Numerical optimization of a finned tube bundle heat exchanger arrangement for passive spent fuel pool cooling to ambient air

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Numerical optimization of a finned tube bundle heat exchanger arrangement for passive spent fuel pool cooling to ambient air ⁎

Sebastian Ungera, , Eckhard Kreppera, Matthias Beyera, Uwe Hampela,b a b

Helmholtz-Zentrum Dresden-Rossendorf, Institute of Fluid Dynamics, Bautzner Landstr. 400, 01328 Dresden, Germany Chair of Imaging Techniques in Energy and Process Engineering, Technische Universität Dresden, 01062 Dresden, Germany

A R T I C LE I N FO

A B S T R A C T

Keywords: Passive cooling Spent fuel pool Natural convection Tube bundle heat exchanger Air cooling Design optimization

The passive cooling of nuclear spent fuel pools is a promising alternative to active cooling. Since such systems work even in safety-critical situations, e.g. station blackout, the reliability of nuclear power plants would be enhanced. As in such systems heat needs to be transfer to the environment, the heat exchanger to air has a crucial influence on the system performance. This paper describes investigations of the Nusselt number, the achievable efficiency and the volumetric heat transfer coefficient of the tube bundle heat exchangers for a passive cooling system located at the bottom of a chimney. The effect of tube bundle configuration, tube shape, longitudinal tube pitch, transversal tube pitch and tube row number on natural convection heat transfer was numerically studied. These parameters were varied to optimize the heat transfer performance of the heat exchanger. It was found, that the staggered configuration performs better than the inline arrangement, since the flow mixing is higher. Furthermore circular tube shape and an oval tube shape with the aspect ratio of 1: 2.1 were optimum for the inline and staggered configuration respectively. The longitudinal and transversal tube pitches of 63mm and 65mm performed best, since higher values reduced heat transfer. A tube row number greater than 5 did not improve the heat transfer and therefore a tube row number of 5 is recommended. The Nusselt number and volumetric heat transfer coefficient of the optimized tube bundle arrangement enhanced by 15.4% and 47.8% respectively at a temperature difference of 40K compared to the initial design.

1. Introduction For removal of decay heat from spent fuel assemblies in nuclear power plants, wet storage is commonly applied. Thereby, the spent fuel pool water is cooled via active heat transfer systems, comprising pumps, heat exchanger and water as a heat transfer medium, which represent a potential danger in case of a longer persisting station black out. Thus, passive heat transfer systems are under consideration as an alternative technology. In passive heat removal systems natural convection and gravitational forces drive a heat transfer medium between a heat source and a heat sink. The natural convection is sustained by the temperature difference between heat source and the heat sink, that is, the difference between water pool temperature and ambient air temperature. Depending on the heat transfer medium passive heat transfer systems can be categorized into single-phase and two-phase circulation loops. In a single-phase loop the natural circulation is driven by thermally induced density difference and the fluid does not undergo phase change. In two-phase heat transfer systems the working fluid evaporates in the heat exchanger, that is located in the spent fuel pool (the

⁎

evaporator) flows as steam to a secondary heat exchanger located in ambient air (the condenser), condenses and then flows back as liquid to the heat exchanger in the spent fuel pool. To enhance the reliability of nuclear power plants passive cooling systems are considered for nuclear reactors and spent fuel pools. Therefore emergency reactor cooling concepts were proposed by Sviridenko (2008) using low temperature heat pipes or thermosiphons. There, heat gets transferred from the nuclear reactor to the ambient air via phase change of the heat transfer medium. RELAP5 was used by Wang et al. (2013) to study the passive residual heat removal from a 300MW nuclear power plant. The heat sink was varied between an air cooled heat exchanger surrounded by a chimney and a heat exchanger placed in a water reservoir. It was shown that a system with a water cooled heat exchanger performs better compared to a system with air cooled heat exchanger in the early period. However, the water in the reservoir evaporated in the later stages and the air-cooled heat removal system is more effective. The effect of a finned tube surfaces compared to plain tubes on the passive residual heat removal from a nuclear reactor after shutdown was investigated by Ayhan and Sökmen (2016).

Corresponding author. E-mail address: [email protected] (S. Unger).

https://doi.org/10.1016/j.nucengdes.2020.110549 Received 16 April 2019; Received in revised form 1 February 2020; Accepted 5 February 2020 0029-5493/ © 2020 Elsevier B.V. All rights reserved.

Please cite this article as: Sebastian Unger, et al., Nuclear Engineering and Design, https://doi.org/10.1016/j.nucengdes.2020.110549

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Nomenclature A Afin Afr Ccomp Ch cp dc g h hf k L Ltp ṁ N Nu Pr Q − q qvol qcross Sf

tf Tair Tf Tin Ttp Tout Ttube ΔTair ΔTHT x,y,z u,v,w

area of convection surface, m2 area of fin surface, m2 area in front of heat exchanger, m2 Heat exchanger compactness, m2/m3 chimney height, m specific heat, kJ/kgK characteristic length based on equivalent circular diameter of the oval tube, m acceleration due to gravity, 9.81m/s2 average heat transfer coefficient, W/m2K fin height, mm Turbulence kinetic energy Flow length, mm Longitudinal tube pitch, mm mass flow rate, kg/s number of tube rows average Nusselt number based on hydraulic diameter Prandtl number heat transfer, W average heat transfer rate, W/m2 volumetric heat transfer coefficient, kW/m3K cross sectional heat transfer coefficient, W/m2K inter-fin spacing, mm

fin thickness, mm average air temperature, °C fin Temperature, °C air temperature in front of the heat exchanger, °C Transversal tube pitch, mm air temperature behind the heat exchanger, °C outer tube surface temperature, °C front-to-behind air temperature difference, K tube base-to-frontal temperature difference, K Cartesian coordinates velocity components in x, y, z directionrespectivelym/s ,

