Effects of geometrical and operational parameters on heat transfer and fluid flow of three various water based nanofluids in a shell and coil tube heat exchanger
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Abstract
Heating and cooling of a system by heat exchanger Plays an important role in various industries. Improvement of heat transfer in heat exchangers resulted in reducing the size of heat exchanger, and utilizing more compressed heat exchangers with higher efficiency. Using helical/spiral tube is a passive method for improving the performance of heat exchangers due to its low geometry and high heat transfer coefficient. Also, in heat exchangers, one of the most important methods is additives such nanoparticles for liquids and classified as a passive method which does not need any external power like in active methods. The objective of this study is to investigate efficient operational and geometrical parameters. The considered geometrical parameters include helix pitch, coil diameter, and helix height. Also, the effect of using Al_{2}O_{3}, CuO, SiO_{2} nanofluids on thermal performance of the heat exchanger is investigated numerically. The results show that the geometric parameters of the coil have a significant effect on the heat exchangers of the shell and coil.
Keywords
Shell and coil heat exchanger Helical coil Heat transfer Nanofluid Thermal performance1 Introduction
The heat exchangers are industrial equipment that can be used to heat or cool a fluid because of an indirect contact between two fluids inside them. This definition implies that in a heat exchanger there are at least two fluids in which the heat transfers between them. Heat exchangers are used widely in several industries, such as power plants, refineries, glass and metal melting industries, pharmaceutical and food industries, paper industry, petrochemicals, cold stores, gases condensation (such as air) and electronic industries. In the following, some explanations are given about different types of heat exchangers, the principles of heat transfer in them, and helical coil heat exchangers.
The classification of heat exchangers is based on contact area between hot and cold fluids, direction of cold and hot fluid flows, mechanism of heat transfer between hot and cold fluids, and mechanical structure of heat exchangers. Heat exchangers can be divided into two heat exchangers according to their structure: plate heat exchanger, and coil heat exchanger. Shell and coil heat exchanger is a type of coil heat exchanger. These heat exchangers consist of helical coils placed in a shell and these coils are also used in refrigeration systems in the form of concentric condensers and vaporizers. The heat transfer coefficient of helical coil is higher than straight tube. These heat exchangers are befitting for thermal expansion and clean fluids because cleaning them is almost impractical.
Studies in the field of heat transfer in helical coils are numerically and experimentally. In general, less experimental studies have been done due to complexity of heat transfer in helical coils. Most investigations are limited to boundary conditions of constant wall temperature and constant heat flux on the wall. The constant temperature of wall is an ideal boundary condition in heat exchangers associated with phase shift at outlet of coil as well as constant heat flux on wall is a suitable boundary condition for coils that are under electric heating or under the influence of heat from nuclear fuel. Despite the fact that in many practical applications transferring heat between fluids is carried out without changing the phase, investigations on helical coils have been done under various boundary conditions.
Kumar et al. [1] studied helical double pipe heat exchangers numerically and experimentally. In a numerical approach, Ansys Fluent software was used in which standard Kɛ method applied for modeling turbulent flow and finally, profiles of velocity and temperature were demonstrated. In an experimental approach, using inlet and outlet temperature measurements and Wilson plot method, Figure s of changes in the total heat transfer coefficient, as well as internal and external Nusselt numbers based on Dean Number are examined. They also reported an increase in total heat transfer coefficient by increasing Dean Number in inner coil with a constant mass flow in shell. A similar trend was observed in increasing total heat transfer coefficient by increasing Dean Number in outer tube, with a constant mass flow in tube.
Salimpour [2, 3] studied helical shell and coil heat exchanger experimentally. Since change in temperature of heat exchanger will change the properties of fluid, it will also affect heat transfer coefficient. Salimpour evaluated the viscosity, thermal conductivity, specific capacity and density, by considering working fluid in the tube (oil) as a function of temperature. At an inlet fluid temperature of 70 °C, the Prandtl number is placed at an interval of Dravid et al. [4] correlation and the results of this study (variable properties) were compared with the results of Dravid et al. (constant properties). In high Dean Numbers, the assumption of constant properties led to a large difference in the results, and finally, a relevance for calculating the heat transfer coefficient of tube with variable properties was presented. They examined experimentally heat exchanger in two different conditions of counter flow and parallel flow. Salimpour by using 72 tests, presented a relevance for calculating the heat transfer coefficient of shell and coil tube separately and eventually, compared the proposed correlation with the others under different boundary conditions.
