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Numerical study of flow and heat transfer in the channel of panel-type radiator with semi-detached inclined trapezoidal wing vortex generators

  • Wenrong Si , Chenzhao Fu , Yue Tian , Jie Chen , Peng Yuan , Zexuan Huang and Jian Yang EMAIL logo
Published/Copyright: January 19, 2024
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Open Physics
From the journal Open Physics Volume 22 Issue 1

Abstract

To improve heat dissipation performance of panel-type radiator for transformer, this study investigated the flow and heat transfer characteristics of semi-detached inclined trapezoidal wing vortex generator (SDITW) in a closed channel on the air-side of the radiator. The SDITW was compared with the inclined delta wing (IDW) and inclined trapezoidal wing (ITW) channels. The effects of SDITW relative separation height (e 1/e 2), longitudinal pitch (p l), blockage ratio (e/(0.5H)), and inclination angle (α) were analyzed. First, compared with the IDW and ITW channels, the SDITW channel generates stable corner vortices and produces weaker transverse vortices and lower flow resistance due to the semi-detached structure of the wing. For Re = 5,125–15,375, the overall heat transfer performance (performance evaluation criteria; PEC) of the SDITW channel increases by 0.5–8.9 and 1.7–4.9% as compared with IDW and ITW channels, respectively. Furthermore, for the same e/(0.5H) and α, both the Nusselt number ratio and friction factor ratio of SDITW channel increase as e 1/e 2 and p l decrease. For p l = 70 mm, the SDITW channel exhibits a relatively better overall heat transfer performance. For the same e 1/e 2 and p l, the PEC of SDITW channel is maximum and the overall heat transfer performance is best when e/(0.5H) = 0.3 at Re = 10,250 and α = 30°–60°.

Keywords: panel-type radiator; longitudinal vortex generator; heat transfer enhancement; numerical simulation

Nomenclature

A f

heat transfer area (m2)

C p

specific heat (J/(kg K))

D h

hydraulic diameter (m)

e

vortex generator height (m)

e 1

vertical distance between trapezoidal wing trailing edge and vertical rib (m)

e 2

vertical distance between trapezoidal wing leading edge and vertical rib (m)

f

friction factor

h

convective heat transfer coefficient (W/(m2·K))

H

panel spacing (m)

k

turbulent kinetic energy (m2/s2)

L

panel length (m)

L 1

length of entrance section (m)

L 2

length of outlet section (m)

m

mass flow rate (kg/s)

Nu

Nusselt number

p

pressure (Pa)

p l

longitudinal pitch of vortex generator (m)

Pr

Prandtl number

Re

Reynolds number

T

temperature (K)

u,v,w

velocity components (m/s)

u m

average inlet velocity (m/s)

W

panel width (m)

Greek letters

α

inclination angle of vortex generator (°)

δ

vortex generator thickness (m)

λ

thermal conductivity (W/(m·K))

λ ci

swirling strength (s−1)

μ

kinetic viscosity (Pa s)

ρ

density (kg/m3)

ω

specific dissipation rate (s−1)

Abbreviations

IDW

inclined delta wing

ITW

inclined trapezoidal wing

PEC

performance evaluation criteria

SDITW

semi-detached inclined trapezoidal wing

TEF

thermal enhancement factor

Subscripts

avg

average

in

inlet

out

outlet

t

turbulent

w

wall

0

smooth channel

1 Introduction

Oil-immersed transformers are essential devices for the power system, as they enable efficient transmission, flexible distribution, and safe utilization of electrical energy. To ensure their reliable operation, the heat generated by the internal windings and core must be dissipated promptly to avoid overheating damage. Panel-type radiators are widely used for cooling oil-immersed transformers. Increasing the air velocity between the panels with fans is a typical way to augment heat dissipation. However, when the heat dissipation demand of the transformer is higher, other heat transfer enhancement techniques are also required. Vortex generators are widely used as a passive heat transfer enhancement technique, which usually consist of metal plates attached to the pipe or fin surface at a certain angle of attack concerning the main flow direction. They induce secondary flows (mainly longitudinal vortices) that disrupt or delay the boundary layer development along the wall, enhancing the mixing of hot and cold fluids and thus improving the heat transfer [1].

