**3.3 Temperature distribution**

vortex intensity than that of RWP because the frontal area of the CRWP is larger than that of the RWP and due to the instability of centrifugal force when the flow passes over the CRWP surface [19, 31]. The longitudinal distribution of the vortex intensity is shown in **Figure 14** for a velocity of 0.4 m/s and **Figure 15** for a velocity of 2.0 m/s. In the case of CRWP and RWP, the longitudinal vortex intensity tends to dissipate after passing VGs due to viscous effects [2, 26, 28]. Therefore, the installation of the second and third rows of VG reinforces the intensity of the longitudinal vortex as illustrated in **Figures 12(c)–(f)** and **Figures 13(c)–(f)** for velocities of

The hole in the VG results in a decrease in the intensity of the longitudinal vortex, as shown in **Figures 12**–**15**. The hole in VG causes jet flow formation, which can interfere with the generation of the longitudinal vortex [26]. For RWP VGs with a velocity of 2.0 m/s, the intensity of the longitudinal vortex experiences the highest decrease, namely 17% at x/L = 0.48 for the case of one pair with holes, 11% at x/L = 0.4 for the case of two pairs with holes and 13% at x/L = 0.48 for the case of three pairs with holes of ones without holes. Meanwhile, in the case of CRWP VGs with a velocity of 2.0 m/s, the intensity of the longitudinal vortex experiences the highest decrease, namely 35% at x/L = 0.48 for the case of one pair with holes, 14% at x/L = 0.68 for the case of two pairs with holes and 22% at x/L = 0.68 for the case

*The longitudinal vortex intensity for the case of three pairs of RWP and CRWP at locations x / L = 0.34 and*

*The longitudinal vortex intensity for the case of three pairs of RWP and CRWP at locations x / L = 0.34 and*

of three pairs with holes compared to ones without holes.

0.4 m/s and 2 m/s, respectively.

*Heat Transfer - Design, Experimentation and Applications*

**Figure 14.**

**Figure 15.**

**68**

*x/L = 0.32 at a velocity of 0.4 m/s, respectively.*

*x/L = 0.32 at a velocity of 2.0 m/s, respectively.*

The temperature distribution for the RWP and CRWP cases with/without holes and the baseline in the spanwise plane at a certain position with a velocity of 2.0 m/s is shown in **Figures 16** and **17**. Visually, the temperature distribution in the channel in the presence of VG is better than the baseline. The placement of VG in the channel increases the temperature distribution due to the counter-rotating pairs of longitudinal vortices, which result in increased fluid mixing [32]. Counter-rotating pairs of longitudinal vortices produce a downwash that pushes the fluid towards the surface of the heated plate resulting in increased local heat transfer coefficients and thinning of the thickness of the thermal and dynamic boundary layers [32, 33].

Meanwhile, counter-rotating pairs of longitudinal vortices also generate upwash on the outer side of the vortex and push the hot fluid on the plate wall towards the flow-stream resulting in a decrease in the local heat transfer coefficient and a

**Figure 16.**

*Temperature distribution in channel with: (a) RWP without holes; (b) RWP with holes.*

**Figure 17.** *Temperature distribution in channel with: (a) CRWP without holes; (b) CRWP with holes.*

thickening of the boundary layer as observed in **Figures 16** and **17** comparing to the baseline case, as shown in **Figure 18**. Visually, the temperature distribution in the CRWP case is more even than the temperature distribution in the RWP case. This is because CRWP produces a higher longitudinal vortex intensity than that of RWP [31]. In addition, the holes in each VG result in the formation of jet flow, which can reduce the intensity of the longitudinal vortex resulting in an increase in temperature gradient [26], as shown in **Figure 16(b)** and **17(b)**.

