Influences of Flow Attack Angles and Flow Directions on Heat Transfer Rate , Pressure Loss , and Thermal Performance in Heat Exchanger Tube with V-Wavy Surface

Numerical investigations on flow and heat transfer characteristics in the heat exchanger tube with the V-wavy surface are presented.+e finite volumemethod with the SIMPLE algorithm is selected to solve the present problem.+e effects of flow attack angles (α � 15°, 20°, 25°, 30°, 35°, 40°, 45°, 50°, 55°, and 60°) and flow directions (V-tip pointing downstream known as “VDownstream” and V-tip pointing upstream known as “V-Upstream”) for the V-wavy surface on flow and heat transfer patterns are considered for both laminar and turbulent regions. +e laminar regime is studied in the range Re � 100–1200, while the turbulent region is investigated in the range Re � 3000–10,000. +e mechanisms on flow and heat transfer in the test section are reported. +e numerical results reveal that the V-wavy surface changes the flow structure in the test section. +e vortex flow is produced by the V-wavy surface.+e vortex flow disturbs the thermal boundary layer on the heat transfer surface that is the reason for heat transfer and thermal performance enhancements. +e optimum flow attack angles of the V-wavy surface for laminar and turbulent regimes are concluded.


Introduction
e developments of the heat exchangers to enhance heat transfer rate and thermal performance have been found in many industries such as chemical industry, automotive industry, and refrigerant system.e augmentations of the heat transfer rate and thermal performance in the heat exchangers can help to conserve the energy and operation cost of the system.e methods to enhance heat transfer rate in the system are divided into two types: active and passive techniques.
e active technique requires the additional power such as vibration to increase heat transfer rate of the heating system.e use of the active technique must consider the economics for the process between the additional power and the increment of the thermal performance.e passive technique is the installation of the vortex generator or turbulator into the heating system to generate the vortex flow and to disturb the thermal boundary layer on the heat transfer surface.
Many researchers had analyzed the augmentation of the heat transfer rate in the heat exchanger by using turbulators.
e investigations on flow configuration and heat transfer characteristics in the tube/channel heat exchanger are done on both experimental and numerical studies.For example, Chen et al. [1] numerically and experimentally investigated the flow and heat transfer of an impingement jet array with V-ribs on the target and impingement plates.e three different cases V-ribs on both the impingement and target plates, V-ribs placed on the impingement plate, and V-ribs placed on the target plate were compared for Re � 15,000-35,000.ey reported that the highest Nusselt number ratio is around 1.16 for the V-rib placed on the impingement plate and on both plates.Jin et al. [2] presented the thermohydraulic performance of a solar air heater installed with staggered multiple V-shaped ribs on the absorber plate.ey concluded that the staggered arrangement gives higher Nusselt number and thermal performance than the inline arrangement around 26% and 18%, respectively.
ey also showed that the maximum thermal performance is around 2.43.Deo et al. [3] studied the heat transfer, pressure loss, and thermal performance in a rectangular duct placed with multigap V-down ribs combined with staggered ribs on one wall.e influences of pitch-toheight ratio, rib height-to-hydraulic diameter ratio, and flow attack angle on flow and heat transfer were considered for Re � 4000 � 12,000.ey summarized that the maximum augmentations on the Nusselt number and thermohydraulic performance were around 3.34 and 2.45 times, respectively.Kumar and Kim [4] reported the effects of the discrete multi-V-rib with the staggered rib in a solar air channel on heat transfer and thermal performance with the numerical method.ey found that the overall thermal performance of the discrete multi-V-rib with a staggered rib shape is higher than the other rib shapes around 6%. Maithani and Saini [5] experimentally investigated the enhancement of heat transfer rate in a solar air heater duct with the turbulence promoter.e V-ribs with symmetry gaps were selected to augment heat transfer rate and thermal performance.e influences of gap number, relative gap