The flow and heat transfer characteristics in the channel with vortex generators and the effects of their structures have been investigated by many studies. For example, Tiggelbeck et al. [2] compared the performance of different types of vortex generators, such as delta wing, rectangular wing, delta winglet pairs, and rectangular winglet pairs. They found that the winglets achieved higher heat transfer than the wing vortex generators but at the expense of higher flow resistance. Fiebig et al. [3] reported that the delta wing was the most effective vortex generator in terms of heat transfer enhancement per unit area, followed by delta winglet pairs, while rectangular wing and winglets were less effective. To reduce the pressure drop caused by the vortex generators, some methods such as using holes or curves on the vortex generators or cutting the wing edges are often employed. Skullong et al. [4] conducted experimental and numerical studies on the flow and heat transfer performances of perforated rectangular and trapezoidal winglet vortex generators. They found that the perforated jet reduced the vortex intensity and the heat transfer performance, but it also decreased the flow resistance considerably. Hence, the overall heat transfer performance of the perforated winglets was higher than that of the non-perforated winglets. Promvonge and Skullong [5] performed an experimental investigation on heat transfer ducts equipped with perforated winglets.

They showed that the perforated delta winglets enhanced the overall heat transfer performance by 7% over the non-perforated delta winglets. Zhou and Ye [6] introduced a curved trapezoidal winglet vortex generator and tested its flow and heat transfer performances in different flow regimes, which were compared with the conventional rectangular winglet, trapezoidal winglet, and delta winglets. The comparison showed that the delta winglet had the highest overall heat transfer performance in the laminar and transition flow regimes, while the curved trapezoidal winglet had the highest overall heat transfer performance in the turbulent flow regime. Lu and Zhou [7] numerically investigated the flow and heat transfer for a variety of plane and curved vortex generators. They compared the performance of triangular, rectangular, and trapezoidal winglet vortex generators. The results indicated that plane vortex generators had not only higher heat transfer performance but also higher pressure losses. Among the vortex generators, the curved trapezoidal winglets showed the best overall thermal performance. Min et al. [8] improved the rectangular winglet by cutting the edges and experimentally investigated its flow and heat transfer performances in a rectangular channel. The results showed that the flow and heat transfer performances of the improved rectangular winglet were better than those of the conventional rectangular winglet. Moreover, the down-sweep of the longitudinal vortices enhanced the heat transfer, i.e., the distance from the main vortex core of the improved rectangular winglet channel to the heated wall was slightly smaller than that of the conventional rectangular winglet. Dogan and Erzincan [9] experimentally investigated the thermal performance of a novel vortex generator and analyzed the effect of transverse pitch ratio and longitudinal pitch ratio of the vortex generator. The results showed that the maximum thermal enhancement factor (TEF) of the vortex row was 1.59 at the transverse pitch ratio of 0.16 and the longitudinal pitch ratio of 1.5. Demirağ et al. [10] experimentally and numerically investigated the heat transfer enhancement and the Darcy friction factor characteristics of a novel-type conical vortex generator in solar air heater and analyzed the effect of various geometrical parameters on the TEF. The TEF is up to 1.316 at optimum geometric conditions. Although many new vortex generators have been designed in the literature, there are still shortcomings in revealing the flow and heat transfer enhancement mechanisms of the new structures, and the analysis of the vortex distribution behind the vortex generator, which plays a crucial role in the flow and heat transfer performance in the channel, is still unclear in most of the available literature.

