DEVELOPMENT OF A NEW TYPE OF FINNED HEAT EXCHANGER

Original scientific paper A new geometric form of fins (needle fins) for finned heat exchangers of gas-liquid type is described. It achieves a higher heat transfer coefficient and lower mass of the heat exchange surface relative to the heat exchangers with circular fins which in this case served as a basis for comparison. For the analysis of the heat transfer, the computational fluid dynamics analysis with ANSYS Fluent software was applied. Numerical simulation was performed for the round fins and fins with a new, innovative geometric shape at air flow speeds of 1 m/s to 5 m/s. The results of numerical simulations, with regard to the exchanged heat and pressure drop were verified by the correlations available in the literature and compared to the simulation results for tubes with innovative fins. Results show an increase in the amount of Nu from 20 % to 30 % for 2300 >Re > 12000 while reducing mass of heat exchange surfaces of 23,8 %.


Introduction
Heat exchangers are used in different technical areas and very often in energy and thermal engineering, petroleum, chemical, food, automotive industry and in various processes where heat exchange is required.Caused by intensity of heat change and the adaptable construction and fabrication, finned tube exchangers with circular fins are often used.In finned tube exchangers, heating fluid is usually flowing through the tubes and the gas flow across finned tubes in staggered or in-line configuration.Heat transfer resistance on the gas side makes 80 % of the total heat transfer resistance, so determining the improvement of the heat transfer on the gas side for different cases is a significant contribution to increasing the effectiveness of the finned heat exchangers.
Increased heat exchange can be achieved by increasing the heat transfer surface, increasing the heat transfer coefficient, or increasing the thermal efficiency of the finned surface.The increase in the exchange surface directly increases the cost of the material, which may amount to up to 80 % of the total price of the exchanger, so researches are focused on the other two parameters that are interconnected.
Increase in the heat transfer coefficient can be achieved by applying different fins shapes that increase the turbulence of the flow, so the thermal boundary layer is periodically interrupted which results in more efficient heat exchange.However, the innovative design of fins with the increase in the heat transfer coefficient causes increase of pressure drop in the gas flow across tube bundle or increases the fan power to transport the gas through the heat exchanger.
In practical application, weight and size of the heat exchanger are often very important and contribute to proper and economical functioning of unit or the entire system (e.g., the space for car access is limited).However, the mass of the heat exchanger is also very important (less mass means less total car mass and lower fuel consumption).