Greek symbols α β ε η μ μT v ρ λair λS ω

The fin parameters were varied until an optimum of 5mm , 90mm and 3mm for fin thickness, fin radius and fin pitch respectively was found. In case of passive heat removal from a nuclear reactor core the temperature difference between reactor and environment are commonly high and so is the heat flux. However, the temperature difference between the spent fuel pool and the ambient air are significantly lower. Merzari and Gohar (2012) studied the natural circulation circuit for a spent fuel pool by CFD. The fuel tank was modeled by a porous medium approach. A similar work was performed by Ye et al. (2013) for spent fuel pool passively cooled by heat pipes to ambient air. The simulation results indicate a water temperature below saturation, which ensures the integrity of the fuel rods. The heat transfer capability of spent fuel pools was also investigated by Hung et al. (2013), using CFD and the porous-medium approach. In this study, the configuration of the spent fuel assembly was varied and the spent fuel was considered to be under full-core discharge as well as a failing external cooling system. For all configurations a local boiling occurred in case of failing external cooling. Xiong et al. (2014) analyzed an experimental loop-type passive residual heat removal system with ammonia as a working fluid and ambient air as a heat sink. The influence of air velocity, hot water inlet temperature and volumetric filling ratio of the heat pipe was studied. In a following study a similar experimental setup was used by the same author, where a large-diameter and long-length evaporator with water as working fluid was applied (Xiong et al., 2015). From these two studies a significant effect of pool water temperature on heat pipe performance was determined. This parameter was followed by air velocity, air temperature and water flow rate. Single phase circulation loops for solar thermal systems and nuclear thermal hydraulic applications were extensively reviewed by Basu et al. (2014). Various model approaches and scaling methodologies as well as unconventional topics like nanofluids, natural circulation loops for marine reactors and system dynamic issues were discussed. In an experimental study the passive cooling of a wet spent fuel storage facility was demonstrated by Fuchs et al. (2015). The operation of single-phase and two-phase circuits was compared to understand the heat transfer capacity for both cases. The results indicate a better performance of the two-phase systems at lower temperature differences between the spent fuel pool and the ambient air. Lu et al. (2016) addressed in their experiments the passive heat

thermal diffusivity, m/s2 thermal expansion coefficient, 1/K turbulence dissipation rate, m2/s3 fin efficiency dynamic viscosity, kg/ms turbulent viscosity, Ns/m2 kinematic viscosity, m/s2 density, kg/m3 thermal conductivity of air, W/mK thermal conductivity of fin material, W/mK turbulence frequency, s−1

removal from a heat exchanger submerged in an in-containment refueling water storage tank. Heat transfer from a heat exchanger represented by C-shaped heated rod bundles was investigated. Particle image velocimetry and thermocouples in different locations were applied to qualitatively measure velocity – and temperature distribution. After about 4000s sub-cooled boiling occurs and thus the heat transfer increases. Different heat transfer correlations were proposed for this scenario. In our previous study we investigated the heat transfer from a finned oval tube heat exchanger of a passive cooling system located in a chimney at ambient air (Unger et al., 2018). In the numerical simulation the fin parameters were changed, in order to find an optimized heat exchanger design. As a result a chimney height of 11m and an optimum heat exchanger with a fin height of 17mm , a fin spacing of 3mm and a fin thickness of 1.5mm was recommended. The radial and axial cladding temperatures were studied for different water levels of a spent fuel pool by Partmann et al. (2018). Experiments were carried out for various decay heats and storage distances. It was found, that with higher heat load, the heat-up becomes faster and as saturation temperature is reached, the water level gets lower. Arlit et al. (2018) applied a thermal anemometry grid sensor for flow velocity and temperature measurements in the center of the sub channels of the rods in the previous mentioned experimental facility. Thus, the rising steam during boil-off experiments and circulating air during heat-up experiments with a dried rod bundle can be measured. In a recent investigation Oertel et al. (2019) studied the heat transfer mechanisms of partially uncovered spent fuel pool racks after loss of coolant (2019). A decrease of cross-flow momentum from the pool center towards the wall was observed. Hence, the storage of fuel assemblies with high decay heat rate near the pool wall was recommended. In a recent article of Wang et al. a passive decay heat removal system for inherently save light water reactors was studied (Wang et al., 2019). Ambient air was assumed as an unlimited heat sink and the design of the primary and secondary heat exchangers were optimized by a MATLAB script. The heat removal characteristics were analyzed by RELAP 5 and a sufficient heat removal was found for a Station Black-Out scenario. In most cases ambient air is considered as an unlimited heat sink for passive cooling systems. Since the heat removal system is supposed to be operated passively, natural convection heat transfer is assumed at 2

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drop becomes higher at higher tube tilt angles and lower fin spacing. The overall best performance was measured, when the tube was perpendicular to the main flow direction. Next to the tube shape the fin design has a significant impact on the heat transfer and flow performance of a finned tube heat exchanger. Commonly applied extended surfaces are plain fins, wavy fins, offset strip fins, louvered fins and perforated fins (Bhuiyan and Islam, 2016). Out of these different fin designs the plain annular fin is the most used one, due its low pressure drop and simple manufacturing process. For instance, various fin designs, such as plain circular fin, serrated fin, crimped fin, plain plate fin, wavy fin and plain fins with punched delta winglet pair, were studied by Kumar et al. (2017) using CFD. From the heat transfer and pressure drop analysis it can be concluded, that the efficiency index, which is the ratio of heat transfer to pressure drop, is highest for circular fins. For the current investigation of natural convection heat transfer low pressure drop and flow disturbance is desired, since the driving forces and the flow velocity are small. Hence plain annular fins seem to be a favourable choice for natural convection and were therefore used. In the experimental study of Wang et al. (1996) and Jang et al. (1996) the effect of tube row number for plain finned multi row heat exchangers was investigated. The tube row number was varied from one to six. From the point of view of optimization the critical balance between high heat transfer and low pressure drop was achieved for the four-row configuration. A similar experimental analysis, with tube row number changing between one and five, was performed by Tutar and Akkoca (2004). It was reported, that the effect of tube row number is insignificant as the number of tube rows becomes more than four. From these studies it seems as the optimum for tube row number is four. However, the mentioned studies were focused on forced convection and the effect of tube row number for a natural convection situation was not studied yet. The majority of the existing literature focuses on the heat transfer from finned tube bundle under forced convection and heat transfer studies considering natural convection are limited to single tube investigations only. Nevertheless in passive cooling systems finned tube bundle heat exchangers in ambient air may be operated under natural convection. In the present study we aim to enhance the heat transfer capacity of such a heat exchanger through the optimization of the tube bundle configuration.