#### **3.4 Pressure distribution**

**Figure 19** shows the pressure distribution for the three-pairs RWP and CRWP cases with/without holes at a Velocity of 2.0 m/s. Installation of VG in the channel results in an increase in pressure drop due to drag generated on the flow [34, 35]. As observed in Figure 3.14, the pressure drop generated by CRWP is higher than that from RWP. This is because the frontal area of the CRWP is larger than that of the RWP, which results in a higher longitudinal vortex intensity and results in increased pressure drop [19]. A low-pressure zone is formed behind VG in the RWP and CRWP cases [26]. The hole in VG causes in the formation of jet flow, which results in a decrease in the low-pressure zone. This is because the jet flow reduces the stagnant fluid in the area behind VG and increases the kinetic energy in this area, causing the pressure difference before and after passing VG to decrease [26].

#### **3.5 Mean spanwise Nusselt number**

The local heat transfer improvement can be identified with the mean spanwise Nusselt number, as informed by Hiravennavar [36]. The equation used by Hiravennavar is as follows:

$$\text{N\'u}\_s = \frac{\text{Bq}(H/k)}{\int\_0^B (T\_w - T\_b) dz} \tag{24}$$

**Figures 20** and **21** compare the mean spanwise Nusselt numbers in the RWP and

CRWP cases at velocities of 0.4 m/s and 2.0 m/s. The use of VG in the channel increases the Nusselt number [30]. **Figures 20** and **21** show that the mean spanwise Nusselt number in the CRWP case is higher than that in the RWP case. This is

*Average spanwise Nusselts numbers the RWP and CRWP at a velocity of 0.4 m/s.*

*Numerical Investigation of Heat Transfer and Fluid Flow Characteristics in a Rectangular…*

*Average spanwise Nusselts numbers the RWP and CRWP at a velocity of 2.0 m/s.*

**Figure 19.**

**Figure 20.**

**Figure 21.**

**71**

*Comparison of the pressure distribution at z = 0.41H.*

*DOI: http://dx.doi.org/10.5772/intechopen.96117*

where *B*, *q*, *H,* and *k* are channel width, heat flux, channel height, and fluid thermal conductivity, respectively. Meanwhile,*Tw* and *Tb* are the wall temperature and bulk fluid temperature, respectively.

**Figure 18.** *Temperature distribution in the channel without VG (baseline).*

*Numerical Investigation of Heat Transfer and Fluid Flow Characteristics in a Rectangular… DOI: http://dx.doi.org/10.5772/intechopen.96117*

#### **Figure 19.** *Comparison of the pressure distribution at z = 0.41H.*

thickening of the boundary layer as observed in **Figures 16** and **17** comparing to the baseline case, as shown in **Figure 18**. Visually, the temperature distribution in the CRWP case is more even than the temperature distribution in the RWP case. This is because CRWP produces a higher longitudinal vortex intensity than that of RWP [31]. In addition, the holes in each VG result in the formation of jet flow, which can reduce the intensity of the longitudinal vortex resulting in an increase in tempera-

**Figure 19** shows the pressure distribution for the three-pairs RWP and CRWP cases with/without holes at a Velocity of 2.0 m/s. Installation of VG in the channel results in an increase in pressure drop due to drag generated on the flow [34, 35]. As observed in Figure 3.14, the pressure drop generated by CRWP is higher than that from RWP. This is because the frontal area of the CRWP is larger than that of the RWP, which results in a higher longitudinal vortex intensity and results in increased pressure drop [19]. A low-pressure zone is formed behind VG in the RWP and CRWP cases [26]. The hole in VG causes in the formation of jet flow, which results in a decrease in the low-pressure zone. This is because the jet flow reduces the stagnant fluid in the area behind VG and increases the kinetic energy in this area, causing the pressure difference before and after passing VG to decrease [26].