width, relative roughness pitch, angle of attack, and relative roughness height on heat transfer and pressure loss were considered for Re � 4000-18,000.ey reported that the maximum Nusselt number and friction factor are around 3.6 and 3.67 times above the smooth duct, respectively.Kumar and Kim [6] numerically studied the heat transfer and flow mechanisms in an air duct with various V-pattern ribs.ey concluded that the best thermal performance is found in the case of the V-pattern rib with groove roughness shapes.Fang et al. [7] investigated the turbulent flow in a square channel with V-shaped ribs placed on one wall.e flow attack angles 30 °, 45 °, 60 °, and 90 °, for the V-shaped rib, were compared.Promthaisong et al. [8] numerically examined the fluid flow and heat transfer characteristic in a square channel heat exchanger with discrete broken V-ribs.ey claimed that the discrete broken V-ribs can induce the longitudinal vortex flow which disturbs the thermal boundary layer on the heat transfer surface which is the reason for heat transfer augmentation.Jin et al. [9] numerically studied the heat transfer and flow behavior in a solar air heater channel with multi-V-shaped ribs on the absorber plate.ey found that the optimum thermal performance is around 1.93.ey also presented that the multi-V-shaped ribs help a better fluid mixing in the tested duct.Abraham and Vedula [10] presented the heat transfer and pressure loss in a square cross-sectional converging channel with V-shaped and W-shaped ribs for Re � 5000-35,000.Ravi and Saini [11] displayed the convective heat transfer in a solar air heater duct with discrete multi-Vshaped and staggered ribs on both sides of the absorber plate.
e effects of relative staggered rib pitch, relative staggered rib size, and relative roughness width on heat transfer and pressure loss in the test section were investigated for Re � 2000-20,000.ey found that the maximum Nusselt number and friction factor are around 4.52 and 3.13 times higher than the smooth duct, respectively.e wavy surface is always selected to help to improve the heat transfer rate and thermal performance of the fin-andtube heat exchanger [12][13][14][15][16][17][18].e wavy surface helps a better fluid mixing and increases the vortex strength of the flow that causes for heat transfer and thermal performance developments in the heat exchanger.Boonloi and Jedsadaratanachai [19,20] reported the influences of the V-wavy plate in a square channel heat exchanger on thermohydraulic performance.ey claimed that the insertion of the V-wavy plate can increase the heat transfer rate and thermal performance with moderate pressure loss penalty.Jedsadaratanachai and Boonloi [21] presented the inclined and V-wavy plated in a circular tube heating system for laminar regime, Re � 100-1200.ey found that the V-Upstream wavy surface performs the highest TEF around 2.4 at Re � 2000.Jedsadaratanachai and Boonloi [22] numerically investigated the effects of wavy height and wavy thickness for the V-wavy plate in a round tube heat exchanger on heat transfer rate, friction loss, and thermal performance.ey concluded that the optimum wavy height and wavy thickness are around 0.10D-0.15Dand 0.15D-0.20D,respectively.
As per the literature reviews above, it is found that the V-shaped turbulator gives high thermal efficiency, while the wavy surface is the turbulator that can be easily manufactured for the industrial system.In the present investigation, the concept of the V-shaped turbulator is combined with the wavy surface called "V-wavy surface".e V-wavy surface is inserted in the middle of the circular tube heat exchanger to enhance heat transfer rate and thermal performance.e influences of the flow attack angles and arrangements for the V-wavy surface in the heating tube on heat transfer and flow behaviors are considered for both laminar and turbulent flow regimes.e laminar flow is presented for Re � 100-1200, while the turbulent flow regime is performed for Re � 3000-10,000.e V-wavy surface may give high thermal performance and heat transfer rate similarly as the V-shaped turbulators.Moreover, the production of the V-wavy surface and installation in the heating system are easier than the V-shaped rib or baffle.

Physical Model
e circular tube heat exchanger inserted with the V-wavy surface is depicted as Figure 1. e tube diameter, D, is set around 0.05 m. e length periodic module of the circular tube equipped with the V-wavy surface is created around D.