the secondary side of the heat exchanger to air. Natural convection heat transfer occurs due to density differences induced by the heat-up of air. Such a heat exchanger is simple, cost effective and requires minimum maintenance (Senapati et al., 2016). Nevertheless, a major drawback is the low heat transfer coefficient compared to a system operated under forced convection. Typically extended heat exchanger surfaces are used, to overcome this disadvantage. The most common design is the finned tube heat exchanger, which is used e.g. in electronics cooling, cooling systems for air conditioning and refrigeration and gas turbines. Chen and Hsu (2007) studied a single finned tube under natural convection. The experiments were carried out for finned tubes with different fin spacing. It was found, that heat transfer coefficient increases and fin efficiency decreases, when fin spacing increases. The same authors performed a numerical and experimental study on a single tube with vertical plate fins and tube diameters of 2mm and 27.3mm as well as different fin spacing between 10mm and 20mm (Chen et al., 2016). For the smaller fin diameter and higher fin spacing the heat transfer coefficient enhances and vice versa. In the investigation of Yaghoubi and Mahdavi (2013) a horizontal finned cylinder surrounded by ambient air was used as the heat sink. Natural convection was studied numerically and experimentally. The air was flowing from the top to the bottom of the finned tube and small heat transfer coefficients were measured. From the results new correlations for the Nusselt number as function of Rayleigh number were derived. An annular finned horizontal cylinder was studied numerically by Senapati et al. (2016) and different fin parameters, such as fin spacing, fin height and tube base temperature were varied. The Nusselt number, fin efficiency and optimum aspect ratio of fin spacing to tube diameter were predicted by correlations. In the experimental study of Unger et al. (2019a,b) the impact of tube tilt angle and fin spacing on the natural convection heat transfer from finned oval tubes was studied. It was found, that the Nusselt number increases with fin spacing and reduces with tube tilt angle. The transferred heat is higher for lower fin spacing and reduces at higher tube tilt angles. Next to the studies on heat transfer from a single tube, there is the investigation of Arshad et al. (2011), which considers the heat transfer from a tube bundle under natural convection. An electrically heated 3x3 array of vertical cylinders in a large tank of water was analyzed in these experiments. At different positions along these cylinders the surface temperature was measured and different correlations, for Nusselt number depending on Rayleigh number, were proposed. An extensive numerical study of the thermal hydraulic characteristics of air cooled finned tube heat exchangers was performed by Kumar et al. (2016). The tube shape was varied from annular tube shape to oval tube shape with axis ratios of 1: 1.5, 1: 2 and 1: 3. A flow separation occurred later for oval tube shapes compared to annular tube shapes and thus the wake region was smaller, which results in a lower pressure drop and slightly higher heat transfer coefficient for oval tube shapes. The influence of tube shape was also considered in the numerical and experimental study by Li et al. (2014). Different axis ratios were taken into account for a single heated cylinder and the heat transfer performance was analysed. Highest heat transfer performance was found for a minor-to-major axis ratio of 1: 2 . Similar results were found by Lin et al. (2008) for tube bundle heat exchanger with circular tubes without vortex generators as well as oval tubes with and without vortex generators. For the oval tubes the pressure drop was lower compared to the circular tubes and an axis ratio of 1: 2 was recommended. Another investigation addressed the axis ratio as well as the flow angle of attack on oval tube bundle heat exchangers (Ibrahim and Gomaa, 2009). When the flow is perpendicular to the heat exchanger or the flow angle of attack is 30° the optimum heat transfer occurs for axis ratios between 1: 2 and 1: 4 or between 1: 1.5 and 1: 2 respectively. A finned oval tube was studied in the experiments of Unger et al. (2019a,b) and fin spacing and tube tilt angle was varied. Heat transfer increases with tube tilt angle and fin spacing, but pressure

2. Numerical modeling 2.1. Geometry and simulation domain In the present investigation finned tube bundle heat exchanger with plain circular fins were investigated. We studied two basic configurations of the heat exchangers, the inline and the staggered tube configuration. The optimum fin design parameters and the chimney height were taken from our previous study (Unger et al., 2018) and kept constant in the present analyses. The heat exchanger designs are shown in Fig. 1 and the corresponding constant dimensions are listed in Table 1. We aimed to analyse and optimize the tube bundle configuration, namely the tube configuration, the tube shape, the longitudinal tube pitch, the transversal tube pitch and the number of tube rows. All geometrical dimensions for inline and staggered tube bundle configuration as well as the boundary conditions for the simulation are shown in Fig. 2. We used symmetry-type boundary conditions at the middle of the fin and at the middle between two neighbouring fins. The gravitational force is directed against the y-direction and the simulation domain is extended in positive y-direction. As ambient air gets heated up while passing the finned tube bundle, the air density changes and natural convection occurs. Thus, a column of heated air above the heat exchanger is created by a chimney in application cases. A chimney enhances the buoyancy forces and the air flow velocity. From our past study we found a chimney height of 11m as optimum (Unger et al., 3

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viscous forces. Therefore, the parameters of the tube bundle configuration were varied until an optimum heat transfer was achieved. 2.2. Governing equations In our investigation ambient air was considered as an ideal gas. The flow is governed by the steady state balance equations for momentum, heat and mass transfer

δui =0 δx i

(1)

δuj ⎞ ⎞ δp δu δ ⎛ ⎛ δui ρ ⎛⎜uj i ⎞⎟ = − + ⎜ (μ + μT ) ⎜ δx + δx ⎟ ⎟ + SM , buoy δx δx δx j i j j i⎠ ⎝ ⎠ ⎝ ⎝ ⎠

(2)

μT cp ⎞ δT ⎞ δT ⎞ δ ⎛⎛ ρcp ⎛⎜uj ⎟ = ⎜ λ + ⎟, PrT ⎠ δx j ⎠ δx δx j j ⎝ ⎠ ⎝⎝

(3)

⎜

Fig. 1. Finned tube bundle heat exchanger in a) inline and b) staggered configuration.

which are known as the Navier-Stokes equations. These partial differential equations are discretized and the velocity vector field u(r) and scalar temperature field T(r) was solved numerically. The other parameters are described in the symbol list. The turbulent Prandtl number has been set to PrT =0.9 as suggested by Yuan (2000) and the turbulent viscosity μT was calculated by

Table 1 Chimney height and fin design dimensions. Ch

hf

tf

sf

dc

11 m

17 mm

1.5 mm

3 mm

27 mm

⎟

μT = ρ

k ω

(4)

with the turbulence kinetic energy k and the turbulence frequency ω. An additional source term was used to model buoyancy via the full buoyancy model