The local heat transfer improvement can be identified with the mean spanwise

<sup>0</sup> ð Þ *Tw* � *Tb dz*

(24)

*Nu*´ *<sup>s</sup>* <sup>¼</sup> *Bq H*ð Þ *<sup>=</sup><sup>k</sup>* Ð *B*

where *B*, *q*, *H,* and *k* are channel width, heat flux, channel height, and fluid thermal conductivity, respectively. Meanwhile,*Tw* and *Tb* are the wall temperature

Nusselt number, as informed by Hiravennavar [36]. The equation used by

ture gradient [26], as shown in **Figure 16(b)** and **17(b)**.

*Heat Transfer - Design, Experimentation and Applications*

**3.4 Pressure distribution**

**3.5 Mean spanwise Nusselt number**

and bulk fluid temperature, respectively.

*Temperature distribution in the channel without VG (baseline).*

Hiravennavar is as follows:

**Figure 18.**

**70**

**Figure 20.** *Average spanwise Nusselts numbers the RWP and CRWP at a velocity of 0.4 m/s.*

**Figure 21.** *Average spanwise Nusselts numbers the RWP and CRWP at a velocity of 2.0 m/s.*

**Figures 20** and **21** compare the mean spanwise Nusselt numbers in the RWP and CRWP cases at velocities of 0.4 m/s and 2.0 m/s. The use of VG in the channel increases the Nusselt number [30]. **Figures 20** and **21** show that the mean spanwise Nusselt number in the CRWP case is higher than that in the RWP case. This is

#### *Heat Transfer - Design, Experimentation and Applications*

because the longitudinal vortex intensity generated by the CRWP is stronger than that of the RWP. The holes in VG result in a decrease in the mean spanwise Nusselt number because the holes in VG reduce the intensity of the longitudinal vortex [16]. The highest decrease of the average spanwise Nusselt number in perforated RWP and CRWP at a velocity of 0.4 m/s was 24% at x/L = 0.32 and 11% at x/L = 0.56 of VG without holes, respectively. Whereas for the same case at a velocity of 2.0 m/s, the highest reduction is 2% at x/L = 0.8 and 7% at x/L = 0.32, respectively.

**3.6 Convection heat transfer coefficient**

*DOI: http://dx.doi.org/10.5772/intechopen.96117*

**Figure 23.**

**73**

*(a) one; (b) two, and (c) three pairs.*

**Figures 22** and **23** show the comparison of the heat transfer coefficient values due to the installation of RWP and CRWP. In general, the convection heat transfer coefficient increases with increasing Reynolds number. From **Figures 22** and **23**, it is found that the convection heat transfer coefficient with the CRWP installation is

*Numerical Investigation of Heat Transfer and Fluid Flow Characteristics in a Rectangular…*

higher than that of the RWP. This is because CRWP produces a stronger

*Comparison of the convection heat transfer coefficient on CRWP with and without holes for installation:*

*Numerical Investigation of Heat Transfer and Fluid Flow Characteristics in a Rectangular… DOI: http://dx.doi.org/10.5772/intechopen.96117*

### **3.6 Convection heat transfer coefficient**

because the longitudinal vortex intensity generated by the CRWP is stronger than that of the RWP. The holes in VG result in a decrease in the mean spanwise Nusselt number because the holes in VG reduce the intensity of the longitudinal vortex [16]. The highest decrease of the average spanwise Nusselt number in perforated RWP and CRWP at a velocity of 0.4 m/s was 24% at x/L = 0.32 and 11% at x/L = 0.56 of VG without holes, respectively. Whereas for the same case at a velocity of 2.0 m/s,

*Comparison of the convection heat transfer coefficient on RWP with and without holes for installation: (a) one;*

the highest reduction is 2% at x/L = 0.8 and 7% at x/L = 0.32, respectively.