Mathematical Foundation and Numerical Method
e mathematical model of the circular tube heat exchanger inserted with the V-wavy surface is governed by the continuity, the Navier-Stokes equations, and the energy equation.For the laminar ow regime, the governing and energy equations are discretized by the power law and SOU schemes, respectively.All governing equations are discretized by the SOU numerical scheme for the turbulent ow regime.e present investigation is answered by the nite volume method with the SIMPLE algorithm.e solutions are considered to be converged when the normalized residual values are less than 10 −5 for all variables, but less than 10 −9 only for the energy equation.
e realizable k-ε turbulent model for the turbulent ow region is written as and where

Modelling and Simulation in Engineering
and the constant values are as follows: e important parameters are Reynolds number, friction factor, local Nusselt number, average Nusselt number, and thermal enhancement factor.
e Reynolds number is calculated as e friction factor, f, is measured by pressure drop, Δp, across the periodic module, L: e local heat transfer is written as e average Nusselt number can be obtained by e insertion of the V-wavy surface increases both heat transfer rate and pressure loss in the heat exchanger.
erefore, the thermal performance in terms of the thermal enhancement factor (TEF) is presented to analyze the advantage of the V-wavy surface.
e thermal enhancement factor is calculated by the increases on both heat transfer and friction factor at a similar pumping power condition: Nu 0 and f 0 are the Nusselt number and friction factor for the smooth circular tube, respectively.

Boundary Condition and Assumption
e assumptions for the present investigation are as follows: (i) e flow and heat transfer are steady in three dimensions (ii) e test fluid is air at 300 K with the Prandtl number around 0.707 (iii) e air is set as incompressible fluid on both laminar and turbulent flows (iv) e thermal properties of the air assume to be constant at the average bulk mean temperature (v) e forced convective heat transfer is considered, while the natural convection and radiation are ignored (vi) e body force and viscous dissipation are uncounted e boundary conditions for the computational domain on both laminar and turbulent flows are concluded as Table 1.

Numerical Validation
e different number of grid cells 80000, 120000, 180000, 240000, and 360000 for the computational domain of the heat exchanger tube inserted with wavy V-surface (α � 30 °, V-Downstream with Re � 600 for laminar and Re � 6000 for turbulent) are compared on both flow and heat transfer.It is found that the augmentation of the grid cell from 120000 to 180000 has no effect for the Nusselt number and friction factor values.erefore, the grid around 120000 cells is created for all investigated cases when considered on both the time for solving the problem and the accuracy result.e computational domains of the smooth circular tube with no wavy surface are validated on both flow and heat transfer.e verifications are done by comparing between the values from the present prediction and the values from the correlations.e numerical results reveal that the deviations on the Nusselt number are around ±0.03 and ±5% for laminar flow and turbulent flow, respectively, and around ±0.05% and ±11% for the friction factor, respectively.e validations of the smooth circular tube for laminar and turbulent regimes are depicted as Figures 2 and  3, respectively.As the preliminary test of the computational domain, it can be concluded that the present computational domain has enough reliability to predict flow and heat transfer in the heat exchanger tube equipped with the V-wavy surface for laminar and turbulent regimes.

Numerical Result
e numerical results are divided into two parts: laminar and turbulent regimes.e flow configuration and heat transfer characteristic in the test section are presented.e performance evaluations for the tube heat exchanger equipped with the V-wavy surface are also concluded.