2018), which was used in the current investigation. The circular outer tube diameter was 27mm and changed to oval tube shapes with different axis ratios of 1: 1.2 , 1: 1.6, 1: 2.1, 1: 3 and 1: 4.8. However the heat transfer surfaces of the tube and fins were kept approximately constant at all axis ratios, in order to allow a fair heat transfer comparison. The initial values for the longitudinal tube pitch, transversal tube pitch and the number of rows were 50mm , 50mm and 4 , respectively. For the heat transfer from finned tube heat exchangers the interplay of buoyancy force and the viscous force are relevant for the induced velocity. To ensure high convective heat transfer buoyancy needs to dominate over

SM , buoy = (ρ − ρref )

(5)

When fluid density is a function of temperature or pressure this model is used, which is the case in the present study. As the approxkg imate density of air ρref = 1.205 m3 was used as a reference. The flow field in between the fins is usually laminar, but the flow over the entire finned heat exchanger may be turbulent. Thus, turbulence models have been recommended for finned tube heat exchanger in natural

Fig. 2. Geometry and boundary conditions of the heat exchangers and simulation domain for a) front view inline configuration, b) front view staggered configuration and c) side view. 4

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The total difference in air temperature across the heat exchanger is

convection by Chen et al. (2016). In the present investigation we applied the Shear Stress Transport (SST) model to calculate the turbulence kinetic energy and the turbulence frequency. This k − ω based model describes the transport of turbulent shear stress and gives a good prediction of the onset and the amount of flow separation under adverse pressure gradients. Boutilier et al. found that this model well predicts the flow characteristics over curved surfaces (Boutilier & Yarusevych, 2012). The SST model was developed by Wilcox (1988) and adapted by Menter (1994). The equations for the turbulence kinetic energy and the turbulence frequency are

μ δk ⎤ δ δ ⎡⎛ (ρuj k ) = μ + T⎞ + Pk − β′ρkω δx j δx j ⎢ σk3 ⎠ δx j ⎥ ⎣⎝ ⎦ ⎜

giving the total heat rate

Q = ṁ cp ΔTair

⎟

(6)

h=

⎟

− β3 ρω2 .

Pk represents the turbulent production due to viscous forces and is calculated by ⎜

ΔTLMTD =

F1 from Eq. (7) is a blending function and can obtain values between 1 or 0 (1 near a surface), depending on the following formula ⎞ ⎟⎟ ⎠

Nu = (9)

(10)

The blending function F1 is used to calculate the constants of the SST model α3, β3, σk3 and σω3 from the constants α1, β1, σk1 and σω1 based on the k − ω model and the constants α2, β2, σk 2 and σω2 based on the standard k− ε model. This calculation is done by a linear combination of the corresponding coefficients

α α α ⎛ 3⎞ ⎛ 2⎞ ⎛ 1⎞ ⎜ β3 ⎟ = F1 ⎜ β1 ⎟ + (1 − F1 ) ⎜ β2 ⎟. ⎜ σk3 ⎟ ⎜ σk 2 ⎟ ⎜ σk1 ⎟ ⎝ σω2 ⎠ ⎝ σω1⎠ ⎝ σω3 ⎠

η=

qvol =

(19)

(20)

A . LAfr

(21)

Ccomp q¯ ΔTHT

=

A Q Q = LAfr AΔTHT LAfr ΔTHT

(22)

is defined. Hence, the heat transfer per unit heat exchanger volume and per unit temperature difference is represented by the volumetric heat transfer coefficient. We already applied this value in our previous study (Unger et al., 2018). Furthermore the area required to set up the heat exchanger, usually described as footprint, may be of interest. Thus the relation of heat flux to the frontal area of the heat exchanger and the temperature difference is calculated as cross sectional heat transfer coefficient

(13)

Another blending function F2 is used to restrict the limiter to the wall boundary layer. The second blending function is expressed as 2

⎛ k 500ν ⎞ ⎤ ⎞ F2 = tanh ⎡ max ⎜⎛ , 2 ⎟⎥ ⎜⎢ ′ β ωy y ω ⎠⎦ ⎟ ⎝ ⎠ ⎝⎣

(18)

Here, L is the length of the array and Afr the frontal area. Hence, the product describes the envelop of the installation space of a heat exchanger. From this definition of compactness, the average heat transfer rate and the temperature difference between the outer tube wall and the air temperature, the average volumetric heat transfer coefficient

(12)

μT . ρ

.

∫ (Tair − Tf ) dAfin . ∫ (Tair − Ttube ) dAfin

Ccomp =

to obtain a proper transport behavior. S is an invariant measure of the strain rate and the eddy viscosity defined as

νt =

)

hdc λair

(11)

= 0.0828, σk 2 = 1 and σω2 = 1/0.856. A limiter is used in the SST model on the formulation for the eddy-viscosity

a1 k max(a1 ω, S F2 )

Tin − Ttube Tout − Ttube

The air temperature Tair was defined from the average air temperature values upstream and downstream of the finned tube bundle heat exchanger. According to Shah and Sekulić (2003), the compactness of a heat exchanger is given as the ratio of heat transfer surface to the heat exchanger volume as

The constants used for the calculation are β′ = 0. 09, α1 = 5/9, β1 = 0. 075, σk1 = 1. 176, σω1 = 2, α2 = 0.44, β2

vt =

(

Even if the tube shape changes in the present study, the perimeter is approximately the same and thus the characteristic length is constant. The temperature is not uniformly distributed on the fin (Chen et al., 2016 and Chen and Hsu, 2007). Therefore, we consider the fin efficiency, which is used to calculate the ratio of real heat transfer to the ideal heat transfer. It is given by the ratio of the fin at real temperature and the fin at outer tube wall temperature (Kumar et al., 2017) as

̂ is the kinetic The symbol y is the distance to the nearest wall, I ½ viscosity and CDkω is defined as

1 δk δω CDkω = max ⎛⎜2ρ , 1.0x10−10⎞⎟. σ ω2 ω δx j δx j ⎝ ⎠

(Tin − Ttube ) − (Tout − Ttube )

Thus, from the average heat transfer coefficient, the thermal conductivity of air and the equivalent circular diameter of the tube as characteristic length dc the average Nusselt number is calculated according to

(8)

4

(17)

ln

⎟

⎛⎡ 4ρk k 500ν ⎞⎟ ⎞ ⎤ F1 = tanh ⎜ ⎢min ⎜⎛max ⎛⎜ , 2 , 2 ⎟⎥ ′ ⎜ β ωy y ω CD σ y kw ω 2 ⎠⎠⎦ ⎝ ⎝ ⎝⎣

Q AΔTLMTD

with the logarithmic mean temperature

(7)

