Increase In Fin Height Research Articles

Numerical investigation on ash accumulation characteristics of serrated spiral finned tube heat exchanger in waste heat utilization

In this study, a comprehensive loose fouling model is established to investigate the fouling characteristics of fly ash on serrated spiral finned tube heat exchangers. This model considers the energy change during particle collision, the velocity change after particle rebound and slip, and the amplification of fouling time under mixed particle sizes. The results show that the fouling position, morphology, and height obtained by the theoretical model agree well with the experiments. Besides, the serrated spiral fin is the main fouling position due to its high fin ratio and the strong disturbance effect. The 5 μm particles have the highest deposition rate, and fine particles tend to adhere to the second row of finned tubes due to the consumption of initial kinetic energy by the first row. With an increase in fin height by 6 mm, the deposition rate only increases by 1.2 %, while an increase in sawtooth height by 5 mm results in a deposition rate increase of 14.3 %. When the flue gas velocity is less than 7 m/s, finned tubes arranged in a staggered configuration provide the best combination of heat transfer, flow resistance, and anti-ash accumulation performance.

Performance prediction of a novel disinfection-enhanced type Trombe wall with transverse fins

Trombe wall is an efficient passive solar heating system, while the utilization form of heated air needs to be expanded. Indoor microorganisms that can be transmitted through aerosol endanger the safety of human health. The fact that microorganisms can be thermally inactivated makes it possible to disinfect the air through Trombe wall. To expand and enhance the disinfection effect of the wall, extending the residence time of bioaerosols in the flow channel and raising the air temperature can be applied. Therefore, a transverse-finned-Trombe wall is proposed. Multiple physical field coupling is studied numerically. Migration, inactivation, and deposition of bioaerosols are described by Eulerian method. The results indicated as follows: As fin height increases, the thermal efficiency first rises and then drops; the single-pass inactivation ratio rises remarkably with its value reaching 90.96 % and 66.98 % for SARS-CoV-1 and SARS-CoV-2 even at low irradiance level (400 W/m2) at a fin height of 35 mm. As fin angle increases from −45° to +45°, the thermal efficiency drops first and then rises. Optimal disinfection performance is achieved at α = 0°. The contribution of deposition to removal of infectious bioaerosols plays a significant role when the thermal inactivation is not strong.

Patterns of allometric and heterochronic changes in the early ontogeny of species of Physalaemus (Anura: Leptodactylidae).

We studied the relationship between shape, size, and developmental time in the embryonic ontogeny of 15 species of the frog genus Physalaemus. As in other anuran exotrophic embryos, shape changes are correlated with size increase and mainly concern tail elongation, decrease in body height, and increase in fin height. Size ranges and developmental times vary interspecifically. Embryos of the P. signifer Clade and the P. gracilis Group are among the largest, are slightly peramorphic, and develop fast regarding congeneric species. Embryos of P. cicada combine the smallest sizes with fast development and the most peramorphic shapes. The paedomorphic shapes of embryos of P. biligonigerus and P. henselii groups are correlated with fast vs. slow developmental times respectively. Trajectories in the P. cuvieri Group are diverse and in general differ in size and developmental time. The embryos of P. cristinae and from the Argentinean lineage of P. cuvieri stand out with the longest development. Sequences of developmental events are overall conserved in the genus, and main differences concern mouthpart ontogeny. This study constitutes the first attempt to evaluate morphological, allometric, and heterochronic parameters of the early ontogeny of anurans and how these can vary and contribute to diversification in taxonomic groups.

A new analytical model of condensation outside low-finned tubes for refrigerants at low temperatures and high heat flux

In this paper, a new analytical model is developed for the condensation of refrigerants outside low-finned tubes. It is based on the flow and heat transfer characteristics at low saturation temperatures and high heat flux, such as those in the LNG intermediate fluid vaporizer (IFV). Due to the increase of viscous effect at lower saturation temperature and higher heat flux, the previous condensate retention angle models are modified by adding the viscous term. At high heat flux and condensate rate, the condensate profile at the fin root is simplified to be arc-shaped and obtained directly by force analysis. Furthermore, considering the heat transfer enhancement caused by the circumferential flow at high heat flux, the convective mechanism is included for the heat transfer through the thick liquid film between the fins. The distributions of liquid film and fin surface temperature are also predicted. The present analytical model is in good agreement with different experimental and numerical results, while most deviations are within 10% for predicting the heat transfer coefficients at high heat flux. Because of the increased flow viscosity and surface tension, the optimal fin spacing and fin height increase as the heat flux increases and the saturation temperature decreases.