Flow and Heat Transfer Configuration.
e flow mechanisms in the heat exchanger tube equipped with the V-wavy surface are reported in terms of λ 2 isosurface, tangential velocity vector in the transverse plane, and longitudinal vortex flow.Figures 4(a) and 4(b) show the λ 2 isosurface in the heat exchanger tube equipped with the V-wavy surface for V-Downstream and V-Upstream, respectively, at Re � 600 and α � 30 °. e λ 2 isosurface is an indicator to describe the core of the vortex flow in the test section.As shown in the figures, the vortex core is detected through the test tube for both arrangements.For the 4 Modelling and Simulation in Engineering V-Downstream, the vortex core appears on the V-groove from sidewall to V-tip before ow across to the next module.
For the V-Upstream, the ow slides on the V-groove from V-tip to sidewall before ow across to the next module.e strength of the vortex ow depends on the ow attack angle, Reynolds number, and ow direction.
e tangential velocity vector in the transverse planes for the heat exchanger tube equipped with the V-wavy surface is presented as Figures 5(a) and 5(b), respectively, for V-Downstream and V-Upstream at Re 600 and α 30 °.As shown in the gures, the vortex ow is found through the test section on both arrangements.e ow includes four main vortex cores.Considering the upper pair of the vortex ow in each plane, the counterrotating ow with commonow-up is found in case of V-Downstream, while the V-wavy surface gives the di erence of the ow rotation.e di erence of the ow structure leads to the change of the heat transfer behavior in the heat exchanger tube.
Figures 6(a) and 6(b) show the longitudinal vortex ow in the heat exchanger tube inserted with V-Downstream and V-Upstream of the V-wavy surface, respectively, at Re 600 and α 30 °.As shown in the gures, it is indicated that the di erence of the V-wavy surface arrangement e ects for the change of the ow structure.e V-Downstream produces the impinging ow on the V-groove from the sidewall to the V-tip, while the V-Upstream performs the impinging ow on the V-groove from the V-tip to the sidewall.
e heat transfer behaviors in the heat exchanger tube inserted with the V-wavy surface are reported in terms of temperature distributions in transverse planes and local Nusselt number distributions on the tube wall.
e temperature distributions in transverse planes of the heat exchanger tube inserted with V-Downstream and V-Upstream wavy surfaces are illustrated as Figures 7(a) and 7(b), respectively, for V-downstream and V-Upstream at Re 600 and α 30 °.As shown in the gures, it is found that the V-wavy surface changes the temperature distributions pattern for both arrangements.e better uid mixing is detected when inserting the V-wavy surface in the heat exchanger tube.
e low temperature of the uid (blue contour) distributes from the center of the plane, while the high temperature of the uid (red contour) near the tube wall performs thinner.e thermal boundary layer disturbance on the heat transfer surface is also found.
e better uid mixing and thermal boundary layer disturbance are reasons for heat transfer rate and thermal performance enhancements.e di erent arrangement of the V-wavy surface e ects for the change of the thermal boundary layer.
Figures 8(a) and 8(b) displays the local Nusselt number distributions on the tube wall of the heat exchanger tube inserted with the V-wavy surface for V-Downstream and V-Upstream, respectively, at Re 600 and α 30 °. e V-Downstream gives the peak of the heat transfer surface at the upper-lower part of the tube, while the V-Upstream provides the highest heat transfer rate the left-right part of the tube.