δuj ⎞ δui δu 2 δuk ⎛ δu − 3μt k + ρk ⎞ Pk = μT ⎛⎜ i + ⎟ δx δx δx 3 δx δxk j i j k ⎝ ⎠ ⎝ ⎠

(16)

The heat transfer coefficient varies along the heat transfer surfaces of a finned tube heat exchanger. Typically the lowest heat transfer coefficient is on the top region of the tube and the highest heat transfer coefficient is on the bottom region of the tube (Chen et al., 2016). However to obtain the overall performance of the heat transfer structure an average heat transfer coefficient was used in the present investigation according to

μ δω ⎤ δ δ ⎡⎛ 1 δk δω ω (ρuj ω) = μ+ T⎞ + (1 − F1 )2ρ + α3 Pk ⎥ δx j δx j ⎢ σ δx σ ω δx δx k ω 3 j ω 2 j j ⎝ ⎠ ⎣ ⎦ ⎜

(15)

ΔTair = Tout − Tin

(14)

A detailed description of this turbulence model is given by Wilcox (1988) and Menter (1994).

qcross = 5

Q ΔTHT Afr

(23)

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deflection at the staggered configuration. In fact the Nusselt number of the staggered configuration is higher by 88.5% compared to the inline configuration at ΔTHT = 40 K and an axis ratio of 1:2.1. These results are similar to the forced convection situation studied by Bhuiyan and Islam (2016). For the inline configuration Nu reduces with tube axis ratio for all temperature differences. The flow is more in-line for the more oval tube shapes and thus the flow mixing as well as the Nusselt number reduces. However the impact of tube axis ratio is much smaller for the staggered configuration compared to the inline one. To be more precise, at a certain temperature difference of 40 K Nu reduces by 24.6% for the inline configuration and by only 5.3% for the staggered pipes, when the tube axis ratio changes from circular to 1:4.8. The velocities around the tube bundles are shown in Fig. 4 as velocity plots in the XY plane in the middle between fin surfaces. As one can see, the wake regions become smaller with increasing axis ratios for both bundle configurations. Furthermore, it becomes clear that for the inline configuration the tubes downstream are placed in the thermal wake regions of the previous tubes and thus the highest flow velocities occur between the tubes. This effect is less crucial for the staggered configuration, which is an additional reason for the higher heat transfer performance. Eventually, the wake regions get slightly more prominent downstream of the heat exchanger, which is similar to the findings of Kumar et al. (2016). The variation of fin efficiency with tube axis ratio at various temperature differences and for the inline and staggered bundle configuration is shown in Fig. 5. Fin efficiency is higher for lower temperature differences for both configurations, since the buoyancy induced velocity is smaller and thus is the heat dissipation, which results in a higher average fin temperature and fin efficiency. For example, η rises for an axis ratio of 1: 2.1 from ΔTHT = 60 K to ΔTHT = 10 K by 6.9 % and 9.4 % for the inline and staggered configuration, respectively. The lower heat dissipation at the inline configuration causes a higher fin efficiency and thus η of the staggered configuration is 18.6 % smaller than for the inline configuration at ΔTHT = 40 K and an axis ratio of 1: 2.1. η increases with tube axis ratio for inline configuration due to higher heat dissipation. Nevertheless, for the staggered configuration η stays almost constant, similar to the Nusselt number. When the tube shape changes from circular to oval with an axis ratio of 1: 4.8 at ΔTHT = 40 K the fin efficiency increases by 3.1% and reduces by 1.0% for the inline and staggered configuration, respectively. In general, the effect of tube shape on fin efficiency is minor. To evaluate the heat transfer performance of the tube bundle configurations from an engineering perspective the volumetric heat transfer coefficient qvol was assessed. In Fig. 6 the graphs of qvol are shown as a function of the tube axis ratios for various ΔTHT . Similar to the Nusselt number the heat transfer performance increases with temperature difference due to enhanced buoyancy. Here qvol improves for an axis ratio of 1:2.1 between 10 K and 60 K for the inline and staggered configuration by 73.3% and 48.8% respectively. Such behaviour is beneficial for the operation of passive heat removal systems, since a rising temperature of the spent fuel pool water will increase the heat exchanger tube wall temperature and consequently the heat transfer.

2.3. Boundary conditions, model assumptions and simulation method The commercial code ANSYS CFX 19.0 was used in the present study. This is a Finite Volume Method (FVM) code, which discretizes the spatial domain into finite control volumes. Hence, the equations given in the chapter above are solved for each control volume to preserve the quantities of mass, momentum and energy. A high resolution advection scheme is used to solve the Reynolds-average Navier-Stokes equations and the RMS residual target was set to 10−4 for mass, momentum and energy equations. A hexahedron grid was created by ANSYS Meshing with fine grid close to the fin and tube surfaces, which gets gradually coarser further away from the surfaces. For the solid W section a thermal conductivity of λs = 16.2 mK was applied. Moreover, the boundary conditions and computational model assumptions are listed in Table 2. 2.4. Grid independency study In order to prove the independency of the numerical results from the grid an analyses with different grid was performed. For that, we modelled finned tube heat exchanger with circular tube shape, Ttp = 50.0mm , Ltp = 50.0mm and a tube row number of 4 at temperature differences of ΔTHT = 60K , 40K and 20K . The resolution of the grid was varied between 0.32 million and 6.3 million nodes and as evaluation criterions frontal velocity, Nusselt number and volumetric heat transfer coefficient were used. The results of the mesh independency study are listed in Table 3. As one can see, the values of the criteria change only little at about 4.6 million nodes. In fact between 4.6 million and 6.3 million nodes the velocity changes less than 0.34%, the Nusselt number changes less than 0.21% and the volumetric heat transfer coefficient changes less than 0.26%. Hence, the grid of about 4.6 million nodes has a maximum y + value below 1.7 and was applied for the numerical investigation. 3. Numerical results and discussion We investigated a finned tube bundle configuration, located at the bottom of a chimney structure. The aim of the study was to optimize the tube shape, the longitudinal tube pitch Ltp , the transversal tube pitch Ttp and the number of tube rows N for an inline and staggered configuration. 3.1. Effect of tube shape For the present study the outer tube surface temperature Ttube was varied from 30 °C to 80 °C. Eventually, we used the temperature difference between the tube wall and the air upstream of the tube ΔTHT = Ttube − Tin as the potential for the heat transfer. The tube shape influences the flow separation from the tube surface and thus the thermal wake region. Hence, the heat transfer along a single tube and the tube bundle in downstream direction change with tube shape. Even though the impact of tube shape on heat transfer flow development was studied in forced convection situation by Lin et al. (2008), Li et al. (2014) and Kumar et al. (2016), the influence on natural convection heat transfer was not studied yet. Starting from a circular tube shape we changed the axis ratio to 1: 1.2 , 1: 1.6, 1: 2.1, 1: 3 and 1: 4.8. The variation of Nu with ΔTHT is presented in Fig. 3 for different tube shapes and the inline and staggered configuration. Nusselt number increases with ΔTHT for all tube shapes and tube bundle configurations, due to growing buoyancy force with higher density difference. Thus the buoyancy induced flow velocity rises and consequently the convective heat transfer increases by 71.0% and 30.1% from ΔTHT = 10 K to ΔTHT = 60 K for an axis ratio of 1:2.1 for the inline and staggered configuration, respectively. The Nusselt number of the staggered configuration is much larger compared to the inline configuration. Because of enhanced flow mixing the heat transfer improves, due to flow