Experimental investigation on the impact of fin structure factors on the finned-Trombe wall thermal performance

By increasing surface area, fins can enhance the heat transfer and improve the Trombe wall thermal performance. However, there is still a lack of detailed experimental research on the impact of fin structure factors on the thermal performance of finned-Trombe wall (F-TW). This experiment establishes a platform under laboratory conditions to investigate the impact of fin height and spacing on the F-TW thermal performance. Electric heating is used to simulate the solar radiation. The results indicate that in areas with relatively low solar radiation intensity, the F-TW is more cost-effective for improving F-TW thermal performance. The F-TW thermal parameters including air temperature rise, mass flow rate, thermal efficiency and overall natural convective heat transfer coefficient are enlarged as the fin height increases and fin spacing decreases, while the heat loss coefficient of glass cover is opposite. The fin spacing has a more significant influence on the F-TW thermal performance and natural convective heat transfer in the channel than the fin height does. The maximum thermal efficiency of 63.75% is obtained at heat flux of 860W/m2, relative fin height of 0.75 and relative fin spacing of 0.06. Finally, for the engineering design and performance assessment of F-TW, the experimental correlation is provided to calculate the average natural convective heat transfer Nusselt number in the channel.

Numerical Analysis of an Aerofoil Fin Integrated Double Pass Solar Air Heater for Thermal Performance Enhancement

The Solar Air Heater (SAH) is considered to be one of the promising devices for the utilization of solar radiation. Extracting more heat to the flowing air is the focus of researchers, and many novel ideas are adopted to improve the efficiency of such collectors. The objective of the present work is the enhancement of thermal performance using a numerical analysis of a single flow double pass solar air heater with two types of arrangements of aerofoil fin configurations. The effect of the aerofoil fin configurations and the height of the fin are investigated for their thermal and thermohydraulic efficiencies. The height of the fin varied parametrically for the Reynolds number ranging from 3000 to 24,000 by keeping the axial pitch of the fin as a constant. It is found that the thermal efficiency increases with the increase in fin height due to an increased flow turbulence causing more absorption of heat to the working fluid. However, it is seen that the varying height of the fin beyond a certain height has yielded an adverse effect in terms of lesser thermal efficiency due to the expected flow blockage in the main stream. The thermohydraulic efficiency increases as the height of the fin decreases. The Computational Fluid Dynamics (CFD) results revealed that the optimum aerofoil fin configuration yields approximately a 23.24% higher thermal efficiency when compared with that of the single pass solar air heater (base model). The thermohydraulic efficiency exceeds the optimum aerofoil fin configuration compared with the base model by approximately 20.94%.

Performance of a thermoelectric generator system for waste heat recovery utilizing plate fin heat sink in bronze ingot casting industry

This study presents a numerical investigation of the performance evaluation of a waste heat recovery (WHR) system from a bronze ingot casting mold via a thermoelectric generator (TEG). A rectangular plate fin heat sink is installed at the hot side of the TEG to recover the waste heat from the casting mold while the flow direction of the flue gas is found to be normal to the fin base. A multi-physics numerical model, which couples the governing equations of fluid, thermal and electrical models are presented and solved by using ANSYS 19.2 software. The numerical results for the thermal characteristics of TEG and its power output show good agreement with the experimental results. The study has been performed to analyze the effect of different fin parameters such as fin height ( H f = 12.6–52.6 mm) and fin number ( N f = 15 to 21), and flue gas parameters such as inlet velocity ( V in = 0.5–7 m/s) and inlet temperature ( T in = 550–650 °C) on the performance of the TEG system during WHR. Results indicate that TEG module power increases with the increase in fin height, fin number, inlet flue gas velocity, and temperature. The maximum net power output and maximum net efficiency are found to be 18.83W and 2.33% at inlet flow velocities of 5 m/s and 3 m/s, respectively. In addition, significant radiation has been observed through the numerical investigation. The fraction of radiation effect ranged from 5.01% to 24.15% in the test conditions.