*Heat Transfer - Design, Experimentation and Applications*

**Figure 22.**

**72**

*(b) two, and (c) three pairs.*

**Figures 22** and **23** show the comparison of the heat transfer coefficient values due to the installation of RWP and CRWP. In general, the convection heat transfer coefficient increases with increasing Reynolds number. From **Figures 22** and **23**, it is found that the convection heat transfer coefficient with the CRWP installation is higher than that of the RWP. This is because CRWP produces a stronger

#### **Figure 23.**

*Comparison of the convection heat transfer coefficient on CRWP with and without holes for installation: (a) one; (b) two, and (c) three pairs.*

longitudinal vortex intensity than that of RWP due to the instability of the flow as it crosses the CRWP surface [25]. The convection heat transfer coefficient in the RWP and CRWP cases with a three-pair installation configuration with holes is increased by 198% and 207%, respectively, from the baseline at the highest Reynolds number. strength and interferes with the formation of boundary layers and increases fluid mixing [29]. Meanwhile, the hole in VG results in a slight decrease in the value of the convection heat transfer coefficient, as seen in **Figures 22** and **23**, because the holes in VG generate jet flow, which can weaken the intensity of the longitudinal vortex [26]. The decrease in the convection heat transfer coefficient at the highest

*Numerical Investigation of Heat Transfer and Fluid Flow Characteristics in a Rectangular…*

*DOI: http://dx.doi.org/10.5772/intechopen.96117*

*Comparison of pressure drop on CRWP with and without holes for installation: (a) one; (b) two and (c) three*

**Figure 25.**

*pairs.*

**75**

The addition of pairs of VG results in an increase in the convection heat transfer coefficient because the addition of VG pairs strengthens the longitudinal vortex

**Figure 24.** *Comparison of pressure drop on RWP with and without holes for installation: (a) one; (b) two and (c) three pairs.*

*Numerical Investigation of Heat Transfer and Fluid Flow Characteristics in a Rectangular… DOI: http://dx.doi.org/10.5772/intechopen.96117*

strength and interferes with the formation of boundary layers and increases fluid mixing [29]. Meanwhile, the hole in VG results in a slight decrease in the value of the convection heat transfer coefficient, as seen in **Figures 22** and **23**, because the holes in VG generate jet flow, which can weaken the intensity of the longitudinal vortex [26]. The decrease in the convection heat transfer coefficient at the highest

**Figure 25.** *Comparison of pressure drop on CRWP with and without holes for installation: (a) one; (b) two and (c) three pairs.*

longitudinal vortex intensity than that of RWP due to the instability of the flow as it crosses the CRWP surface [25]. The convection heat transfer coefficient in the RWP and CRWP cases with a three-pair installation configuration with holes is increased by 198% and 207%, respectively, from the baseline at the highest Reynolds number. The addition of pairs of VG results in an increase in the convection heat transfer coefficient because the addition of VG pairs strengthens the longitudinal vortex

*Heat Transfer - Design, Experimentation and Applications*

*Comparison of pressure drop on RWP with and without holes for installation: (a) one; (b) two and (c) three*

**Figure 24.**

*pairs.*

**74**

Reynolds number for the perforated RWP and CRWP cases of three pairs is 2% and 8% of the without holes, respectively.

*<sup>β</sup>* <sup>¼</sup> *cos* �<sup>1</sup> *<sup>U</sup>*´ � <sup>∇</sup>´*<sup>T</sup>*

*Numerical Investigation of Heat Transfer and Fluid Flow Characteristics in a Rectangular…*

*DOI: http://dx.doi.org/10.5772/intechopen.96117*

0

B@

**Figures 26** and **27** illustrate the local synergy angle in the RWP and CRWP cases, respectively, with speeds of 0.4 m/s and 2.0 m/s. In general, inserting VG in the channel reduces the synergy angle because VG generates a longitudinal vortex [39]. The longitudinal vortex alters the flow and temperature fields resulting in improved heat transfer. From **Figures 26** and **27**, it can be observed that the decreased synergy angle is higher in the case of CRWP than that of RWP because the strength of the longitudinal vortex produced by CRWP is stronger than that of

*Synergy angle at a speed of 0.4 m/s for the case of (a) one-pair of RWP; (b) one pair of CRWPs; (c) two pairs*