Jayakumar et al. [5] checked heat transfer in helical coils with boundary condition of constant temperature and constant heat flux in the wall. The results indicated that helix pitch is effective only in the developing area, and local Nusselt number is dependent on helix pitch when torsion is occurred in the flow. It is worth mentioning that average Nusselt number does not depend on the helix pitch. Thus, the Nusselt number depends only on coil diameter. In addition, they provided a correlation for calculating Nusselt number according to their boundary conditions. The results of the proposed correlations are the same in Reynolds numbers over 50,000. In another study, Jayakumar [6] studied helical shell and coil heat exchanger experimentally and numerically and presented a correlation for calculating heat transfer coefficient in tube.
Hashemi and Behabadi [7] studied nanofluid flow inside the helical coil under constant heat flux boundary condition. In this experimental study, they used cuo nanofluid with the weight percentages of 0.5, 1 and 2%. The experimental system designed by them is as follows. The geometry of heat exchanger kept constant during the experiment, while heat flux of the outer wall of the tube, flow rate and nanofluid weight percentage have been changed. Based on the tests, they concluded that the effect of using nanofluid in helical coils with a constant flow rate is far greater than that in a smooth pipe. In 1995, Choi [8] for the first time introduced nanofluid as a new environment for heat transfer at Argonne National Laboratory. Nanofluids obtained by suspending nanoparticles within ordinary and commonly used heat transfer fluids, which are known as basic fluids.
Sheikholeslami et al. [9] studied the heat recovery and the use of latent heat energy storage systems (LHTESS). The effects of both inorganic nanoparticles as an additive for PCM (phase change materials) and magnetic field on the strength of PCM inside a porous energy storage system are modeled. For this purpose, a mixture of CuO nanoparticles and water was used and an external magnetic field was applied to the system. The influence of various parameters such as Lorentz strength, copper concentration/water content and the number of rails during charging have been investigated [10]. The solidification process has accelerated by adding copper nanoparticles to the pure PCM, according to the study. As the number of insulators increases, the average temperature increases and the total energy profiles decrease as the solid fraction profile increases [11].
Hardik et al. [12] consequence the effect of helical coil curvature on Reynolds number, Prandtl number, friction coefficient, and Nusselt number. In this study, water was used as a working fluid. Murshed et al. [13] have studied that addition of copper dioxide nanoparticles in water at a volume concentration of 0.5%.
Wen and Ding [14] observed a high heat transfer coefficient in the laminar nanofluid flow, based on the calculations performed on experimental data. Yang and Ebadian [15] investigated a turbulent flow of a helical coil with finite length, numerically. The consequences showed that by increasing helix pitch, temperature distribution in vertical section is asymmetric and effect of helix pitch is intensified by increasing flow rate.
Sheikholeslami [16] investigated the forced convection studies of CuO–H_{2}O nanoparticles in a doordriven porous cavity affected by magnetic field. The effect of nanoparticle shape and Brownian motion on nanofluid properties have been considered. The solutions of the final equations are obtained by CVFEM. The graphs for different values of Darcy number (Da), CuO–H2O volume fraction (%), Reynolds (RA) and Hartmann (ha) are shown. According to the results of the selection of nanoparticles, the platelet shape has the highest heat transfer rate. Total energy enhances with rise of amplitude [17].
Austen et al. [18] found that if curvature of a pipe is small, there is always a tendency to create critical velocity that is a characteristic of changing a laminar flow to turbulent flow. They observed the secondary flow for the first time by injecting acid into the water current in helical coils and utube pipes. They also observed the same trend by inserting sand into a turbulent flow. Jamshidi et al. [19] examined a helical shell and coil heat exchanger, experimentally and numerically. According to the outcome helix diameter, helix pitch and flow rate in the shell and tube can improve heat transfer in this type of heat exchanger.
Andrzejczyk et al. [20] presents a method for increasing the thermal penetration in the form of reflections to increase the heat energy efficiency of the coil shell. This paper successfully shows that it is possible to increase the efficiency of heat exchange in the coil of the heat exchanger shell using buffer ports. It has been shown in Tien that, due to the presence of curiosity, natural sesame has a significant effect on the values Little Reynolds and the great flame of heat. Configuration of the buffer and input also has a great impact on the results.
Hameed et al. [21] conducted an experimental and numerical study on the heat exchanger converter shell and splint. The spiral tube is made of Cu material. The fluid was working on both sides of the shell and the water pipe. Eight K type thermocouples have been installed at the inlet and outlet on each side and distributed over the length of the shell. To measure the flow rate of hot and cold water, two routers have been used. The key to this study was the coil volume and mass flow rate for both sides. Everywhere in the Earth, the Caleis Coil has changed. The consequences are compared with the case of 0 (direct tube). The consequences of this research show that the enhancement of the heat exchanger performance by reducing the spiral coil field due to the increase of secondary flow. Also, decreasing the mass flow increases the efficiency of the heat exchanger due to the increase in contact time.