Investigation on vibration parameters in aluminum finned tube arrays subjected to water cross flow

PurposePredicting the critical velocity is crucial at the instability threshold for shell and tube heat exchangers in order to prevent tube failure due to vibrations. In this study, the vibration response of an aluminum tube bundle subjected to water cross flow was analyzed experimentally. Aluminum tubes are preferred over steel tubes because of aluminum tubes' excellent corrosion resistance, ease of manufacture, and high thermal efficiency.Design/methodology/approachThe fluid elastic instability and vortex shedding mechanisms in a finned tube array of aluminum tubes with a base tube diameter of 19.05 mm and pitch of 34 mm were investigated. The current study considers parallel triangular finned tube arrays with fin heights of 3 mm and 6 mm with a uniform fin thickness and fin pitch. The plain tube array was tested to compare the finned tube array results. The tube vibration response was measured using an accelerometer mounted on the middle tube of the third row. In order to define the fluid elastic instability behavior of various tube arrays, the critical velocity at the instability threshold is measured. By finding the Strouhal number at the small peaks before instability, the vortex shedding behavior of the tube arrays is examined.FindingsThe results reveal that the critical velocity at instability for coarse finned tube arrays increases as the fin height increases. The effect of the tube material is evaluated by comparing the results with those previously reported for parallel triangular tube arrays made of steel. Finally, the occurrence of vortex shedding in a tube array is confirmed based on the Reynolds number and Strouhal number relationship. The instability constant K for the plain tube array of steel and aluminum material are 4.97 and 4.87, respectively.Originality/valueThis paper provides the research findings on the effect of fin height on coarse density finned tube array. This will add substantial knowledge to the literature in the field of fluid elastic instability and vortex shedding, which is needed for the safe functioning of shell and tube heat exchangers.

Optimization analysis of passive fin-concrete heat sinks for thermal environment control in main control room

When an accident occurs in a nuclear power plant, the main control room (MCR) is isolated while initiating emergency measures. To keep the indoor temperature from increasing to dangerous levels, heating loads need to be mitigated by heavy concrete insulation, on which rectangular fins are installed to improve the heat transfer. However, the effect of optimized fins for the thermal environment has not been investigated. In this study, a parametric model based on COMSOL Multiphysics is proposed to describe the dynamic heat transfer process of a fin-concrete heat sink and validated by an experiment on a 1200 mm × 1200 mm × 610 mm module. A COBYLA algorithm has been implemented to optimize the fin parameters combination with different steel consumption. Results show that both steel consumption and fin structure parameters need to be taken into consideration when optimizing. The optimal heat transfer increases by 2.84%, 7.33%, and 9.26%. The maximum indoor temperature is 0.77, 1.85, and 2.39 °C lower than the prototype when the steel consumption is 100, 150, and 200 kg/m 2 , respectively. Furthermore, the heat storage will improve as increasing the steel consumption if the fin structure is optimized. And it does not necessarily so without optimization. Finally, the optimization potential increases with the decrease in fins space, the increase in fin height, and the increase in fin thickness. In the case of only taking reducing the maximum indoor temperature into account, reducing fins space and increasing fin height are the superior choices for the optimal design of heat sink.

Numerical investigation of the performance of rectangular micro-channel equipped with micro-pin-fin

To investigate the thermal and flow characteristics in a microchannel with pin fins, numerical simulation is carried out. The influence of variation in fin height is adjudged on thermo-hydraulic performance where the fin height is varied from 0.2 mm to 1 mm and Reynolds numbers from 200 to 1000 with constant heat flux imposed at the bottom of the channel. In general, heat transfer is observed to be significantly increasing with an increase in fin height and Reynolds number. However, heat transfer increases at a similar rate for each cases up to a Reynolds number of 600 but later heat transfer growth for a height of 0.8 mm is found pronounced over that for fin height of 1 mm as the Reynold number continues to increase. This may be attributed to the fact that fin height of 0.8 mm seems to have greater wetted as well as convective surface area as compared to the fin of 1 mm height. Further, available the flow passage around 0.8 mm fin is prone to form vortices much easily as compared to 1 mm fin. The profiles of temperature distribution, pressure drop, and velocity all seem to corroborate this observation.