Vortex generators are widely used in channel heat exchangers such as solar air heaters and fin-tube heat exchangers [11,12,13,14,15]. For example, Promvonge et al. [12] conducted an experimental study on the thermal behavior in heat exchanger channels with rib-groove devices on the surface, comparing rib/baffle-groove channels with different rib heights and rib pitches, and the results showed that the baffle-groove yields the highest combined heat transfer performance around 2.14 or about 13% higher than the rib-groove, compared with the thin rib (called “baffle”). Skullong et al. [13] experimentally investigated the flow and heat transfer performances of a combined wavy groove-perforated delta wing vortex generator in a solar air heater channel. They found that the overall heat transfer performance of the combined wavy groove-perforated delta wing vortex generator was 12.4 and 45.5% higher than that of the combined wavy groove-delta wing and single wavy groove at different Reynolds numbers. Promvonge et al. [14] performed experimental and numerical investigations on the flow and heat transfer characteristics of the combined trapezoidal louvered winglets-wavy groove vortex generator in a solar air heater channel. The louver structure was created by punching square holes at the mass center of the trapezoidal winglet and then bending it over. They found that the overall heat transfer performance of the combined trapezoidal louvered winglets-wavy groove vortex generator was 6.3 and 114% higher than that of the combined trapezoidal winglets-wavy groove and single wavy groove at different Reynolds numbers. Hu et al. [15] numerically investigated the effect of staggered concave curved vortex generators on the thermal performance in a wavy finned-tube heat exchanger. The results showed that the Nusselt number and thermal performance factor of the wavy channel with concave curved vortex generator increased by 30.4 and 25.9%, respectively, compared with that of the wavy smooth channel. The application of vortex generators in closed channels for heat transfer augmentation is well-studied in the literature, while the air-side heat dissipation channel of the panel-type radiator for transformers is typically an open channel. The effect of vortex generators on the air-side heat dissipation augmentation of the panel-type radiator has received relatively less attention. Min et al. [16] numerically investigated the heat transfer performance of a panel-type radiator with rectangular winglet vortex generators in the air-side channel. They reported that the heat transfer coefficients of the radiator with different sizes of rectangular winglet vortex generators increased by 23.6–32.0% under natural convection conditions. However, they neglected the effect of the air intake at the side of the radiator. Garelli et al. [17] numerically investigated the heat transfer performance of a panel-type radiator with delta wing vortex generators in the air-side channel. The vortex generator was placed at a certain height above the panel surface. The results showed that the heat transfer of the radiator improved by 12% under natural convection conditions. They also observed that the air intake at the side of the radiator influenced the longitudinal vortex formation behind the vortex generator, which also affected its heat transfer performance. These studies have demonstrated that the natural convection heat dissipation of the panel-type radiator can be significantly improved by arranging vortex generators in the air-side channel. However, the forced convection heat transfer in the air-side vortex generator channel of the panel-type radiator was still not reported in the literatures.

Based on the above analysis, this study intends to investigate the forced convection heat transfer in the air-side vortex generator channel of the panel-type radiator for the transformer with numerical method. To eliminate the adverse effect of the air intake from the side of the radiator, the baffle plates on both sides of the panel-type radiator are added to form a closed air flow channel. Improvement of trapezoidal wing in literature review has a greater potential to improve the heat transfer performance of the channel, while the delta wing has a simple structure and is more studied and applied. In the present study, the traditional inclined trapezoidal wing (ITW) is structurally improved and the semi-detached inclined trapezoidal wing vortex generators (SDITW) were designed and arranged on the surface of the radiator. The SDITW is obtained by cutting the trailing edge of the ITW, which can separate the ITW from the radiator surface and enhance the heat transfer in the channel while reducing the flow resistance. First, the flow and heat transfer characteristics of SDITW in closed channels at the air-side of the panel radiator were investigated and the performance of SDITW was compared with that in the inclined delta wing (IDW) and ITW channels with the same geometrical configuration. Second, the effects of SDITW relative separation height (e 1/e 2), longitudinal spacing (p l), blockage ratio (e/(0.5H)), and inclination angle (α) on the flow and heat transfer in SDITW channels were analyzed in detail. This study can act as an important reference for the heat transfer enhancement on the air-side of the panel-type radiator used for transformers and structure design of corresponding vortex generator.

2 Physical model and computational methods

2.1 Physical model

A simplified physical model is developed to investigate the heat transfer performance of the panel-type radiator, based on the models reported in previous studies [16,17]. Figure 1 shows the panel-type radiator model, where Figure 1(a) presents the vertical closed channels formed by baffles on both sides of the radiator. The baffles avoid side air intake, which affects the formation of longitudinal vortices in the edge region [z17]. Figure 1(b) shows the radiator unit extracted from the panel-type radiator. Considering the symmetry of the geometry and physical model, a quarter of the air channel of the radiator unit is simplified as the computational domain, as shown in Figure 1(c). The physical model simplifies the air passage as a rectangular duct, neglecting the trapezoidal oil channel structure on the panel surface [16]. This simplification is also adopted in other studies [18,19]. In the physical model, the surfaces at y = 0 and z = H/2 are symmetrical. The bottom surface of the channel is isothermal, and the side wall is no-slip and adiabatic wall. The dimensions of the flow channel are as follows: the spacing between panels is H = 45 mm, the width of the panel is W = 450 mm, the length is L = 1,524 mm, and the hydraulic diameter is 81.82 mm. The flow channel dimensions are consistent with the panel dimensions, detailed dimensions can be found in the study by Garelli et al. [17]. Since most of the area in the flow channel is fully developed, the entry and exit sections are set according to the ASHARE standard to eliminate inlet and outlet effects [20]. The length of the inlet section L 1 should be larger than 5 WH and the length of the outlet section should be larger than 2.5 WH . Therefore, L 1 is set as 800 mm and L 2 is set as 500 mm.