KumarNaik et al. [22] investigated the heat transfer using three different nonNewton nanotubes including Fe_{2}O_{3}, Al_{2}O_{3}, and CuO nanoparticles in the CMC carboxymethylcellulose fluid (CMC). Studies have been done to determine the increase of heat transfer in comparison with the base fluid (CMC blue solution) in the shell and the hydraulic coil heat exchanger. NonNewtonian nanoparticles containing nanoparticles have been prepared in the range of 0.2–1.0 wt%. Nanofluid and water were used respectively on the side of the tube and tube. Thermal analysis to determine the coefficient of total heat transfer and the number of shells in various mood, such as the flow rate of cold water, the temperature of the nanotube and the agitator speed in minutes. The consequences show that the Nusselt number increases with increasing nanofluide concentration, the temperature of the lateral fluid of the bottle, the number of religions (coil side flow velocity), and the agitator speed. According to the consequence, the consequence indicated that nanofiltration based on CuO/CMC provides more heat transfer than two other types of liquid (Fe_{2}O_{3} and Al_{2}O_{3}). The heat transfer function of the nonNewtonian nanofluids significantly increased in the higher nanofloid concentration, lefthand thermometer, stirrer speed and number of religions.
Sheikholeslami simulated the nanofluid flow in a threedimensional porous cavity by the magnetic field. The area is filled with Al_{2}O_{3}–H_{2}O nanoparticles. Mesoscopic simulations were performed for different values of Darcy number, Hartmann number, and Reynolds number. The results showed that the temperature gradient is directly related to Darcy number and Reynolds number [23].Nanofluidic Properties, Viscosity of Nanofluid Changes with Brownian Motion Effects. The role of radiation, buoyancy and Hartmann number in alumina treatment has been shown. The results show that the effects of convection decrease with increasing magnetic forces. Radiation can reduce the temperature gradient [24].
Zare et al. [25] used Nanophile tubes and couplings as two passive ways to increase heat transfer. In this scrutiny, the current of turbulent CuOwater nanopilot in coiled and conical coils is numerically has been studied with a fixed wall temperature through a mixed specimen. Simulation results have been confirmed by using empirical data on the heat transfer coefficient and the drop in pressure of the spiral twisted tubes for the number of different Reynolds. They compared four different simulation geometries. The first tube was a twisted cone. Others were twisted tubes whose coil diameter was at least the maximum and average diameter of the coil coil winding. The profiles of the stronger secondary flow velocity in the cone coil pipe were indicated in a specific religion.
Taraprasad Mohapatra et al. [26] modeled three liquid heat exchangers analytically to forespeak the effects of different plan parameters on its thermal performance. The current heat exchanger is an improved heat exchanger for two pipes, where a silicon coil in the occupied space space is inserted between two straight pipes. This differs from the other three heat exchangers in terms of structure, flow regulation and thermal point, where hot water flows through a heliumcoil coil as a heattransfer fluid and continuously transfers heat to the water and the natural air is flowing, in the outer ring and the inner tube is straight. The consequence of the analytical approach are comparative and authoritative compared to the literature and have been wellmatched with them.
In the present study, the effects of efficient geometrical parameters on the thermal performance of the shell and coil tube heat exchanger are investigated numerically. The considered geometrical parameters are coil diameter (d_{C}), pitch (P_{C}) and height (H). Also, the nanofluid is utilized as working fluid in the coil tube and different nanoparticle volume concentration including 2, 3, 4 and 5% are studied. It is worth mentioning that in all investigated models, the heat transfer area is kept constant. Accordingly, the helix diameter (Dc) is considered as free parameter.
The novelty of present work: The investigation includes of two section which at the first part, the effect of the geometry and at the second section, the effect of utilizing different waterbased nanofluid on the thermal performance of the shell and coil tube heat exchanger are evaluated. In the first part, effects of efficient parameters are investigated by keeping constant the heat transfer area and using a free parameter. In all previous studies, the geometrical parameters have been investigated without focusing on keeping constant the heat transfer area. Obviously, by increasing and decreasing a geometrical parameter which leads to an increase in the heat transfer area, the heat transfer rate will be increased. But here, a comprehensive study is presented to investigate the effects of geometrical parameters (by keeping constant the heat transfer area) and to study the effect of using Al_{2}O_{3}, CuO, SiO_{2}water nanofluid in comparison with the pure water on the thermal performance of the shell and coil tube heat exchanger.
2 Governing Equations
Singlephase equations include conservation equations for mass, momentum, and energy. The mass and momentum equations are used to calculate velocity vectors. The energy equation is used to calculate the temperature distribution and heat transfer coefficient. These equations are divided into three categories:
The above equation is the general form of mass conservation equation and is valid in compressible and incompressible flows. The added mass to continuous phase of the second phase of diffusion is such as evaporation of liquid droplets or any other defined source.
In the above equation, \(\mu\) is molecular viscosity and I is the right term of the secondorder tensor that is effect of volume change.
It can be seen from the correlation between length and area of helical coil that length of helical coil depends on helix height, helix pitch, and helix diameter. Also, helical coil area depends on length of the helical coil and helix diameter.
3 Numerical domain and methods
Geometrical parameters of the considered shell and coil heat exchanger
Parameter  Value 