Numerical Study on Heat Transfer Characteristic of the Plate-Fin Microchannel Heat Sink for Water-Based Thermal Management of CPU Chip

For effective water-based thermal management of high heat generating CPU chip, a series of numerical simulation has been conducted to study the effects of heat flux, fin height and flow rate on convective thermal performance of the plate-fin microchannel heat sinks. The characteristics of heat transfer and flow resistance have been quantificationally discussed and <i>JF</i> factor is employed to evaluate the comprehensive efficiency of convective heat transfer of microchannel heat sink. Results show that the increase in fin height and flow rate of cooling water is helpful to decrease the maximum temperature of CPU chip. Large flow rate and heat flux and short fin height are benefit to improve Nusselt number <i>Nu</i>, but they lead to large resistance coefficient <i>fRe</i> simultaneously. Analysis of <i>JF</i> factor shows that the microchannel with short fins shows better convective thermal performance when the thermal power of the CPU chip is small. The fins should be heightened when the CPU is operating at higher thermal power. The employment of <i>JF</i> factor in the present work shows its pertinence and convenience in the application of design of microchannel heat sink.

Numerical and experimental investigation on heat transfer enhancement by adding fins on the pot in a domestic gas stove

Heat transfer and premixed combustion are two working processes of domestic gas stoves, and poor heat transfer is the primary cause of low thermal efficiency. The investigation aims to strengthen the heat transfer capacity of the pot numerically and experimentally, thus improving the thermal efficiency of gas stoves and saving energy. With the increase in loading height Z, the thermal efficiency predicted by numerical simulation decreases gradually in agreement with the experimental results. After adding fins to the pot wall, it is found that the thermal efficiency increases with an increase in fin height H. The fin height H = 8 mm is used because of the better compromise between thermal efficiency and the max temperature of fins. By considering the total mass of the pot and thermal efficiency, we select the fin number N = 42, and its thermal efficiency is increased by 7.12% compared with the original pot. Experimental results confirm that the increase is 8.2% under the same conditions. Moreover, it is shown that the thermal efficiency at first increases to a maximum value then decreases with the augment of inclination angle. The optimal angle occurs at α = 30°, and its thermal efficiency is 9.48% higher than that of the original pot.

Fe3O4-Water Nanofluid Free Convection within an Inclined 2D Rectangular Enclosure Heated by Solar Energy Using Finned Absorber Plate

This work investigates a hydrodynamic problem involving the Fe3O4-Water nanofluid. The novelty of this investigation lies in the fact that the nanofluid free convection is evaluated within a specific rectangular enclosure having a finned absorber plate as the top wall, heated by solar energy. The fins below the absorber plate permit to enhance heat transfer towards the nanofluid. A numerical simulation is carried out in order to predict the influence of Rayleigh number, nanofluid layer position, enclosure inclination angle, and absorber plate fins height on the nanofluid flow (in terms of streamlines and velocity magnitude) and heat transfer (in terms of temperature and Nusselt number divided by a certain thermal conductivity ratio). Numerical results show a nanofluid buoyancy enhancement and a temperature distribution homogenization, when the Rayleigh number increases, all the more important and pushed to the right area of the enclosure, as the inclination angle of the enclosure is higher. For relatively low fin heights, the nanofluid buoyancy enhancement is all the more important and pushed to the right area of the enclosure as the inclination angle is high. As the fin height increases, the temperature distribution becomes more homogenous.

Experimental research on the ash deposition characteristics of 3-D finned tube bundle

Ash deposition on the flue gas side of a heat recovery device can cause significant industrial problems. 3-D finned tube is a new type of heat exchanger element with potential anti-fouling property. However, the ash deposition characteristics of 3-D finned tube bundle are still unclear. In the current study, experiments were conducted to study the ash distribution characteristics of 3-D finned tube bundle with six-tube rows. The effects of the tube bundle structure, including the transverse tube pitch, longitudinal tube pitch and fin height, were investigated on the ash distribution around the tube along with the overall ash deposition weight. The results indicate that ash particles primarily distribute on the fin surface under different arrangements of the 3-D tube bundle. Larger particles prefer to settle on the tube surface of the top side and the leeward side, whereas smaller particles primarily settle on the fin surface of the windward side and the leeward side. The weight measurement results indicate that a longer transverse tube pitch and a shorter longitudinal tube pitch significantly restrict the ash deposition under current operating conditions. The ash deposition first decreases and then intensifies with an increase in fin height from 2 mm to 5 mm. The optimal fin height for anti-fouling is 3 mm.

