Khanlari, and A. D. Tuncer, "Heat transfer enhancement of finned shell and tube heat exchanger using Fe2O3/water nanofluid," Journal of Central South University, vol. 28, pp. 32973309, 2021.
[12] É. Nogueira, "Theoretical analysis of a shell and tubes condenser with r134a working refrigerant and waterbased oxide of aluminum nanofluid (Al2O3)," Journal of Materials Science and Chemical Engineering, vol. 8, pp. 122, 2020.
[13] E. Nogueira, "Thermal performance in heat exchangers by the irreversibility, effectiveness, and efficiency concepts using nanofluids," Journal of Engineering Sciences, vol. 7, pp. F1–F7, 2020.
[14] M. Monfared, A. Shahsavar, and M. R. Bahrebar, "Second law analysis of turbulent convection flow of boehmite alumina nanofluid inside a doublepipe heat exchanger considering various shapes for nanoparticle," Journal of Thermal Analysis and Calorimetry, vol. 135, pp. 15211532, 2019.
[15] A. Fakheri, "Heat exchanger efficiency," Transactions of the ASME, vol. 129, pp. 1268 1276, 2007.
[16] A. Bejan, "The thermodynamic design of heat and mass transfer processes and devices," International Journal of Heat and Fluid Flow, vol. 8, pp. 258276, 1987.
Views and opinions expressed in this article are the views and opinions of the author(s), International Journal of Chemical and Process Engineering Research shall not be responsible or answerable for any loss, damage or liability etc. caused in relation to/arising out of the use of the content. 