Shell length (L_{sh})  700 mm 
Shell diameter (D_{sh})  620 mm 
Inlet and outlet diameter of the shell (d_{sh})  50 mm 
Coil diameter (d_{c})  16 mm 
Helix diameter (D_{c})  Free Parameter 
Coil pitch (P_{c})  40 mm, 60 mm, 90 mm, 120 mm 
Height of spiral coil (H)  0.24 m, 0.3 m, 0.36 m, 0.42 m 
Heat transfer area (A)  0.00097 m^{2}, 0.0012 m^{2}, 0.0016 m^{2} 
Thermos physical properties of the pure water
Properties  Value  

Density (kg/m^{3})  ρ  998.2 
Specific heat (j/kg k)  C_{p}  4182 
Thermal conductivity (w/m k)  k  0.6 
Viscosity (kg/m s)  µ  0.001003 
The problem is solved using the commercial software ANSYS Fluent 18.2 based on the finite volume method. The discretization of the mass, momentum, turbulence kinetic energy, turbulence dissipation rate and energy equations are performed by the secondorder upwind scheme. The velocity–pressure coupling is overcome by the SIMPLE algorithm. The Green–Gauss cellbased method is employed to evaluate all gradients. The convergence criterion was fixed to 10^{−6} for the residuals of the continuity, momentum, turbulence kinetic energy and turbulence dissipation rate equations and 10^{−8} for the energy equation.
4 Results and discussion
4.1 Validation and grid independent studies
In this section, results obtained by solving the governing equations for fluid flow in the shell and coil heat exchanger are obtained and compared with the experimental results. Validation of present numerical solution (using water) with experimental results [19] is conducted. The water is assumed to flow in both of helical coil and shell. A specific geometry with a helix pitch of 0.015 m and a helix diameter of 0.0813 m is considered here for validation study. The results of present numerical solution are compared with experimental results of Jamshidi et al. [19].
The difference between the present numerical results and the experimental results of Jamshidi et al. [19]
Volume flowrate (Q)  Experimental results (Jamshidi et al. [19])  Present study (numerical simulation)  Error (%) 