*of RWP; (d) two-pairs of CRWP; (e) three pairs of RWP; (f) three-pairs of CRWP.*

**Figure 26.**

**77**

*U*´ � � � � � � ∇´*T* � � � �

1

CA (28)

#### **3.7 Pressure drop**

A comparison of pressure drop between experiment and simulation for the RWP and CRWP cases is observed in **Figures 24** and **25**, respectively. From the two figures, it is found that the pressure drop for all cases increases with increasing Reynolds number. The main reason is the increase in the drag generated with increasing flow velocity [14]. Installation of RWP and CRWP in the channel results in an increase in pressure drop due to the drag formed on the flow. The pressure drop due to CRWP insertion is higher than RWP because CRWP produces a stronger longitudinal vortex than RWP [37]. For the perforated RWP case, the increase in pressure drop with variations of one, two, and three pairs at the highest Reynolds number is 4.26 times, 8.98 times, and 9.96 times, respectively, from the baseline. Meanwhile, for the perforated CRWP case with the highest Reynolds number in the same case, it is 12.52 times, 19.27 times, and 26.31 times from the baseline. The hole in VG causes a decrease in the pressure drop value because the hole in VG reduces fluid resistance due to the longitudinal vortex [31]. The highest reduction in pressure drop due to the hole in the RWP with variations of one, two, and three pairs is 7%, 4%, and 13%, respectively. On the other hand, the decrease in pressure drop on CRWP with the highest Reynolds number for the same case is 5%, 5%, and 11%, respectively.

#### **3.8 Field synergy principle (FSP)**

FSP is a method for analyzing improvement in heat transfer rate, which was informed by Guo et al. [38]. In their study, Guo et al. define the increase in the rate of heat transfer by decreasing the angle of the intersection of the velocity vector and the temperature gradient. The energy conservation equation used by Guo et al. in their research are as follows:

$$
\rho \mathbf{C}\_p \int\_0^{\delta\_t} \left( U \cdot \dot{\nabla} T \right) d\mathbf{y} = -\lambda \frac{\partial T}{\partial \mathbf{y}} \tag{25}
$$

where *ρ*, *Cp*, and *λ* are assumed to be constant so that the dimensionless form of Eq. (25) is

$$\Re\_{\mathbf{x}} Pr \int\_{0}^{1} \left( \dot{U} \cdot \dot{\nabla} T \right) d\mathbf{y} = \mathbf{N} u\_{\mathbf{x}} \tag{26}$$

where *<sup>U</sup>*´ <sup>¼</sup> *<sup>U</sup>=U*∞, <sup>∇</sup>´ *<sup>T</sup>*� <sup>¼</sup> <sup>∇</sup>´*<sup>T</sup>* ð Þ *T*∞�*Tw =δ<sup>t</sup>* , *y* ¼ *y=δt*. *U*<sup>∞</sup> and *T*<sup>∞</sup> are the velocity and temperature of the fluid in the free stream region, respectively. Meanwhile, *δ<sup>t</sup>* is the thickness of the thermal boundary layer. Vector dot product, *<sup>U</sup>*´ � <sup>∇</sup>´ *<sup>T</sup>*, in Eq. (26) can be described as follows:

$$
\acute{\dot{U}} \cdot \acute{\nabla} T = \begin{vmatrix} \acute{U} \\ \acute{U} \end{vmatrix} | \acute{\nabla} T | \cos \beta \end{vmatrix} \tag{27}
$$

where *β* is the angle between the velocity vector and the temperature gradient. Thus, Eq. (27) can be written as follows:

*Numerical Investigation of Heat Transfer and Fluid Flow Characteristics in a Rectangular… DOI: http://dx.doi.org/10.5772/intechopen.96117*

$$\beta = \cos^{-1}\left(\frac{\acute{U} \cdot \acute{\forall} T}{|\acute{U}||\acute{\forall} T|}\right) \tag{28}$$