Figure 1 Panel-type radiator and simplified physical model of air channel between panels. (a) Panel-type radiator. (b) Radiator unit. (c) Computational domain.
Figure 1

Panel-type radiator and simplified physical model of air channel between panels. (a) Panel-type radiator. (b) Radiator unit. (c) Computational domain.

In this study, the SDITW vortex generators are attached to the panel surface to enhance the convective heat transfer of the air-side in the panel-type radiator. Figure 2 shows the arrangement and geometric structure of the SDITWs. The SDITWs are uniformly arranged along the x-direction with p l as the longitudinal pitch, and the first and last rows of vortex generators are 62 mm away from the edge of the channel. With the trapezoidal oil channel structure of ref. [16], the SDITWs are mounted along the y-direction corresponding to the locations of the oil channel bumps.

Figure 2 Geometry and arrangement of SDITWs. (a) Top view. (b) Side view. (c) SDITW.
Figure 2

Geometry and arrangement of SDITWs. (a) Top view. (b) Side view. (c) SDITW.

The SDITW is composed of an ITW, a vertical rib, and a connecting rib. The ITW deflects the fluid to scour the heated wall and generates longitudinal vortices. The vertical rib and connecting rib can enhance the disturbance and fix the SDITW on the heated wall narrow oil channel bump. According to the delta wing vortex generator design in the study by Bekele et al. [21] and actual panel structural features [16], the dimension parameters of SDITW is designed. The geometrical parameters of the SDITW are as follows: the vertical rib height is 1 mm, the width is 4 mm, the leading edge width of the ITW is 4 mm, the vertical distance between the trailing edge and vertical rib is e 1, the vertical distance between the leading edge and vertical rib is e 2, the total height of the SDITW is e, and its thickness δ is 0.3 mm.

To analyze the flow and heat transfer characteristics of the SDITW, four main geometric parameters are selected for parametric analysis, namely, the relative separation height (e 1/e 2), the longitudinal pitch (p l), the inclination angle (α), and the blockage ratio (e/(0.5H)). These parameters are listed in Table 1.

Table 1

Geometric parameters of SDITW

Parameters Values
e 1/e 2 0, 0.25, 0.5, and 0.75
p l (mm) 40, 50, 70, 100, and 140
α/(°) 20, 30, 40, 50, and 60
e/(0.5H) 0.15, 0.3, 0.45, and 0.6

2.2 Governing equations and computational methods

The working fluid in this study is air. Due to small variation in air temperature, the air properties are assumed to be constant and 303.15 K is set as the qualitative temperature. Radiation and natural convection of air are neglected. The flow and heat transfer processes are described by the mass, momentum, and energy equations [22] as follows:

(1) ∂ ρ u i ∂ x i = 0 ,

(2) ∂ ∂ x j ( ρ u i u j ) = − ∂ p ∂ x i + ∂ ∂ x j ( μ + μ t ) ∂ u i ∂ x j + ∂ u j ∂ x i ,

(3) ∂ ∂ x j ( ρ u j c p T ) = ∂ ∂ x j λ + μ t c p Pr t ∂ T ∂ x j ,

where u i is the velocity component in the i-direction. ρ, μ, λ, and c p are the density, kinetic viscosity, thermal conductivity, and specific heat capacity of the fluid, respectively. The turbulent Prandtl number is Prt = 0.85, and the turbulent viscosity μ t is calculated by the turbulence model.

The SST k–ω turbulence model is adopted in this study, which combines the advantages of both the k–ω and k–ε models. The k–ω model is applied in the boundary layer, while the k–ε model is applied in the turbulent region away from the wall, which avoids the sensitivity of the k–ω model to the inlet free-stream turbulence properties. The turbulence model has high accuracy and reliability in adverse pressure gradient and separated flow conditions. Moreover, the SST k–ω model has also been used by several researchers for the curvature flow similar to this study, and showed good agreement with the experimental results [23,24,25].

The SST k–ω model transport equations are as follows:

(4) ∂ ∂ x j ( ρ k u j ) = ∂ ∂ x j Γ k ∂ k ∂ x i + G k − Y k ,

(5) ∂ ∂ x j ( ρ ω u j ) = ∂ ∂ x j Γ ω ∂ ω ∂ x i + G ω − Y ω .

For a detailed discussion of the model, please refer to the study by Menter [26].