1 LPM  42.11  44.91  6.6 
2 LPM  59.97  57.26  4.5 
3 LPM  73.74  71.88  2.5 
4 LPM  85.39  83.96  1.6 
4.2 Effect of efficient geometrical parameters
Parameters for considered model at various helix pitches
Model  Height of spiral coil  Coil pitch  Helix diameter  Spiral coil length  Coil diameter  Heat transfer area 

H (m)  P_{c} (m)  D_{c} (m)  L (m)  d_{c} (m)  A (m^{2})  
Effect of coil pitch  
Model 1  0.36  0.04  0.17  4.829  0.016  9 × 10^{−4} 
Model 2  0.36  0.06  0.24  4.547  0.016  9 × 10^{−4} 
Model 3  0.36  0.09  0.36  4.547  0.016  9 × 10^{−4} 
Model 4  0.36  0.12  0.48  4.547  0.016  9 × 10^{−4} 
Effect of coil diameter  
Model 5  0.36  0.09  0.48  6.05  0.016  1.2 × 10^{−3} 
Model 6  0.36  0.09  0.39  4.92  0.018  1.2 × 10^{−3} 
Model 7  0.36  0.09  0.32  4.04  0.02  1.2 × 10^{−3} 
Model 8  0.36  0.09  0.25  3.16  0.022  1.2 × 10^{−3} 
Effect of coil height  
Model 9  0.24  0.04  0.43  8.12  0.016  1.6 × 10^{−3} 
Model 10  0.3  0.04  0.35  8.26  0.016  1.6 × 10^{−3} 
Model 11  0.36  0.04  0.29  8.22  0.016  1.6 × 10^{−3} 
Model 12  0.42  0.04  0.25  8.27  0.016  1.6 × 10^{−3} 
4.2.1 Influence of coil pitch
In this section, the effect of coil pitch on heat transfer is investigated numerically. Four different coil pitch, including 0.04, 0.06, 0.09, and 0.12 m are considered here which are presented here as models (1–4), respectively. According to Table 4, from model (1–4), as the coil pitch increases, to keep constant the heat transfer area, the helix diameter increases, too. Here the heat transfer area is kept constant as 9 × 10^{−4} m^{2}. Here helix height (H) and coil diameter (d_{C}) are kept constant as 0.36 m and 0.016 m, respectively.
4.2.2 Influence of Coil Internal Diameter
Figure 14 shows that as the diameter of the coil increases, the COP increase in all studied Reynolds number of hot fluid flow. Also, it should be noted that the highest COP in all studied coil diameter belongs to lowest Reynolds number of hot fluid flow (Re = 1300). Model 8 (d_{C} = 0.022 m) at Re = 1300 has the highest COP.
4.2.3 Influence of Helix Height
According to Fig. 14, as height of helix increases, Nusselt number rises. Also, at a constant helix of the height, increment of the Reynolds number leads to higher average Nusselt number. As demonstrated in Fig. 14, by decreasing the height of helix, better contact is made between fluid flow of tube and shell, so the heat transfer between two fluids improves.
Figure 16 shows that as the height of helix increases, to keep constant the heat transfer area, helix diameter declines which covering region by the coil decreases. So, the temperature distribution at low height of helix is better which leads to higher heat transfer rate.
4.3 Utilizing nanofluid as working fluid
The use of accurate values of fluid properties in designing a heat exchanger is important in a particular process. Especially when the fluid is complex and is also under the effect of cooling and heating processes. In fact, fluid properties that are function of temperature result in some problem in designing a heat exchanger.
4.3.1 Effects of various water based nanofluid
Thermophysical properties of studied nanofluid
Fluid  Nanosilicon concentration  Thermal conductivity coefficient (W/m K)  Density (kg/m^{3})  Specific heat capacity (J/Kg K) 