**Figures 26** and **27** illustrate the local synergy angle in the RWP and CRWP cases, respectively, with speeds of 0.4 m/s and 2.0 m/s. In general, inserting VG in the channel reduces the synergy angle because VG generates a longitudinal vortex [39]. The longitudinal vortex alters the flow and temperature fields resulting in improved heat transfer. From **Figures 26** and **27**, it can be observed that the decreased synergy angle is higher in the case of CRWP than that of RWP because the strength of the longitudinal vortex produced by CRWP is stronger than that of

**Figure 26.** *Synergy angle at a speed of 0.4 m/s for the case of (a) one-pair of RWP; (b) one pair of CRWPs; (c) two pairs of RWP; (d) two-pairs of CRWP; (e) three pairs of RWP; (f) three-pairs of CRWP.*

Reynolds number for the perforated RWP and CRWP cases of three pairs is 2% and

A comparison of pressure drop between experiment and simulation for the RWP

and CRWP cases is observed in **Figures 24** and **25**, respectively. From the two figures, it is found that the pressure drop for all cases increases with increasing Reynolds number. The main reason is the increase in the drag generated with increasing flow velocity [14]. Installation of RWP and CRWP in the channel results in an increase in pressure drop due to the drag formed on the flow. The pressure drop due to CRWP insertion is higher than RWP because CRWP produces a stronger longitudinal vortex than RWP [37]. For the perforated RWP case, the increase in pressure drop with variations of one, two, and three pairs at the highest Reynolds number is 4.26 times, 8.98 times, and 9.96 times, respectively, from the baseline. Meanwhile, for the perforated CRWP case with the highest Reynolds number in the same case, it is 12.52 times, 19.27 times, and 26.31 times from the baseline. The hole in VG causes a decrease in the pressure drop value because the hole in VG reduces fluid resistance due to the longitudinal vortex [31]. The highest reduction in pressure drop due to the hole in the RWP with variations of one, two, and three pairs is 7%, 4%, and 13%, respectively. On the other hand, the decrease in pressure drop on CRWP with the highest Reynolds number for the same case is 5%, 5%, and 11%,

FSP is a method for analyzing improvement in heat transfer rate, which was informed by Guo et al. [38]. In their study, Guo et al. define the increase in the rate of heat transfer by decreasing the angle of the intersection of the velocity vector and the temperature gradient. The energy conservation equation used by Guo et al. in

> *<sup>U</sup>* � <sup>∇</sup>´ *<sup>T</sup>* � �

where *ρ*, *Cp*, and *λ* are assumed to be constant so that the dimensionless form of

*<sup>U</sup>*´ � <sup>∇</sup>´ *<sup>T</sup>* � �

temperature of the fluid in the free stream region, respectively. Meanwhile, *δ<sup>t</sup>* is the thickness of the thermal boundary layer. Vector dot product, *<sup>U</sup>*´ � <sup>∇</sup>´ *<sup>T</sup>*, in Eq. (26) can

where *β* is the angle between the velocity vector and the temperature gradient.

*dy* ¼ �*λ*

*∂T ∂y*

*dy* ¼ *Nux* (26)

�*cosβ* (27)

, *y* ¼ *y=δt*. *U*<sup>∞</sup> and *T*<sup>∞</sup> are the velocity and

(25)

*ρCp* ð*δt* 0

R*xPr* ð1 0

ð Þ *T*∞�*Tw =δ<sup>t</sup>*

*<sup>U</sup>*´ � <sup>∇</sup>´ *<sup>T</sup>* <sup>¼</sup> *<sup>U</sup>*´ � � � � � � ∇´ *T* � � �

8% of the without holes, respectively.

*Heat Transfer - Design, Experimentation and Applications*

**3.7 Pressure drop**

respectively.