The governing equations are solved based on the finite volume method using the CFD commercial software Ansys Fluent. The pressure-velocity coupling is performed by the SIMPLE algorithm, and the second-order upwind scheme is applied for the convective terms in the momentum, energy, turbulent kinetic energy, and specific dissipation rate equations to ensure the computational accuracy. The convergence criteria for the continuity and momentum equations are set to 10−4, and the convergence criteria for the energy equation is set to 10−8. A uniform velocity profile and a uniform temperature of 303.15 K are given at the inlet. The pressure outlet boundary condition is used at the outlet. A symmetry boundary condition is applied on the plane of y = 0 and z = H/2. The heated wall temperature in the test section is assumed to be 340 K, which are similar to those in the study by Garelli et al. [17]. No-slip wall conditions are applied on the channel walls.

In this study, some of the parameters are defined as follows:

Hydraulic diameter:

(6) D h = 2 W H W + H .

Reynolds number [27]:

(7) Re = ρ u m D h μ ,

where u m is the average inlet velocity.

Darcy friction factor [27]:

(8) f = Δ p ( 0.5 ρ u m 2 ) ( L / D h ) ,

where Δp and L are the pressure drop and channel length of the test section, respectively.

Nusselt number [27]:

(9) Nu = h D h λ ,

where the convective heat transfer coefficient h of the heated wall is defined as follows:

(10) h = m C p ( T out − T in ) A f ( T w − T avg ) ,

(11) T avg = T in + T out 2 ,

where m is the inlet mass flow rate, T in and T out are the average inlet and outlet temperatures, respectively, and A f is the heat transfer area.

The performance evaluation criterion (PEC) [27] is defined as the ratio of Nusselt number of the enhanced heat transfer channel (Nu) to Nusselt number of the smooth channel (Nu0) at equal pumping power and is expressed as follows:

(12) PEC = Nu / Nu 0 ( f / f 0 ) 1 / 3 ,

where Nu0 and f 0 represent the average Nusselt number and friction factor for the smooth channel, respectively. It can be seen that PEC is a comprehensive evaluation index of heat transfer enhancement effect and pumping power loss cost. When PEC is greater than 1, the positive benefit of heat transfer enhancement can be achieved, indicating that the heat transfer enhancement effect is greater than the cost of pumping power loss.

3 Grid independence test and model validations

3.1 Grid independence test

To ensure the accuracy of the numerical simulation, the computational mesh is first examined for grid independence. A 3D hybrid mesh consisting of hexahedral and polyhedral cells is generated using Fluent Meshing software. And the mesh near the wall is refined to capture the flow and heat transfer phenomena within the boundary layer, as shown in Figure 3. In this study, the SDITW vortex generator with an inclination angle (α) of 30°, a relative separation height (e 1/e 2) of 0.5, a blockage ratio (e/(0.5H)) of 0.3, and a longitudinal pitch (p l) of 70 mm are selected. Six sets of computational grids are generated, and the Nu and f values under different grids are listed in Table 2. When the grid number increases from 6,238,234 (Case 4) to 9,128,832 (Case 5), the relative deviations of Nu and f are 0.06 and 0.64%, respectively. It indicates that the calculation results under this grid (Case 4) setting are grid independent. Therefore, the grid setting of Case 4 is adopted in this study.

Figure 3 Computational grid.
Figure 3

Computational grid.

Table 2

Variations in Nu and f with different computational grids (Re = 5,125)

Case Grid number Nu f
1 1,664,183 73.63 0.1111
2 2,693,174 77.57 0.1169
3 3,755,845 79.96 0.1242
4 6,238,234 81.40 0.1251
5 9,128,832 81.35 0.1259
6 16,734,914 82.19 0.1268

3.2 Model validations

To verify the accuracy of the numerical model and computational method, the simulation results are compared with the empirical correlation formula and experimental results. Figure 4(a) shows the comparison between the present results in the smooth channel and the predicted results from the empirical correlations (13) and (14) as reported by Incropera et al. [28]. The two results agree well with each other, and the average deviations of Nu and f are 1.8 and 5.1%, respectively. It indicates that the numerical model used in this study can accurately simulate the flow and heat transfer process in the smooth channel. Figure 4(b) compares the simulation results with the experimental results of the study by Skullong et al. [13] for the case with delta wing vortex generators. Due to the similarities between the delta wing vortex generator and SDITW, the experimental results of the study by Skullong et al. [13] can be used to further validate the accuracy of the numerical model proposed in this study. As shown in Figure 4(b), the two results agree well with each other, and the average deviations of Nu and f are 5.1 and 6.2%, respectively. It indicates that the numerical model can capture the effect of the delta wing vortex generator on the flow and heat transfer. Therefore, the numerical model and computational method used in this study are reliable, which can be used for the subsequent analysis of flow and heat transfer characteristics of SDITW channel.