Filmwise Condensation of Steam on Pin Fin Arrays Fabricated by Selective Laser Melting

In this study, nine vertical flat plates of pin fin arrays were fabricated by selective laser melting to investigate the possible enhancements of external condensation. These specimens are cylindrical pin fins of the same fin diameter of 300 μm but are of different fin heights (l) and fin pitches (p) from 300 μm to 900 μm. Experiments were conducted in a condensation chamber with near quiescent vapor to simulate free-convection condensation. The aim is to investigate the effects of fin pitch and fin height on the condensation heat transfer performance of the surfaces. The results of this study show that the increase in fin height and the decrease in fin pitch lead to a systematic increase in the condensation heat flux (q''). At the same fin pitch, the increase in fin height from 600 μm to 900 μm resulted in a more significant increase in q'' as compared to the increase in fin height from 300 μm to 600 μm. On the other hand, at the same fin height, a larger increase in q'' is observed when the fin pitch is reduced from 900 μm to 600 μm as compared to the reduction in fin pitch from 600 μm to 300 μm. It can be deduced that increasing the fin height enables the fins to protrude out of the thick condensate film and increases the effective heat transfer area of the surfaces. However, when the fin density is large, it impedes the condensate drainage path and limits the enhancement in q''. The enhancement factor (η), which is the ratio of the average condensation heat flux of a pin fin surface to that of a plain surface, was computed for each specimen. The highest η value of 1.72 was achieved with the specimen of 900 μm fin height and 300 μm fin pitch. Finally, a relationship between η and the dimensionless fin pitch-to-height ratio (p/l) is proposed.

Performance boost using spacer-confined cavity for advanced FinFET technology

We present a method to form a spacer-confined cavity to enable the deeper cavity for performance improvement while keeping the lateral width of epitaxial silicon doped with phosphorous (SiP EPI) from creating an EPI bridging issue. An extra non-selective etch step is introduced to leave the sidewall spacer but etch away the Si fin. The SiP EPI is confined between the sidewall spacer for EPI lateral width control. In this work, TCAD simulation shows that the effective gate length (Leff) near the bottom of the fin decreases when cavity depth increases. The deeper junction provides another performance boost on top of the performance improvement from the fin height increase. In addition, the spacer-confined cavity demonstrates a 6% device performance improvement with comparable drain-induced-barrier-lowering at +8 nm cavity depth. The device performance starts saturation when the cavity depth extends beyond +15 nm. The spacer-confined cavity offers a solution to increase cavity depth without suffering from the EPI bridging issue for advance finFET technology.

Investigation of phase change in a spiral-fin heat exchanger

• Melting process in a spiral finned tube is numerically studied. • Fin height influences total melting time of PCM. • The best selection of pitch and thickness improves the performance about 56%. • Tilted spiral fin unit performs more efficiently. In this study the effect of a spiral fin on the melting process of a phase change material in a heat exchanger is investigated. Water as the heat transfer fluid enters the tube at 348 K and the phase change material, RT50, the melting temperature of which is in the range of 318 K to 324 K, fills the space between the tube and the shell. This study focuses on the effect of geometrical parameters of the fin including the fin thickness and fin pitch on the melting process. In addition, the effect of changing the heat exchanger angle with respect to the horizontal is examined. Results indicate that fin shape is a critical parameter in every modification. In fact, for constant fin thickness, provided the fin pitch varies from 10 mm to 20 mm, due to 58% increase in fin height, the melting time reduces about 35%. Moreover, considering constant fin pitch, when the fin thickness increases from 1.5 mm to 2.5 mm, because of the 28% reduction of fin height, the melting time increases 59%. Also, an increase in the angle of the heat exchanger from zero to 90°, affects the melting process considerably.