Literature review
The analytical approach to solving heat transfer for simple geometry of finned surfaces dates from the last century when basic functions were defined for temperature profiles and fin efficiency for different fin shapes.Hashizume et al. [1] analysed the thermal efficiency of rectangular cross sectional circular fins and performed an analytical solution in the form of a modified Bessel function.
Kays and London [2] provided experimental correlations for a wide range of configurations adopted in compact extended surface heat exchangers and presented test data on finned circular tubes.Ward and Young [3] developed heat transfer and pressure drop correlations for plain finned tubes with triangular pitch.They compared their pressure drop data with a correlation from literature.
Kearney and Jacobi [4] investigated experimentally local heat transfer behaviour in staggered and in-line arrangements with the help of optical adaptation of the naphthalene sublimation technique in order to evaluate the analytical fin efficiency.Experimental investigations of round (solid) and serrated finned-tubes have been studied by [5÷9].Taborek [10] and Frasz [6] compared the varying influences of round and segmented fins.Weierman [11] investigated the performance of in-line and staggered tube arrangement of segmented finned tubes.
For crossflow over finned tube banks, a fairly large set of experimental data can be found in the Russian literature (Zhukauskas, [12]) and the recommended correlations for tubes with circular and helical fins.
Stasiulevicius et al. [13] developed correlations of the convective heat transfer coefficient and resistance of finned-tube bundles in a cross flow including the effects of geometric parameters of fins and tube arrangement within the bundle.Mon and Gross [14] investigated the effects of the fin spacing on four-row round-finned tube bundles in staggered and in-line arrangements by three dimensional numerical study.
Ali Shakir Al-Jaberi et al. [15] performed experiments on circular fins with slanted blades attached on the copper tube surface in order to reduce the thermal boundary layer.They examined effects of number of slanted blades and Reynolds number on the heat transfer characteristics.Results show 20 % to 27,5 % higher Nusselt number for slanted fins than for circular fins, but they did not examine pressure drop in tube bundle.
A. Lemouedda et al. [16] presented the results of numerical calculations of spiral finned tubes and compared them with the results for bare tubes.Naess [17] experimentally tested heat transfer and pressure drop for L-fins and in this case gave correlations for heat transfer and pressure drop.
Martinez at al. [18] conducted a comparative study of heat transfer and pressure drop for spiral serrated fins.Cléirigh and Smith [19] studied three spiral shapes of fins: full fin; partially segmented and fully segmented.
B. Anoop, C. Balaji, and K. Velusamy [20] investigated the heat transfer on one tube with serrated fins combining experimental approach and numerical calculation.The depth of the segment, the pitch of the fins, fin height and thickness were investigated.
Rene Hofmann et al. [10] experimentally investigated heat exchanger with finned tubes in order to optimize it.U and L shaped fins were full and serrated.Fin height, thickness, fin spacing and the width of the fin segment were varied.They found an average increase in Nusselt's number by 22 % when using serrated fins.
The complex turbulent flow pattern across the fin and tube surface made the theoretical prediction of pressure drop very difficult and therefore most of the published correlations were related to the experiments.All of them use the fluid velocity at the minimum flow area of tube bundle.One group of correlations is based on tube outside diameter (d 0 ) or fin collar diameter as the characteristic length for calculations of Re and Nu number.
Numerous methods used in computational fluid dynamics have been developed today.A review of all the methods applied today in computer fluid dynamics was given by Md Lokman Hosain and Rebei Bel Fdhil [26].Hossain Nemati and Mohammad Moghimi [27] analysed the influence of choice of different models of turbulence at the flow simulation in a four-row tubular tube bundle.Detailed analysis shows that computational fluid dynamics can be used as a flow visualization tool.Due to certain deviations in the results between certain models it is necessary to compare the results with experimental research.

Research object, material and method
The geometric model of the tubular heat exchanger on which its thermal efficiency and thermal effectiveness will be estimated in relation to the reference model, consists of an insulated casing inside which is a bundle of tubes with needle shaped fins.Water as a heating medium is introduced into the inlet chamber, passes through the tubes and goes to the outlet chamber.Across the finned tubes flows colder air.The new and innovative shape of the needle-shaped fins enables achievement of higher turbulence levels of the fluid flowing around the fins, and thus higher heat exchange.

Physical model of heat exchanger with needle-shaped fins
For research implementation, the tube ∅20×1,5 is selected.As a reference geometry, a round fin ∅40/∅20 with thickness 0,5 mm was selected (Fig. 1a).The new needle type fin is shown in Fig. 1b and has eight vertices spaced uniformly along the circumference.Different materials are used for making heat exchangers.Steel, copper and aluminium are the most common.For the implementation of comprehensive research, the selected material of the tubes and fins is stainless steel.Stainless steel is selected because of a wider range of application, higher temperature resistance, resistance to corrosion and resistance to fouling, and facility to easy clean the fin surface even though it has smaller heat conductivity coefficient than aluminium and copper.
Initial diameter, thickness and pitch of the fins were selected according to the recommendations of the authors dealing with the problem of finned tubular heat exchangers [4,12,13,14,22,28,29,30,31].