(13) Nu = 0.023 Re 0.8 Pr 0.4 ,

(14) f = 0.316 Re − 0.25 .

Figure 4 Model validation for Nu and f. (a) smooth channel. (b) Delta wing vortex generator channel.
Figure 4

Model validation for Nu and f. (a) smooth channel. (b) Delta wing vortex generator channel.

4 Results and discussion

In this study, the flow and heat transfer characteristics of the SDITW vortex generator in a closed channel on the air-side of the panel-type radiator are numerically investigated. The flow characteristics and heat transfer enhancement mechanism of the SDITW were revealed by comparing with the IDW and the ITW with the same geometric configuration. The effects of relative separation heights (e 1/e 2), longitudinal pitch (p l), blockage ratio (e/(0.5H)), and inclination angle (α) on the flow and heat transfer for the SDITW channel were analyzed in detail.

4.1 Comparison of flow and heat transfer performances in different vortex generator channels

Three kinds of vortex generators with the same geometric configuration are selected for comparison and analysis. The relative separation height (e 1/e 2), longitudinal pitch (p l), blockage ratio (e/(0.5H)), and inclination angle (α) are fixed at 0.5, 70 mm, 0.3, and 50°, respectively. The flow and heat transfer characteristics in the channel of the SDITW vortex generator are compared with those of the traditional IDW and the ITW. Figure 5 shows the specific geometric structures of three vortex generators, which have the same height and pitch angle. The bottom edges of the IDW and ITW are equal in width, and the SDITW is obtained by cutting the trailing edge of the ITW.

Figure 5 Front view of different vortex generators.
Figure 5

Front view of different vortex generators.

Figure 6 shows the streamline and the vortex intensity distributions at different yz planes between two adjacent vortex generators at the center of the channel for Re = 5,125. The vortex intensity is quantified by the swirling strength λ ci, which is the imaginary part of the eigenvalue of the velocity gradient tensor. The swirling strength λ ci can visualize the vortex and identify its core and size. The detailed definition and description of the swirling strength λ ci can be found in the study by Zhou et al. [29]. The streamline distribution in Figure 6 shows that three vortex structures are generated behind the vortex generator, including the main vortex, corner vortex, and induced vortex. The main vortex is located in the central region of the channel, which promotes the mixing of hot and cold fluid. The corner vortex is located in the near-wall region, which enhances the wall convection heat transfer, and the induced vortex is induced by the primary vortex, which is distributed in the edge near-wall region. The IDW and ITW form the corner vortex at x = 767 mm and x = 769.5 mm, respectively, and then the corner vortex disappears rapidly, while the SDITW forms the corner vortex at x = 764.5 mm and it can maintain at a certain distance. The vortex intensity distribution indicates the location and intensity of the vortex. Generally, the vortex intensity in the near-wall region is higher than that in the central region, and the vortex intensity decreases gradually with the increase in the flow distance. The vortex intensity distribution of SDITW also shows that the corner vortex in the near-wall region spreads to both sides as the flow distance increases. Among the three vortex generators, the ITW shows the widest influence range of vortex spreading and the SDITW shows the narrowest influence range, which is related to the transverse span of the vortex generator. The average vortex intensity λ ci,ave of the three vortex generator channels shows different trends along the flow direction. At the initial position (x = 764.5 mm), the ITW channel has the highest λ ci,ave, followed by the IDW channel and the SDITW channel. However, as the flow moves downstream, λ ci,ave of the IDW channel and the ITW channel decreases sharply, while that of the SDITW channel changes slightly. In the range of x = 764.5 mm to x = 797 mm, λ ci,ave of the IDW, ITW, and SDITW channel reduces by 73.5, 70.93, and 53.74%, respectively. This indicates that the SDITW channel can preserve better flow mixing capability than the other two channels. Moreover, the SDITW channel has the largest local vortex intensity, followed by the ITW channel, and the IDW channel has the smallest local vortex intensity. Larger local vortex intensity means better heat transfer performance, which means the SDITW channel may have the best heat transfer performance among the three vortex generators.