Performance Assessment.
In this part, the heat transfer rate, pressure loss, and thermal performance are concluded in term of Nusselt number (Nu), friction factor (f ), and thermal enhancement factor (TEF), respectively.8 Modelling and Simulation in Engineering performs higher friction loss than the smooth circular tube with no wavy surface in all cases (f/f 0 >1).e ow attack angles around 15 °-25 °can help to reduce the pressure of the heating system for both arrangements.f/f 0 for the V-Downstream wavy surface is found to be around 8.89-12.21and 28.57-71.32 at Re 100 and 1200, respectively, and around 9.29-13.03and 31.16-70.81,respectively, for the V-Upstream wavy surface.
Figures 11(a) and 11(b) display the relations of the TEF with the Reynolds number at various ow attack angles of the V-Downstream and V-Upstream wavy surfaces in the heat exchanger tube, respectively.As shown in the gures, the TEF tends to increase when enhancing the Reynolds number for both arrangements.e Re 100 provides the lowest of TEF, while the maximum TEF is detected at Re 1200.Almost in all cases, the insertion of the V-wavy surface  in the heating tube performs higher thermal performance than the smooth tube without the V-wavy surface (TEF > 1).For V-Downstream, the TEF is around 0.86-1.22 and 1.64-2.87,respectively, for Re 100 and 1200.For V-Upstream, the TEF is around 0.88-1.04 and 2.22-2.93 for Re 100 and 1200, respectively.
Figures 12(a) and 12(b) plot the variations of Nu/Nu 0 with the ow attack angle for the tube heat exchanger inserted with the V-wavy surface for V-Downstream and V-Upstream arrangements, respectively.Considering at Re 1200, the optimum Nu/Nu 0 is detected at the ow attack angle of 35 °for the V-Downstream, while around 40 °for V-Upstream.
e relations of f/f 0 with the ow attack angle for the heat exchanger tube inserted with the V-wavy surface are displayed in Figures 13(a e relations of the TEF with the ow attack angle for the heating tube inserted with the V-wavy surface are depicted as Figures 14(a) and 14(b), respectively.As shown in the gures, it is found that the optimum attack angles for the V-Downstream and V-Upstream wavy surfaces are 30 °and 40 °, respectively.In addition, the terrible attack angle, which gives the lowest thermal performance for both arrangements, is 60 °V-wavy surface.15(a 12 Modelling and Simulation in Engineering inserted with the V-wavy surface for V-Downstream and V-Upstream, respectively, at Re 6000 and α 30 °. e vortex core is found for both arrangements of the V-wavy surface in the test section.e con guration of the ow is nearly detected as the laminar ow regime, but the vortex strength is not equal.Figures 16(a) and 16(b) plot the tangential velocity vector in transverse planes for the heat exchanger tube inserted with V-Downstream and V-Upstream wavy surfaces, respectively, at Re 6000 and α 30 °.As seen in the gures, the V-wavy surface can produce the vortex ow through the test section.e vortex ow helps a better uid mixing between hot uid near the tube wall and cold uid at the center of the test tube.e four main vortex ows are found for both arrangements.Considering at the upper pair of the vortex ow, the V-Downstream wavy surface creates the counterrotating ow with common-ow-up, while the V-Upstream wavy surface produces the counterrotating ow with common-ow-down.e di erent ow structure in the test section e ects for the di erent heat transfer behavior.

Flow and Heat Transfer Con guration. Figures
Figures 17(a  V-Downstream and V-Upstream, respectively, at Re 6000 and α 30 °. e V-wavy surface in the heat exchanger tube produces the longitudinal vortex ow through the test section on both arrangements.e swirling ow slides on the wavy groove from the sidewall to the V-tip for V-Downstream.e V-Upstream produces the swirling ow, which slides on the wavy groove from the V-tip to the sidewall.e vortex ow is an important factor to augment heat transfer rate and thermal performance due to the vortex ow that disturbs the thermal boundary layer on the heat transfer surface. e turbulent kinetic energy (TKE) distributions in transverse planes for the heat exchanger tube equipped with V-Downstream and V-Upstream wavy surfaces are plotted as Figures 18(a) and 18(b), respectively, at Re 6000 and α 30 °. e high TKE is detected when inserting the wavy V-surface in the heat exchanger tube for both arrangements.
Figures 19(a) and 19(b) report the temperature distributions in transverse planes for the heat exchanger tube equipped with the V-wavy surface for V-Downstream and V-Upstream arrangements, respectively, at Re 6000 and α 30 °.As shown in the gures, the insertion of the wavy V-surface in the tube helps a better uid mixing for both cases.
e lower temperature of the air (a blue contour) moves from the center of the test section to the tube surface.e high temperature of the air (a red layer) seems to be thinner.
e local Nusselt number distributions on the heat transfer surface for the heat exchanger tube inserted with the V-wavy surface are created as Figures 20(a) and 20(b), respectively, at Re 6000 and α 30 °. e presence of the V-wavy surface in the tube heat exchanger provides higher heat transfer rate than the smooth circular tube with no wavy surface for both cases.
e thermal boundary layer is disturbed by the vortex ow which was created from the V-wavy surface.e thermal boundary layer disturbance, vortex ow, and impinging ow are important factors for heat transfer and thermal performance improvement.