Table 2 Boundary values and conditions.

6

Interfaces

Temperature

Velocity

Pressure

Inlet

Fixed value(293.15K)

δu δy

=0

Atmospheric

Outlet

δT δy

δu δy

=0

Atmospheric

Outer tube surface Fin surface

Fixed values

No slip

Calculated by ANSYS CFX

No slip

Symmetry planes

δT δx

δu δx

=0

= 0,

δT δz

=0

= 0,

Calculated by ANSYS CFX Calculated by ANSYS CFX δu δz

=0

δp δx

= 0,

δp δz

=0

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longitudinal tube pitch is shown in Fig. 7 for the inline and staggered configuration. As one can see, the Nusselt number increases with increasing Ltp for the inline configuration and reduces with increasing Ltp for the staggered configuration. Furthermore Nusselt number as well as the change in Nu with Ltp is higher for the staggered configuration compared to the inline configuration. Actually the Nusselt number of the inline configuration changes only little with longitudinal tube pitch. This is, because the following tubes downstream the tube bundle lie within the wake region of the previous tubes and this wake region changes only slightly downstream. Hence the longitudinal tube pitch has small influence on the heat transfer for inline configuration. For the staggered configuration the wake region gets stronger influenced by the next shifted tube. Thus a smaller Ltp increases the flow mixing and consequently the convective heat transfer. For a particular temperature difference of ΔTHT = 40 K and an increase of longitudinal tube pitch from 73 mm to 93 mm the Nusselt number increases for the inline configuration by 2.7 % and reduces for the staggered configuration by 4.8 %. The increase of heat transfer with Ltp for the staggered configuration is similar to the findings by Bhuiyan and Islam (2016). The relative effect of Ltp on Nusselt number is higher at lower ΔTHT and vice versa for both configurations. The velocity distribution over the tube bundle are shown in the middle of the fin thickness in Fig. 8 for the inline and staggered configuration for various Ltp and at ΔTHT = 40K . One can see the larger wake regions of the inline compared to the staggered configuration as well as the stagnation points in front of the first fin. Even if the wake region becomes smaller in upstream direction, this effect is small for the inline configuration. At the staggered configuration the wake regions become significantly smaller at lower Ltp , since the deflected flow is closer to wake region. Thus, the flow mixing is very close to the downstream part of the fins and heat transfer enhances. The variation of the fluid dynamics due to Ltp will also impact the heat dissipation from the fin surface and thus the fin efficiency. The impact of longitudinal tube pitch on η can be seen in Fig. 9 for several temperature differences and both tube configurations. Similar to the Nusselt number η changes only slightly for the inline configuration, but η increases stronger for the staggered configuration with Lpt . Reason for that is the heat dissipation from the fin surface that has already been discussed above. In fact, the fin efficiency reduces for the inline configuration by 0.6% and rises for the staggered configuration by 2.8% for a temperature difference of ΔTHT = 40K , when Ltp changes from 63mm to 98mm . The volumetric heat transfer coefficient is influenced by convective heat transfer as well as the required installation space for the heat exchanger. Thus, a higher longitudinal tube pitch extends the installation space and a heat exchanger with the same amount of heat transfer surface needs more volume. One can see the volumetric heat transfer

Table 3 Grid size independence results. Number of nodes

Velocity in

m s

Nusselt number

Volumetric heat transfer coefficient in kW 3

m K

Temperature differenceΔTHT

60K

40K

20K

60K

40K

20K

60K

40K

20K

320, 000 1, 000, 000 2, 200, 000 3, 300, 000 4, 600, 000 6, 300, 000

1.52 1.44 1.40 1.39 1.38 1.38

1.25 1.18 1.15 1.14 1.13 1.13

0.88 0.83 0.81 0.81 0.80 0.80

22.47 22.27 22.22 22.22 22.21 22.17

21.34 21.14 21.11 21.10 21.09 21.09

19.41 19.19 19.14 19.11 19.11 19.07

2.72 2.65 2.62 2.61 2.60 2.60

2.48 2.41 2.39 2.38 2.37 2.37

2.06 2.00 1.97 1.96 1.95 1.95

The better convective heat transfer of the staggered configuration results in a better volumetric heat transfer coefficient, which is 72.1% higher compared to the inline configuration at ΔTHT = 40 K and an axis ratio of 1:2.1. The trends of qvol with tube axis ratio are different for the inline and staggered configuration. In fact, the circular tube outperforms the oval shaped tube, when the tube configuration is inline and the more oval shaped tubes perform better for the staggered configuration. Hence qvol reduces for the inline configuration for ΔTHT = 40 K from circular-shape to oval-shape tubes with axis ratio of 1: 4.8 by 20.6%. However, for the staggered configuration qvol enhances for ΔTHT = 40 K from the circular to the oval shaped tube with an axis ratio of 1:2.1 by 5.7% and from the last one to the tube with axis ratio of 1:4.8 by 0.7% only. This result agrees with the findings from Lin et al. (2008), Li et al. (2014) and Ibrahim and Gomaa (2009), where the optimum axis ratio for oval tubes was found to be at 1:2 and between 1:1.5 and 1:2 respectively, as the heat transfer does not change substantially for higher axis ratios. Eventually, the circular tube shape was used for the inline tube configuration and the oval tube shape with an axis ratio of 1:2.1 was used for the staggered tube configuration, since the impact of a further increase of the axis ration is insignificant. This tube shapes were used for the following tube bundle parameter analysis. 3.2. Effect of longitudinal tube pitch Behind each finned tube a thermal wake region appears with a certain length in downstream direction, depending on the flow velocity. Hence the longitudinal tube pitch influences the location, where the wake region penetrates the fins and tubes in downstream direction. However the required installation space increase with longitudinal tube pitch and the compactness of the heat exchanger reduces. The variation of Nusselt number with temperature difference and

Fig. 3. Variation of Nusselt number Nu against tube axis ratio for various temperature differences a) inline configuration and b) staggered configuration. 7

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Fig. 4. Velocity distribution in the XY plane in the middle between fin surfaces along the tube bundle with a) inline and b) staggered configuration for different tube shapes at a temperature difference of ΔTHT = 40K .