Figure 6 (a) Velocity streamlines and vortex intensity distributions in different yz planes between adjacent vortex generators in the middle of the channel and (b) detailed view of the velocity streamlines and vortex intensity distributions in the yz plane at x = 764.5 mm in the SDITW channel (Re = 5,125).
Figure 6

(a) Velocity streamlines and vortex intensity distributions in different yz planes between adjacent vortex generators in the middle of the channel and (b) detailed view of the velocity streamlines and vortex intensity distributions in the yz plane at x = 764.5 mm in the SDITW channel (Re = 5,125).

To visualize the longitudinal vortex structure for the SDITW channel and compare it with the IDW and ITW channels, the Q criterion vortex identification method is used for analysis. The Q criterion is defined as follows [30]:

(15) Q = − 1 2 ∂ u ∂ x 2 + ∂ v ∂ y 2 + ∂ w ∂ z 2 − ∂ u ∂ y ∂ v ∂ x + ∂ u ∂ z ∂ w ∂ x + ∂ v ∂ z ∂ w ∂ y .

Figure 7 shows the Q criterion distribution in the channel of different vortex generators. Regions with Q values greater than 1 indicate the presence of longitudinal vortices in the flow field. As shown in Figure 7(a)–(c), longitudinal vortices are generated behind all three types of vortex generators. Near the vortex generator, the vortex intensity is high and it decreases as the flow distance increases. When the fluid flows through multiple vortex generators, the longitudinal vortex gradually strengthens and reaches a steady state after passing through the third vortex generator. Then, the longitudinal vortex varies periodically along the flow direction. In different vortex generator channels, the main vortex behind IDW and ITW, and the main vortex and corner vortex behind the SDITW can be clearly observed. The induced vortex is small and cannot be easily observed. As shown in Figure 7(d), the Q value of the main vortex on both rear sides of SDITW is low, which is similar to the IDW and ITW. However, its Q value of the corner vortex near the central axis is high. The corner vortex exists stably in the SDITW channel and gradually spreads to both sides as the flow distance increases. Therefore, compared with the IDW and ITW, the longitudinal vortex generated in the SDITW channel is stronger.

Figure 7 Distributions of vortex Q criterion in different vortex generator channels (Re = 5,125). (a) Axial side view of IDW channel. (b) Axial side view of the ITW channel. (c) Axial side view of the SDITW channel. (d) Top view of SDITW channel.
Figure 7

Distributions of vortex Q criterion in different vortex generator channels (Re = 5,125). (a) Axial side view of IDW channel. (b) Axial side view of the ITW channel. (c) Axial side view of the SDITW channel. (d) Top view of SDITW channel.

Figure 8 shows the local streamline and velocity distributions at xy plane (z = 2 mm) in different vortex generator channels at Re = 5,125. It can be seen that a pair of strong transverse vortices are generated behind the IDW and ITW, which can cause strong backflow and form a low-speed recirculation zone. Compared with the ITW, the SDITW channel has weaker transverse vortices and a smaller low-speed recirculation zone due to its semi-detached structure. In addition, the flow velocity in the high-speed region in the SDITW channel is obviously higher than that in the IDW and ITW channels, which is beneficial to enhance convective heat transfer in the near-wall region of the channel.

Figure 8 Local streamline and velocity distributions at xy plane (z = 2 mm) in different vortex generator channels (Re = 5,125). (a) IDW channel. (b) ITW channel. (c) SDITW channel.
Figure 8

Local streamline and velocity distributions at xy plane (z = 2 mm) in different vortex generator channels (Re = 5,125). (a) IDW channel. (b) ITW channel. (c) SDITW channel.

Figure 9 shows the distributions of local three-dimensional streamline in different vortex generator channels. It can be seen that, the IDW and ITW generate more transverse vortices due to their larger transverse spans and projection areas. However, the SDITW generates fewer transverse vortices and forms a pair of longitudinal vortices. It indicates that the semi-detached structure of SDITW can reduce transverse vortices and flow resistance while increase the longitudinal vortex effect.

Figure 9 Local 3D streamline distributions of different vortex generator channels (Re = 5,125). (a) Front view of the IDW channel. (b) Front view of the ITW channel. (c) Front view of the SDITW channel.
Figure 9

Local 3D streamline distributions of different vortex generator channels (Re = 5,125). (a) Front view of the IDW channel. (b) Front view of the ITW channel. (c) Front view of the SDITW channel.