Numerical analysis
The numerical analysis is focused on air flow across tubes because the air side resistance of the heat exchange makes up 80 % of the total resistance to the heat exchange.
Certain assumptions and simplifications were adopted for the mathematical description of the thermal phenomena within the heat exchanger.
The most common assumption that is applied when defining fluid flow is fluid continuity.The characteristic dimensions of the analysed innovative exchanger are large enough and the conditions of the continuum hypothesis are fulfilled.
The assumptions of homogeneity and isotropy were also introduced.Homogeneity implies that the physical properties of the substance are the same at all points.Thus, the air is considered a homogeneous mixture of gases because the proportion of individual gases that compose the air is equal at all points of the fluid.Isotropy implies that the physical properties of the observed substance are the same in all directions.It is assumed that the thermal conductivity of the fin is equal in all directions, though, for example, the fin composed of different materials layers does not have the same thermal conductivity in the layer direction and in the direction normal to the layer.
Air is considered as homogeneous mixture of gases and is treated as a one-component fluid (dry air).There is no fluid leakage through the walls of the finned exchanger and the heat exchange with the environment is negligible.The fins are completely and tightly attached to the tube and there is no contact resistance between the tube and the fin surface.Steady state analysis is performed.
The numerical domain was chosen to perform the numerical analysis of the tube heat exchanger.For a heat exchanger with a uniform fluid flow field at the inlet, a typical repeating section in the heat exchanger is selected for the domain (Fig. 2), and the solutions obtained are assumed valid for the entire heat exchanger.

Boundary and initial conditions include defining:
• The air entering the computational domain is assumed to have uniform velocity over the cross section and ranges from 1 m/s to 5 m/s, and turbulence intensity 5 %.
• The air temperature at the inlet to the heat exchanger is 288 K. • Hot water at the inlet to tubes has temperature 353 K.
Because water has a high thermal capacity, it is assumed that the temperature of the tube inner wall is constant and equal to the water temperature.• At the sides of the computational domain it is set symmetry boundary condition.
• The gauge pressure p out,c at the outlet of channel is set to zero.This corresponds to atmospheric conditions p a .• Hydraulically smooth walls were defined for outer tube and the fin walls.• Symmetry condition is set for top, bottom, left and right side of computational domain.Symmetry condition is applied due to simplifying the calculation where it is possible to reduce computational domain.
The basic requirement is that the geometry is symmetric and also that the expected solution of the temperature field and the fluid flow fields are symmetric.At the symmetry planes a zero heat flux is assumed.The normal velocity component at the symmetry plane equals zero, i.e. no convective flux across that symmetry plane exists.Thus, the temperature gradients and tangential components of the velocity gradients in normal direction are set to zero.• Physical properties of air are defined as polynomial function of temperature (and pressure) and thus set in Ansys Fluent software.Density of the air is based on incompressible ideal gas law.• The physical properties of the fin and tube material are set constant (λ t =16,2 W/(m•K), ρ t =7860 kg/m 3 ).

Properties of materials
The definition of physical properties of used materials includes the determination of thermal conductivity, dynamic viscosity, density, specific heat capacity of fluid flowing across the tube bundle (dry air) and the material of the fins and tubes.The material of the tubes and fins is stainless steel, the surfaces are clean without any additional heat resistance.
The calculation of non-dimensional numbers Re, Nu, Pr and Eu is based on the physical properties of the working fluid (air) that are generally dependent on temperature and pressure.For a precise calculation of the above non-dimensional features it is necessary to clearly define the temperature at which the physical properties of the fluid are taken.The fluid temperature in the thermal boundary layer varies from T w at the surface to freestream temperatures at the outer edge of the boundary.The fluid properties also vary with temperature, and thus with position across the boundary layer.In order to account for the variation of the properties with temperature, the fluid properties are usually evaluated at the so-called film temperature, defined as 2 / ) ( av w bl which is the arithmetic average of the surface and the average free-stream temperatures.Average free-stream temperature is defined as The fluid properties are then assumed to remain constant at those values during the entire flow. An alternative way of accounting for the variation of properties with temperature is to evaluate all properties at the average free stream temperature T av and to multiply the Nusselt number relation by (Pr av /Pr w ) r or (μ av /μ w ) r , where r is appropriate coefficient [32].
In this paper, the temperature of the tube outer wall is assumed approximately equal to the inner wall temperature.
Reynolds number (Eq. 3) is a measure of the relative importance between the momentum flux by advection and by diffusion in the same direction.It is important that velocity (u ff ) and length (L) are taken in the same direction.For calculating the Reynolds number, the physical properties (density, dynamic viscosity) are taken at mean air temperature T av .Characteristic dimension (L) is based on the outer diameter of the tube (d 0 ), and the mass flux, i.e. velocity through the narrowest free flow area within the tube bundle.This is consistent with the relevant literature For the geometries considered in the present study, the narrowest free flow area is the area between two tubes in the transversal direction, and can be defined as For heat transfer correlations, the Nusselt number (Nu) is defined where α 0 is actual average gas-side heat transfer coefficient.
For pressure drop correlations, the Euler number (Eu) is defined as