Performance Assessment. Figures 21(a) and 21(b)
present the variations of Nu/Nu 0 with the Reynolds number at various ow attack angles for V-Downstream and V-Upstream wavy surfaces in the heat exchanger tube, respectively.As shown in the gures, the heating tube with the V-wavy surface gives higher heat transfer rate than the smooth circular tube for both arrangements.Nu/Nu 0 tends to decrease with increasing Reynolds number for all cases.Modelling and Simulation in Engineering respectively.f/f 0 is higher than the smooth tube in all cases when inserting the V-wavy surface in the heat exchanger tube.f/f 0 slightly increases when enhancing the Reynolds number.e peak of the friction loss is detected at Re 10000, while the opposite trend is found at Re 3000.f/f 0 for the V-Downstream wavy surface in the heat exchanger tube e TEF decreases when augmenting the Reynolds number due to the increment of the friction factor and the reduction of the Nusselt number ratio.e maximum TEF is detected at Re 3000, while the reverse trend is found at Re 10000 for both arrangements.As Re 3000, the TEF is around 1.5-2.1 and 1.6-2.0,respectively, for the V-Downstream and V-Upstream arrangements.
e variations of Nu/Nu 0 with the ow attack angles of the V-wavy surface in the tested tube are reported as Figures 24(a  that the 15 °V-wavy surface can produce the lowest strength of the vortex ow.f/f 0 versus the ow attack angles for the V-Downstream and V-Upstream wavy surfaces in the test section are depicted as Figures 25(a) and 25(b), respectively.As shown, the maximum friction loss for the present problem is found at the ow attack angle around 40 °for both arrangements.In addition, the low values of the ow attack angle (around 15 °-20 °) can help to reduce the pressure loss in the test section.
e relations of the TEF with the ow attack angles for the heat exchanger tube equipped with V-Downstream and V-Upstream wavy surfaces are presented as Figures 26(a 18 Modelling and Simulation in Engineering 30 °-45 °gives the highest heat transfer rate, it also provides enlarged pressure loss in the heating system.erefore, the optimum TEF is found at the ow attack angle around 20 °for both arrangements when considering at Re 3000.e present results are compared with the previous works [23,24] for the ow attack angle of 45 °, BR 0.20, as Figures 27(a), 27(b), and 27(c) for heat transfer rate, pressure loss, and thermal performance, respectively.Jedsadaratanachai and Jayranaiwachira [23] studied the heat transfer rate and thermal performance in a tube heat exchanger inserted with V-ba e at the center of the tube.Jedsadaratanachai et al. [24] reported the ow and heat transfer mechanisms in a tube heat exchanger with V-shaped ba e placed on the tube wall.As shown in the gures, the V-Upstream wavy surface gives the highest on both heat transfer rate and pressure loss.e V-Upstream wavy surface performs the nearly value of TEF with V-Upstream ba e [24].

Conclusion
e investigations on ow and heat transfer characteristics in the circular tube heat exchanger inserted with the V-wavy surface are investigated numerically in three dimensions.e laminar and turbulent ows with Re 100-1200 and Re 3000-10000, respectively, are considered for the present study.e e ects of the ow attack angles and ow directions for the V-wavy surface on ow con guration and heat transfer characteristic are performed.In accordance with the numerical results, the major ndings can be concluded as follows.e V-wavy surface can generate the vortex ow that disturbs the thermal boundary layer on the heat transfer surface.e thermal boundary layer disturbance is the cause for heat transfer and thermal performance improvements in the heat exchanger tube.
e optimum ow attack angle for laminar ow is 30 °and 40 °for V-Downstream and V-Upstream wavy surface, respectively, when considered at TEF.For the turbulent regime, the greatest ow attack angle for the V-wavy surface, which gives the highest TEF, is 20 °for both arrangements.Temperature, K u i : Velocity in X direction, m s −1 u: Mean velocity in the channel, m s −1 α: Angle of attack, degree TEF: ermal enhancement factor ( (Nu/Nu 0 )/(f/f 0 ) 1/3 ) ρ: Density, kg m −3 in: Inlet 0: Smooth tube pp: Pumping power.