AL_{2}O_{3}  2  36  1050.236  3947.74 
CuO  2  17.65  1108.236  3753.95 
SiO_{2}  2  1.4  1022.636  4032.77 
Water  –  0.6  998  4180 
In Fig. 18a, the heat transfer coefficient of the base model is compared with three types of nanofluids with similar concentrations (2%), and different flow rates. As is clear, the heat transfer coefficient of the tube side usually increases with the increase in the flow rate of the tube side. The reason for this is that the higher the velocity of the fluid is, the lower the difference in temperature between the fluid, and the surface of the tube will be. This is due to the presence of an additive substance, the Nano fluid particles, which is considered as passive method for heat transfer enhancement e.g., methods that do not require external power, and if necessary, additional power is supplied from available system power). Variations in pressure drop for different flow rates of the coil is presented in Fig. 18b.
As shown in Fig. 18b, the pressure drop in the tube direction increases as the flow rate of the tube direction increases with a constant volume concentration (2%). Moreover, pressure drop in Nano fluid CuO is more than SiO_{2}, and Al_{2}O_{3}. Generally, the pressure drop in the CuO is higher than other models.
4.3.2 Effect of volume concentration of waterbased nanofluids
As mentioned in the previous section, the best choice between heat exchangers with nanofilms was nanofluid CuO. In this section, the basic fluid as well as other different nanowires with different concentrations in the heat exchanger are examined.
Fluid  Nanosilicon concentration  Diameter of nanoparticles (dpp) (nm)  Thermal conductivity coefficient (W/m K)  Density (kg/m^{3})  Specific heat capacity (J/Kg K) 

CuO  2  29  17.65  1108.236  3753.95 
3  29  17.65  1163.254  3570.30  
4  29  17.65  1218.272  3403.24  
5  29  17.65  1273.290  3250.61 
By proliferating the volume concentration of the nanofluids, the heat transfer coefficient on the helical tube side increases, as is shown in Fig. 20a. In numerical calculations, the heat transfer coefficient expressed as a percentage of the nanofluid concentration is usually expressed as upward or downward. However, in experimental experiments, the heat transfer coefficient does not always increase with increasing concentrations. The reason is that in case of excessive increase in nanofluids, the effect of the heat transfer enhancement may be reduced or even eliminated, as increased viscosity can occur in high concentrations. It is shown in Fig. 20b that by increasing the volume concentration of nanofluid, the pressure drop of fluid in coil tube rises.
5 Conclusions

By increasing helix pitch 50% (0.04 to 0.12 m), outlet temperature of hot fluid, pressure drop of flow inside tube and temperature difference of hot fluid reduce by less than 1%, 1% and 5%, respectively. Also, outlet temperature of cold fluid and temperature difference of cold fluid increase by less than 1% and 5%, respectively.

By increasing helix diameter 11% (0.016 to 0.022), outlet temperature of hot fluid and temperature difference of cold fluid increase by less than 1% and 8%, respectively. Also, outlet temperature of cold fluid, pressure drop of flow inside tube and temperature difference of hot fluid reduce by less than 1%, 37% and 8%, respectively.

By increasing helix height 25% (0.24 to 0.36 m), outlet temperature and temperature difference of hot fluid reduce by less than 1% and 8%, respectively. Also, outlet temperature and temperature difference of cold fluid increase by less than 1% and 8%.

Between the considered water based nanofluid, the highest coefficient of performance belongs to water/CuO nanofluid at Re = 3950.

Heat transfer coefficient in tube does not change considerably with increase in volumetric concentration of nanofluid. The lowest and highest coefficient coefficient are obtained for 2% and 4% volume concentration of nanofluid, respectively.
Notes
Compliance with ethical standards
Conflict of interest
The authors declare no conflict of interest.
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