Governing equations
The mathematical model used to describe a physical problem is a set of differential equations and constitutive relations and initial and boundary conditions.The basic equations of fluid dynamics are derived from: Conservation of Mass: Conservation of Momentum: Conservation of Energy: The established mathematical model is solved by using the finite volume method that is based on dividing the computational domain into small volumes and integration of equations of conservation at these volumes thus obtaining a system of discrete algebraic equations that are then solved iterative.Computational domain is meshed by ANSYS software.Meshing was performed by using a hybrid mesh where most of the volume is structured mesh, and the smaller part around the fins is unstructured mesh.The area along the fins and tubes where the convection heat transfer is performed is covered with eight boundary layers and the thickness of the first layer is 0,025 mm (Fig. 4).By successive refining of the mesh, we found the solution, independent of the computational mesh.In the final analysis we used the mesh with 10,9 million of the finite volumes (elements).
Numerical calculation was performed with ANSYS Fluent software.A steady state model of heat exchange is assumed.Two models of turbulence were used: k-ε Realizable with Enhanced Wall Treatment (EWT) method and k-ω SST.The calculation results of both models were used for the computation of Nu and Eu, which were compared with the results of the literature with the aim of selecting a turbulence model whose results coincide more with the results of the literature.

Solution methods and convergence of the solution
An important aspect when performing numerical simulations is to judge whether the simulation is complete and converged, or not.There are several different ways to check this and ensure convergence.The most used method is to look at the residuals for each variable being solved.In ANSYS Fluent software the default convergence criterion is defined using globally scaled residuals.The default convergence criterion in ANSYS Fluent states that needs to be reduced to 10 −3 for all solved equations, except the energy equation for which the criterion is set to 10 −6 .Scaled residuals may not give the full picture.A good indicator to judge convergence is to look at how the residuals develop with the iterations.A good indication that convergence is reached is if the residuals continue to decrease or remain low for several iterations.Overview of solution methods and convergence criteria is visible in Tab. 1. Solution is converged after about 11000 iterations.
The convergence error is verified on the amount of heat delivered by the inner wall of the tube through the outer surface of the tube and the fins and the amount of heat received by the air.The maximum deviation is 0,077%.

The results of numerical calculation 3.1 The results for round fins
The input and output data of the heat calculations are summarized in the tables below.
For the calculation of the necessary flow variables at boundaries (for example at inlet and outlet of tube bundle), mass flow averaging was used.

The results for needle type fins
The input and output data of the heat calculations are summarized in the tables below.