Figure 1 :
Figure 1: (a) Physical model of the heat exchanger tube inserted with the V-wavy surface and (b) tube geometry in the transverse plane.

Figure 3 :
Figure 3: Validation of the smooth circular tube for the turbulent ow.

Figure 2 :Figure 5 :
Figure 2: Validation of the smooth circular tube for the laminar ow.

Figure 9 :
Figure 9: Relations of Nu/Nu 0 with Re for the heat exchanger tube inserted with the V-wavy surface for (a) V-Downstream and (b) V-Upstream at the laminar regime.

Figure 8 :
Figure 8: Local Nusselt number contour on the tube wall of the heat exchanger tube inserted with the V-wavy surface at α 30 °and Re 600 for (a) V-Downstream and (b) V-Upstream.

Figure 11 :Figure 10 :
Figure 11: Relations of the TEF with Re for the heat exchanger tube inserted with the V-wavy surface for (a) V-Downstream and (b) V-Upstream at the laminar regime.

Figure 13 :Figure 12 :Figure 15 :Figure 14 :
Figure 13: Relations of f/f 0 with α for the heat exchanger tube inserted with the V-wavy surface for (a) V-Downstream and (b) V-Upstream at the laminar regime.
) and 17(b) report the longitudinal vortex ow in the test section inserted with the V-wavy surface with

Figure 16 :
Figure 16: Tangential velocity vector in transverse planes of the heat exchanger tube inserted with the V-wavy surface at α 30 °and Re 6000 for (a) V-Downstream and (b) V-Upstream.

Figure 17 :
Figure 17: Longitudinal vortex ow of the heat exchanger tube inserted with the V-wavy surface at α 30 °and Re 6000 for (a) V-Downstream and (b) V-Upstream.

Figure 18 :
Figure 18: TKE in transverse planes of the heat exchanger tube inserted with the V-wavy surface at α 30 °and Re 6000 for (a) V-Downstream and (b) V-Upstream.

Figure 19 :
Figure 19: Temperature contour in transverse planes of the heat exchanger tube inserted with the V-wavy surface at α 30 °and Re 6000 for (a) V-Downstream and (b) V-Upstream.
) and 24(b), respectively, for V-Downstream and V-Upstream arrangements.e optimum hat transfer rate is found at the ow attack angle around 30 °-35 °for the V-Downstream and around 40 °-45 °for the V-Upstream.Considering at Re 3000, the lowest values of the Nusselt number is detected at the ow attack angle around 15 °for both arrangement.e reason is

Figure 20 :
Figure 20: Local Nusselt number contour on the tube wall of the heat exchanger tube inserted with the V-wavy surface at α 30 °and Re 6000 for (a) V-Downstream and (b) V-Upstream.

Figure 22 :Figure 21 :
Figure 22: Relations of f/f 0 with Re for the heat exchanger tube inserted with the V-wavy surface for (a) V-Downstream and (b) V-Upstream at the turbulent regime.

Figure 24 :Figure 23 :
Figure 24: Relations of Nu/Nu 0 with α for the heat exchanger tube inserted with the V-wavy surface for (a) V-Downstream and (b) V-Upstream at the turbulent regime.

Figure 26 :Figure 25 :
Figure 26: Relations of the TEF with α for the heat exchanger tube inserted with the V-wavy surface for (a) V-Downstream and (b) V-Upstream at the turbulent regime.

Table 1 :
Boundary condition for the computational domain of the heat exchanger tube equipped with the V-wavy surface.