(2016). Especially the inline configuration benefits strongly from small transversal tube pitches. As the transversal tube pitch reduces, the amount of bypassing flow between the tubes becomes less. Thus, the mixed air downstream of the heat exchanger has a higher temperature, the buoyancy induced velocity enhances and consequently the convective heat transfer improves. When Ttp reduces from 100mm to 64mm and 65mm the Nusselt number enhances by 67.5% and 29.2% for the inline and staggered configuration at a particular temperature difference of 40K . Nevertheless, for the staggered configuration Nu does not increase significantly, when Ttp becomes smaller than 65mm . Fig. 12 shows the fin efficiency as a function of Ttp for various temperature differences for both tube configurations. The fin efficiency performs opposite to the Nusselt number, since higher convective heat transfer reduces average fin efficiency. Particularly interesting is the minimum value of η at Ttp between 70mm and 75mm for the higher and lower ΔTHT , where the global minimum is at Ttp = 70mm . This behaviour can be explained by a higher convective heat transfer (Fig. 11) up to Ttp = 70mm due to enhanced mixing. From this value on the convective heat transfer stays almost constant but the air gets heated up to higher temperatures, since the flow channel between the tubes is narrower. Consequently, the temperature difference and heat flux between the air and the fins reduces and fins become warmer. To be more precise, the fin efficiency reduces from Ttp = 100mm to Ttp = 70mm by 5.6%

coefficient as a function of the longitudinal tube pitch for different ΔTHT and the inline and staggered configurations in Fig. 10. It becomes clear, that the lowest Ltp gives highest qvol for all temperature differences and both configurations. The required volume of the heat exchangers becomes less as Ltp reduces and thus the ratio of heat transfer per volume rises. For the staggered configuration the enhancement of qvol at reducing Ltp is greater compared to the inline configuration, since the volume reduces and the Nusselt number increases. qvol improves from Ltp = 98mm to Ltp = 63mm by 30.5% and 37.2% for the inline and staggered configuration respectively. For both configurations a longitudinal tube pitch of Ltp = 63mm was chosen, as qvol becomes maximum there. 3.3. Effect of transversal tube pitch The required volume of the heat exchanger and the fluid dynamics changes with rising transversal tube pitch. Ttp impacts the flow in downstream direction as well as the flow between neighboring tubes. The effect of transversal tube pitch on Nusselt number can be seen in Fig. 11 for different ΔTHT and the inline and staggered configuration. Since the tube shape of the staggered configuration is more oval, the transversal tube pitch can be at lower values, without getting in contact with neighboring fins. For both configurations Nu enhances, when Ttp reduces, which corresponds to the findings of Bhuiyan and Islam

Fig. 5. Variation of fin efficiency η against tube axis ratio for various temperature differences a) inline configuration and b) staggered configuration. 8

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Fig. 6. Variation of volumetric heat transfer coefficient qvol against tube axis ratio for various temperature differences a) inline configuration and b) staggered configuration.

Fig. 7. Variation of Nusselt number Nu against longitudinal tube pitch (Ltp) for various temperature differences a) inline configuration and b) staggered configuration.

Fig. 8. Velocity vectors in the XY plane along the tube bundle in the middle of the fin thickness with a) inline and b) staggered configuration for different longitudinal tube pitches (Ltp) at a temperature difference of ΔTHT = 40K . 9

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Fig. 9. Variation of fin efficiency η against longitudinal tube pitch (Ltp) for various temperature differences a) inline configuration and b) staggered configuration.

Fig. 10. Variation of volumetric heat transfer coefficient qvol against longitudinal tube pitch (Ltp) for various temperature differences a) inline configuration and b) staggered configuration.

velocity reduces from Ttp = 100mm to Ttp = 95mm by 0.2% and from Ttp = 60mm to Ttp = 56mm by 7.6% for a temperature difference of 40K . Altogether qvol increases for the inline configuration from Ttp = 100mm to Ttp = 64mm by 77.4% at ΔTHT = 40K . For the staggered configuration the volumetric heat transfer coefficient increases from Ttp = 100mm to Ttp = 65mm by 40.4% and reduces from Ttp = 65mm to Ttp = 56mm by 1.6% at ΔTHT = 40K . Thus, transversal tube pitches of 64mm and 65mm were chosen for the inline and staggered configuration respectively.

and from Ttp = 56mm to Ttp = 70mm by 4.3% for the staggered configuration and ΔTHT = 40K . The fin efficiency of the inline configuration increases from Ttp = 64mm to Ttp = 100mm by 10.5% at ΔTHT = 40K . The impact of the transversal tube pitch on the volumetric heat transfer coefficient can be seen in Fig. 13 for the inline and staggered configuration. qvol rises as the transversal tube pitch reduces for the inline at all temperature differences, since the required volume of the heat exchanger becomes less. Although qvol increases at lower Ttp for the staggered configuration, there is a reduction of qvol when Ttp becomes lower than 65mm . Here, the flow resistance is particular high and as a result the frontal flow velocity strongly reduces. For example the flow

Fig. 11. Variation of Nusselt number Nu against transversal tube pitch (Ttp) for various temperature differences a) inline configuration and b) staggered configuration. 10

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Fig. 12. Variation of fin efficiency η against transversal tube pitch (Ttp) for various temperature differences a) inline configuration and b) staggered configuration.