Data Reduction and interpretation
The heat duty is calculated from the calculated mass flow rates and overall temperature changes.
To calculate the overall heat transfer coefficient (U), the log-mean (LMTD) method is used.
The logarithmic mean temperature difference for counter-current flow is chosen.According to Naess [17] this method has proven to be accurate to within 0,1 % of the actual cross-counter-current arrangement mean temperature difference.
The overall heat transfer coefficient is then calculated The effective/apparent air-side heat transfer coefficient is L t is tube length that is equal to model width.In the case of air temperatures lower than 300 °C, the value of radiation heat transfer coefficient could be negligible and then its value may be taken as zero.Outside and inside fouling factors are also taken as zero.The effective heat transfer coefficient in Eq. ( 14) is the apparent heat transfer coefficient including fin efficiency.In order to calculate the actual average gas-side heat transfer coefficient α o , the fin efficiency η f is needed.
The thermal conductivity of the fin material has a strong effect on the temperature distribution along the fin and therefore influences the degree to which the heat transfer rate is enhanced.In practice, the fin is thin and temperature changes in the transverse direction within the fin are small compared with the temperature difference between the fin and the environment (Fig. 5b).
Ideally, the fin material should have a large thermal conductivity to minimize temperature variations from its base to its tip.In the limit of infinite thermal conductivity, the entire fin would be at the temperature of the base surface, thereby providing the maximum possible heat transfer enhancement.However, since a finite conduction resistance characterizes any fin, a temperature gradient must exist along the fin.In our case, fin material is stainless steel with relative small thermal conductivity 16 W/(m•K) and therefore temperature variation in longitudinal direction (Fig. 5b) will be important causing heat transfer less than maximum possible.
In addition, temperature field across fin area is not uniform (Fig. 5a) and temperature of fin tip is different for each needle.All these parameters are taken in account by fin efficiency.
Corrected fin length h e is based on assumption of equivalence between heat transfer from the actual fin with tip convection and heat transfer from a longer, hypothetical fin with an adiabatic tip.
For new type of fins proposed in the article, there is no expression for efficiency in literature.As serrated fins are similar to new type of fins expression for serrated fins will be used.This means some error in calculation and has to be examined in future.
The appropriate theoretical fin efficiency for serrated fins, which compensates for the finite conductance in the fins, under the assumption of a uniform air side heat transfer coefficient, can be expressed as [1] e e f th, where the parameter m e is given by where w s is average width of needle fin and t e is equivalence thickness of fin, d r,f is root diameter of fin needle.
Due to the formation of vortices and boundary layers, the assumption of uniformity of heat transfer coefficient across the fin does not hold in actual situations.Experiments have shown lower heat transfer coefficients than predicted theoretically.In the present analysis for needle type fins an empirical correction factor to the theoretical fin efficiency proposed by Weierman [5] for serrated fins is used.
Efficiency of serrated fins is defined acc. to Eq. 21.
Recall that fins are used to increase the heat transfer from a surface by increasing the effective surface area.However, the fin itself represents a conduction resistance to heat transfer from the base surface.For this reason, there is no assurance that the heat transfer rate will be increased by the use of fins.An assessment of this matter may be done by evaluating the fin effectiveness ε ƒ .
Both the fin efficiency and fin effectiveness are related to the performance of the fin, but they are different quantities.However, they are related to each other by Numerical pressure drop in tube bundle is calculated from the next expression out in where p in and p out is the mass weighted average pressure at inlet and outlet of tube bundle (see Fig. 2).

Validation with literature results for round fins
Flow through tube banks is studied experimentally since it is too complex to be treated analytically.Engineers are primarily interested in the average heat transfer coefficient for the entire tube bank, which depends on the number of tube rows along the flow as well as the arrangement and the geometry of the tubes and fins.Several correlations from literature, all based on experimental data, have been proposed for the average Nusselt number for cross flow over tube banks with round fins.
It should be noted that in most cases the correlations that define Nu number do not specify whether the physical properties of the fluid should be selected for the boundary layer or for the bulk flow.For the evaluation of Nu number in this article, physical properties of the fluid boundary layer are taken.This can potentially make a certain error in the results.In Fig. 6 to Fig. 9 there is a comparison of the calculation results of the analysed model with round fins and the results obtained by correlations from the literature.The values of Nu numbers obtained on the SST k-ω turbulence model show max.deviation of 13 % according to the reference correlations which can be evaluated as very good (Fig. 7).
Eu values for the SST k-ω turbulence model show slightly greater deviation from literature.The deviations are higher for lower Re values and up to 29% while for higher values of Re deviations are up to 16% (Fig. 9).Also, the values of Eu are less than by correlations.Interestingly, the k-ε Realizable model shows a better trend of results than the SST k-ω model in the observed range of Re compared to the literature although the deviations are higher.From the previous diagrams, it can be seen that the SST k-ω model of turbulence in the observed area of Re numbers shows a better match to the results of literature than the k-ε Realizable model.
In accordance with the previously discussed for further comparison of the round fins and the new type of needle fins, the SST k-ω turbulence model will be selected.