Eq. (25) is

**76**

**3.8 Field synergy principle (FSP)**

their research are as follows:

where *<sup>U</sup>*´ <sup>¼</sup> *<sup>U</sup>=U*∞, <sup>∇</sup>´ *<sup>T</sup>*� <sup>¼</sup> <sup>∇</sup>´*<sup>T</sup>*

Thus, Eq. (27) can be written as follows:

be described as follows:

RWP [25, 40]. The lowest synergy angle in the case of three pairs of perforated RWP at a velocity of 0.4 m/s are 78.25°, 77.98°, and 79.33° at x/L = 0.28, 0.52, and 0.76, respectively. Meanwhile, at velocity of 2.0 m/s, they are 81.15°, 79.42°, and 81.19° at x/L = 0.28, 0.52, and 0.76, respectively.

**4. Conclusion**

*DOI: http://dx.doi.org/10.5772/intechopen.96117*

In this study, a numerical fluid flow simulation was performed to determine the effect of installing RWP and CRWP with/without holes at 45° angle of attack on heat transfer and pressure drop in the rectangular channel. The hole in VG results in a slight decrease in the convection heat transfer coefficient. The reduction of the convection heat transfer coefficient in the channel with the installation of three pairs of perforated RWP and CRWP for the highest Reynolds number was 2% and 8% of the without holes, respectively. The hole in the VG was able to reduce the pressure drop in the channel. The highest reduction in pressure drop due to holes in RWP with variations of one, two, and three pairs was 7%, 4%, and 13%, respectively. On the other hand, the decrease in pressure drop on CRWP with the highest Reynold number for the same case was 5%, 5%, and 11%, respectively. The hole in VG caused a decrease in the mean spanwise Nusselt number in all cases. The decrease in the average spanwise Nusselt number in the perforated RWP and CRWP cases at a velocity of 0.4 m/s was the greatest of 24% at x/L = 0.32 and 11% at x/L = 0.56, respectively, from those without holes. Whereas for the same case at a velocity of 2.0 m/s, the largest decrease was 2% at x/L = 0.8 and 7% at x/L = 0.32, respectively. The synergy angle increased due to the holes in the RWP and CRWP. The average synergy angle increase in the use of RWP and CRWP three pairs was

*Numerical Investigation of Heat Transfer and Fluid Flow Characteristics in a Rectangular…*

This work was supported by the Fundamental Research of Minitry of Education

and Culture, Indonesia, with contract number: 225-110/UN7.6.1/PP/2020. The authors are grateful to all research members, especially Lab. Thermofluid of

Mechanical Engineering Department of Diponegoro University, Semarang,

© 2021 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

\*Address all correspondence to: syaiful.undip2011@gmail.com

Mechanical Engineering of Diponegoro University, Indonesia.

0.25 and 0.29 at a velocity of 2.0 m/s, respectively.

**Acknowledgements**

**Author details**

Indonesia

**79**

Syaiful\* and M. Kurnia Lutfi

provided the original work is properly cited.

In the case of CRWP with the same configuration, the largest synergy angles are 71.64°, 77.52°, and 79.04° at x/L = 0.24, 0.52, and 0.76 at 0.4 m/s, respectively. Meanwhile, at velocity of 2.0 m/s, they were 72.68o, 78.81o, and 81.57o at x/L = 0.28, 0.52, and 0.8, respectively. The hole in VG increases the synergy angle due to a decrease in the heat transfer coefficient [41]. The increase in the mean synergy angle due to the addition of holes in the RWP and CRWP three pairs is 0.25° and 0.29° at a velocity of 2.0 m/s, respectively.

**Figure 27.** *Synergy angle at a speed of 2.0 m/s for the case of (a) one-pair of RWP; (b) one pair of CRWPs; (c) two pairs of RWP; (d) two-pairs of CRWP; (e) three pairs of RWP; (f) three-pairs of CRWP.*

*Numerical Investigation of Heat Transfer and Fluid Flow Characteristics in a Rectangular… DOI: http://dx.doi.org/10.5772/intechopen.96117*