configuration at ΔTHT = 40K . The effect of tube row number on η can be seen in Fig. 16 for the inline and staggered configuration for various ΔTHT . Fin efficiency changes opposite to the Nusselt number, that is an increase with tube row number for all ΔTHT . Since the heat dissipation reduces as the temperature differences between heat exchanger and air reduces, the average fin temperature as well as fin efficiency increases. In fact η increases from N = 2 to N = 8 by 13.5% and 17.1% for the inline and staggered configuration at ΔTHT = 40K . The tube row number influences the volumetric heat transfer coefficient by several aspects. First, by the change in convective heat transfer described by the Nusselt number, second by the amount of heat transfer surface due to the finned tube rows and third by the required volume of the heat exchanger. As N increases the heat transfer surfaces and the required volume of the heat exchanger increase as well. Nevertheless, the additional heat transfer surface is less efficient, as described for the Nusselt number and thus the highest qvol occur for the lowest N. More precisely qvol enhances from N = 8 to N = 2 by 95.0% and 89.6% for the inline and staggered configuration at ΔTHT = 40K . Even through the present study is focused on heat transfer performance of the heat exchanger, it is worth to mention that parts like flow distributor, collector and the piping system are needed independent of the tube row number (Fig. 17). Thus, low tube row number would generate higher investment cost per heat exchanger at a certain heat capacity. Therefore, we studied the heat flux per cross-section of the heat exchanger, which is often described as the footprint. In Fig. 18 the cross sectional heat transfer coefficient qcross is shown as a function of the tube row number for different ΔTHT and both tube configurations. It becomes clear, that qcross improves as N increases up to a tube row number between 4 and 6. At this point the additional tube rows give no

3.4. Effect of row number Usually, tube bundle heat exchangers comprise several tube rows. However, the amount of tube rows can vary and so does the heat transfer performance. The air gets further heated up with every additional tube row in downstream direction and increases the buoyancy. Nevertheless, the additional tube rows represent an additional flow blockage as well. Furthermore, the temperature of the air increases after each tube row downstream of the heat exchanger and thus the temperature difference between air and heat exchanger reduces. Consequently, additional tube rows downstream contribute less to the heat flux compared to the tube rows further upstream of the heat exchanger. In Fig. 14 the variation of Nu with tube row number N is shown for various temperature differences and for the inline and staggered configuration. As one can see, Nu enhances as the tube row number reduces for both configurations. This is, because the temperature difference between heat exchanger and air and the flow velocity is highest at lowest N. Consequently Nu becomes maximum for small N. As a result, the Nusselt number enhances from N = 8 to N = 2 by 49.1% and 6.4% for the inline and staggered configuration respectively for a certain temperature difference of 40K . It becomes clear, that the effect is much greater for the inline than for the staggered configuration. Since the intermixing of air flow is much less for the inline configuration, the tube rows in downstream direction are shaded by the hotter air flow coming from the tubes in upstream direction. Thus, the effect of tube row number is more significant for the inline configuration than for the staggered configuration. These effect as well as the most uniform fin temperature further downstream can be seen in Fig. 15 for the inline and staggered

Fig. 13. Variation of volumetric heat transfer coefficient qvol against transversal tube pitch (Ttp) for various temperature differences a) inline configuration and b) staggered configuration. 11

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Fig. 14. Variation of Nusselt number Nu against tube row number (N) for various temperature differences a) inline configuration and b) staggered configuration.

the present findings. For a particular temperature difference of 40K the cross sectional heat transfer coefficient increases from N = 2 to N = 5 by 33.3% and 43.5% for the inline and staggered configuration respectively. However, from N = 5 to N = 8 qcross increases by 2.9% and

additional heat transfer advantage, since the additional flow blockage reduces the convective heat transfer over the whole heat exchanger. In the studies of Wang et al. (1996) and Jang et al. (1996) an optimum heat transfer was found for 4 row heat exchanger, which corresponds to

Fig. 15. Temperature contours in XY plane along the tube bundle for 2, 4, 6 and 8 row heat exchanger at ΔTHT = 40K for a) inline and b) staggered configuration. 12

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Fig. 16. Variation of fin efficiency η against tube row number (N) for various temperature differences a) inline configuration and b) staggered configuration.

Fig. 17. Variation of volumetric heat transfer coefficient qvol against tube row number (N) for various temperature differences a) inline configuration and b) staggered configuration.

Fig. 18. Variation of cross sectional heat transfer coefficient qcross against tube row number (N) for various temperature differences a) inline configuration and b) staggered configuration.

heat exchanger for passive residual heat removal systems was studied in terms of heat transfer and compactness of the heat exchanger. The tube bundle configuration parameters, such as tube configuration, tube shape, longitudinal tube pitch, transversal tube pitch and tube row number, were analysed by the commercial CFD code ANSYS CFX 19.0. A passive operation of the heat exchanger is expected and thus flow is driven only by buoyancy. The natural convection heat transfer from the staggered configuration was significantly higher compared to the inline configuration. The best performance for both configurations was found for the circular tube shape and the oval tube shape with an axis ratio of 1: 2.1. As the longitudinal tube pitch reduces, the heat transfer performance enhances and the required volume becomes low. Hence, a minimum longitudinal tube pitch of 63mm was chosen for both

reduces by 4.9% for the inline and staggered configuration at ΔTHT = 40K . In fact, it is not worth to increase the tube row number higher than 6, since the heat transfer is not increasing or is even reducing for most temperature differences. These results differ from the findings for forced convection situations by Tutar and Akkoca (2004), were heat transfer does not increase at a tube row number greater than 4 . For the present study we recommend a tube row number of 5 for both configurations, since the heat transfer performance is high for most temperature differences. 4. Conclusion In the present work the heat transfer performance of an air cooled 13

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configurations. The heat transfer improves and the required volume of the heat exchanger reduces for a lower transversal tube pitch until 65mm for the staggered and 64mm inline configuration. Eventually, the tube row number was studied. As the number of tube rows increase the surrounding air gets heated up with every additional tube row, but the flow blockage increases. In fact, a tube row number greater than 5 increases the heat transfer insignificantly and is not recommended for both configurations. Compared to the initial tube arrangement the Nusselt number and volumetric heat transfer coefficient enhanced by 15.4% and 47.8% respectively at ΔTHT = 40K for the staggered configuration. Our results may be helpful for the design of optimum finned tube bundle heat exchanger for passive cooling systems under natural convection. From the previous and the present investigations an optimized finned tube bundle heat exchanger design under natural convection was derived. The impact of different fin designs, such as serrated fins, plain plate fins, wavy fins, circular integrated pin fins or serrated integrated pin fins, on heat transfer was not studied. Such various fin designs may be focused in future investigations, in order to determine the optimum thermal performance for passively air cooled heat exchanger.

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