Comparison of calculation results for round fins and needle type fins 6.1 Flow characteristic
The global velocity distribution in the bundle is essential for understanding the local flow and heat transfer phenomena.Fig. 10 shows velocity fields in a cross-section passing through the middle of fin thickness.Figs. 9, 10, 11 and 12 show the local characteristics of the temperature, pressure, turbulent kinetic energy and the air speed of the needle type finned exchanger and round finned exchanger for inlet air velocity of 5,0 m/s.Cross flow over a tube exhibits complex flow patterns.The fluid approaching the tube branches out and encircles the tube, forming a boundary layer that wraps around the tube.The fluid particles on the mid-plane strike the tube at the stagnation point, bringing the fluid to a complete stop and thus raising the pressure at that point.The pressure decreases in the flow direction while the fluid velocity increases.Fluid embraces the tube on the frontal side, but it is too fast to remain attached to the surface as it approaches the top of the tube.As a result, the boundary layer detaches from the surface at approximately 120°, forming a separation region behind the tube.Flow in the wake region and especially after the 5 th row of tubes is characterized by vortex formation and pressures much lower than the stagnation point pressure.Caused by the slower air flow, higher temperatures persisted in wake areas.The difference in the air velocity field (Fig. 12) and the level of turbulence, and thus the difference in heat transfer coefficient increases with row number because of the combined effects of upstream rows.In the case of a needle shaped fins, the formation of the vortex is more emphasized than in the case of round fins.It is also apparent that the amount of turbulence energy is greater for the needle shape fins (Fig. 13).To ensure accuracy in calculating the thermal boundary layer, the low-Re approach to modelling the near-wall flow was used.Consequently, the near-wall mesh resolution places nodes within the viscous sublayer, avoiding reliance on a wall function.Accordingly, on fluid-side the wall-adjacent mesh spacing (Δy) was sufficiently small so that y + < 1 at the fin and tube surfaces.For inlet air velocity 1 m/s and 2,4 m/s max.value of y + is 1,0.For nominal velocity 5 m/s on the largest part of the surface y + is less than 1 and in a small part of the surface reaches a value of 1,8 (Fig. 15).SST kω model switches automatically from a wall function to a low-Re formulation, based on the grid density provided by the user.It ensures therefore an optimal accuracy of the CFD solution on a given grid and allows the use of coarser near-wall grids, which also benefits the cell aspect ratio.In general, it can be concluded that the two types of fins have substantially similar flow characteristics but turbulence is somewhat higher for needle type fins that results in better heat transfer.

Non-dimensional numbers Nu and Eu
The numerical results of the calculation based on the data given in Tab. 5 and Tab.7 can be graphically displayed.
As can be seen from Fig. 16 and Fig. 17, Nu number is greater than 20 % to 30 % for needle type fins compared to Nu number for round fins.The difference is more significant for higher Re numbers.In the analysis of finned heat exchanger with segmented fins R. Hofmann [24] stated the average increase in the Nu number of 22 % relative to the finned exchanger with circular round fins.In our case, increase in Nu number is higher and it is around 26 %.19 show that Eu number is approximately equal for both fin types.Even for the needle type fin Eu decreases a little with its value.Although the fin shape varies the net free area in a tube row is nearly the same in both cases.Thus, a significant difference among pressure drop is not expected.