Natural convection heat transfer from a hollow horizontal cylinder with external longitudinal fins: A numerical approach

The continuity, momentum, and the energy equations have been solved in 3D to predict the thermal plume and flow field around an isothermal horizontal longitudinally finned hollow cylinder in air. Effect of Rayleigh number (Ra), L/D, H/D, and s/D on heat transfer from the finned cylinder have been investigated where the input parameters are varied in a wide range of 104 ≤ Ra ≤107, 0.5 ≤ L/D ≤ 5, 0.0833 ≤ H/D ≤ 2, and 0.0785 ≤ s/D ≤ 0.785. Average surface Nusselt number (Nu) increases with increase in Ra and decreases with increase in cylinder length and fin number for all H/D. Nu for a finned solid cylinder is found to be marginally higher than that of the hollow cylinder except at low H/D of 0.0833 and high Ra of 107 when s/D is less than 0.2617 for all L/D. Fin effectiveness is found to be increased with addition of taller fins for both the solid and hollow cylinder with longitudinal fins. Efficiency of the finned cylinder decreases with increase in fin height and Ra for all L/D and s/D. A general correlation of Nu as a function of all the pertinent input parameters (Ra, L/D, H/D, and s/D) has been proposed separately for the hollow isothermal cylinder having longitudinal fins, which can be used for industrial and academic purposes.

Thermal management of a distribution transformer: An optimization study of the cooling system using CFD and response surface methodology

In this paper, a numerical scheme has been developed to examine the effective parameters on thermal management of distribution transformers and subsequently to optimize their cooling systems. In this regard, the response surface methodology (RSM) was used as the optimization method to minimize the hotspot temperature in the transformer as the response factor. A comprehensive three-dimensional computational scheme was employed considering the detailed geometrical specifications of an actual 200kVA distribution transformer to obtain the temperature field and the hotspot temperature. The accuracy of the numerical model was established via comparing the numerical results with the measured temperatures of a running transformer. The thermal variations of the thermo-physical properties of the transformer oil are determined experimentally and incorporated in the numerical modeling. A comprehensive parametric study among seven evidently effective parameters has been performed to identify the most effective parameters on the thermal performance of the transformer. It was found that fin height, length, and spacing are the more influential parameters among the examined parameters, which are also considered as the input variables in the optimization procedure. According to the RSM, the effects of the variations of these input variables in pre-specified ranges on the response, which is the hotspot temperature, are examined through the suggested runs by RSM. The results indicated that the hotspot temperature is more influenced by the fin height as compared to the fin length and spacing. Furthermore, the hotspot temperature decreases with the increase in fin height and length, while decreases as fin spacing increases. In addition, a correlation for the variations of the hotspot temperature as a function of the fin height (H), length (L), and spacing (S) is suggested using RSM. The significant finding is that the proposed optimum transformer configuration (H = 0.9 m, L = 0.08 m and S = 0.036 m) leads to the hotspot temperature reduction of about 16 °C as compared to the actual transformer geometry, which greatly affects the transformer life expectancy and safer performance.

A comparative study of 2-D and 3-D conjugate natural convection from a vertical rectangular fin array with multilayered base subjected to distributed high heat flux

This paper presents a comparative numerical study of 2-D and 3-D steady, laminar conjugate natural convection heat transfer from a vertical rectangular aluminium fin array subjected to a distributed high heat flux related to the cooling of a 105 W LED street lighting luminaire. The effect of radiation is also considered in the aforementioned models. The 2-D model uses the Stream function-Vorticity-Temperature approach. The finite-difference methodology is used to discretize the governing equations. The discretization method in the 3-D model is finite-volume. The solution algorithm is SIMPLE (Semi-Implicit Method for Pressure-linked Equations). A detailed parametric study based on a realistic lamp data is conducted to observe the effect of heat flux, fin spacing, fin height, fin width, fin thickness and fin material (aluminium, brass, copper, mild steel) on the fluid (air) velocity and temperature distributions, heat transfer and LED junction temperature. A novel finding of this work is the revelation of asymmetric flow and thermal fields in the successive channels of the fin array, as predicted by the 3-D model. In contrast with the existing studies in which fin base is treated as isothermal, an optimal fin spacing is found to exist corresponding to the maximum heat transfer coefficient in the present study. The difference between 2-D and 3-D model-predicted average heat transfer coefficients increases with increase in fin height to fin spacing ratio. The contribution of radiation heat transfer is about 8–14% of the total heat transfer in the range of dimensions of the fin array considered in this work. A penalty function based optimization study is carried out to maximize the average heat transfer coefficient while maintaining the LEDs below the safe limit of 353 K. Finally, correlations for predicting the average heat transfer coefficient in the vertical rectangular fin array heat sink, and the maximum LED temperature as a function of luminaire wattage and geometric parameters of the fin array have been presented.