Performance assessment
The performance rating of the two observed heat exchangers will be analysed through multiple parameters.The efficiency and effectiveness of round fin and needle type fin are analysed first.It is evident that round fin has a much greater effectiveness of needle type fin proportionally larger surface.The efficiency of the round fin is also greater than needle type fin efficiency, meaning that the temperature difference is smaller between the fin root and fin tip.For a given material and flow conditions it actually means lower heat exchange which is evident from Fig. 22 and Fig. 23.The exchanged heat per unit of heat exchanger surface area is higher for the needle type fins by 35 % at Re = 2340 and 39,3 % at Re = 12000.
The power required to keep a fluid flowing through the tube bank (and thus the operating cost) is proportional to the pressure drop.Therefore, the benefits of enhancing heat transfer via fins should be weighed against the cost of fan power requirements.Specific fan power can be defined as fan in air fan s, Specific fan power is about 10 % greater for needle type fins than round fins.

Conclusion
Numerical simulations of heat exchanger with needle type fins and round fins were performed in the same way, under the same initial assumptions and parameters applying two turbulence models.Comparing data obtained from CFD and data from literature, SST k-ω turbulence model was selected.For the selected turbulence model and air input speeds of 1,0; 2,4 and 5,0 m/s, a comparison was made between the Nu and Eu numbers for round fins and needle fins.The needle fins showed better results in terms of increasing the Nu number to 30 % while simultaneously reducing the weight of the exchange surfaces by 23,8 %.Increase in the required specific fan power for the operation of exchanger with needle type is about 10 %.On the other side, round fins are more effective, primarily because of the larger surface for heat exchange.
The variance of the fin geometry, the fin pitch and the tube pitch will be the subject of the next research to give a more complete picture of the new needle type fin.

Figure 1
Figure 1 Geometry of round fin and needle type fin

Figure 2 Figure 3
Figure 2 Mathematical model of computational domains

Figure 4
Figure 4 Part of mesh with round fins

Figure 5
Figure 5 Temperature over fins in 3 rd row for air velocity 5 m/s Round fins efficiency is calculated according to Schmidt

Figure 6
Figure 6 Calculated Nu and the results from literature for the round fins

Figure 7 Figure 8
Figure 7 The difference between the computed Nu and the results from the literature

Figure 9
Figure 9 The difference between the computed Eu and the results from the literature

Figure 10
Figure 10 Temperature fields comparison of round and needle type fins

Figure 11
Figure 11 Pressure fields comparison of round and needle type fins

Figure 12
Figure 12 Velocity fields comparison of round and needle type fins

Figure 13 Figure 14
Figure 13 Turbulence kinetic energy fields comparison of round and needle type fins

Figure 15 y+
Figure 15 y+ values of round and needle type fins

Figure 16 Computational
Figure 16 Computational Nu results for round and needle type fins

Figure 17
Figure 17 Nu difference between round and needle type fins

Figure 18 ComputationalFigure 19
Figure 18 Computational Eu results for round and needle type fins

Fig. 18 and
Fig.18and Fig.19show that Eu number is approximately equal for both fin types.Even for the needle type fin Eu decreases a little with its value.Although the fin shape varies the net free area in a tube row is nearly the same in both cases.Thus, a significant difference among pressure drop is not expected.

Figure 20
Figure 20 Fin efficiency

Figure 21
Figure 21 Fin effectiveness

Figure 22 Figure 23 Figure 24
Figure 22 Exchanged heat per unit of the exchanger surface

Table 1
Solutions methods and convergence criteria

Table 2
Characteristic dimensions of tube and fins

Table 3
Boundary conditions

Table 4
Output data from Ansys Fluent for k-ε Realizable with EWT turbulence model

Table 5
Output data from Ansys Fluent for k-ω SST turbulence model

Table 6
Characteristic dimensions of tube and fins

Table 7
Output data from Ansys Fluent for k-ω SST turbulence model