Figure 10 shows the local temperature and velocity vector distributions of different channels at yz plane (x = 782 mm). As shown in Figure 10, near the vortex generators, the temperature field shows an alternating distribution of hot and cold fluids. This is due to the influence of the longitudinal vortex, which causes the cold fluid behind the vortex generator moving from the core region towards the heated surface to absorb heat and then diffuse to the side regions. Meanwhile, the hot fluid between the two transverse adjacent vortex generators moves from the wall to the core region. In addition, the ITW and SDITW channels show more uniform temperature distributions as compared to the IDW channel, which indicates they would have better heat transfer performance. The temperature distributions in the ITW and SDITW channels are similar, but thinner thermal boundary layer is observed near the wall in the middle region between two adjacent ITWs, which represents higher heat transfer rate. This phenomenon is due to the large transverse span of the ITW, which can induce longitudinal vortices and lead to significant transverse effect on the flow and heat transfer.

Figure 10 Local temperature and velocity vector distributions at yz plane (x = 782 mm) (Re = 5,125).
Figure 10

Local temperature and velocity vector distributions at yz plane (x = 782 mm) (Re = 5,125).

Figure 11 shows the local heat flux distribution at the heating surface of different vortex generator channels. It is obvious that the IDW and ITW channels exhibit low local heat transfer in the wake region of the vortex generators, which is attributed to the existence of large transverse vortices. On the other hand, in the SDITW channel, the semi-detached structure of the SDITW diminishes the transverse vortices and generates a pair of corner vortices, which will enhance the local heat transfer behind the vortex generator.

Figure 11 Local heat flux distribution at the heating surface of different vortex generator channels (Re = 5,125). (a) IDW channel. (b) ITW channel. (c) SDITW channel.
Figure 11

Local heat flux distribution at the heating surface of different vortex generator channels (Re = 5,125). (a) IDW channel. (b) ITW channel. (c) SDITW channel.

Figure 12 shows the variations in the heat flux on the heating plate and the temperature rise between the inlet and outlet of different vortex generator channels with Re. It shows that the temperature rise decreases, while the heat flux increases as Re increases, which indicates the improvement of heat transfer. The temperature rise and heat flux of ITW and SDITW channels are higher than the IDW channel, indicating that the heat transfer performances of ITW and SDITW channel are better. The heat transfer performances of the ITW and SDITW channels are close with each other, where the SDITW channel shows better heat transfer performance at low Re (Re = 5,125), while the ITW channel shows better heat transfer performance at high Reynolds number (Re = 15,375). According to previous analysis, it reveals that the SDITW channel exhibits higher local heat transfer performance behind the vortex generator, but lower heat transfer performance in the near-wall zone in the middle of the adjacent vortex generator, due to the smaller transverse influence range of the longitudinal vortex. Conversely, the ITW channel shows the opposite trend, resulting in different heat transfer performances between ITW and SDITW channels at different Re. In addition, it is also found that the effect of heat transfer in the near-wall region in the middle of the adjacent vortex generator is gradually obvious as Re increases.

Figure 12 Variations in heat flux on the heating plate and the temperature rise between the inlet and outlet of different vortex generator channels with Re.
Figure 12

Variations in heat flux on the heating plate and the temperature rise between the inlet and outlet of different vortex generator channels with Re.

Figure 13 shows the variations in the Nusselt number ratio (Nu/Nu0), friction factor ratio (f/f 0), and PEC with Reynolds number (Re) in different vortex generator channels. The Nu/Nu0 indicates the enhancement of heat transfer in the vortex generator channel relative to the smooth channel. The f/f 0 represents the increase in pressure loss, and the PEC evaluates the overall thermal performance of the vortex generator channel. As shown in Figure 13, the heat transfer enhancement (Nu/Nu0) of the vortex generator decreased, the pressure loss (f/f 0) increased, and the overall heat transfer performance (PEC) decreased as the Reynolds number (Re) increased. The IDW channel showed the lowest Nu/Nu0 and PEC, which indicates that it has poor flow and heat transfer performance. The heat transfer enhancement (Nu/Nu0) is increased by 12.6–15.69% and the pressure loss (f/f 0) is increased by 39.1–48.3% in the ITW channel as compared to the IDW channel at different Re. Due to the larger projected area of the ITW and stronger disturbance effect, it has a better heat transfer performance and higher flow resistance. Moreover, the overall heat transfer performance (PEC) of the ITW channel is 3.9% higher than that of the IDW channel at low Reynolds number (Re = 5,125), whereas it is lower than that of the IDW channel at high Reynolds number (Re = 15,375). At different Reynolds numbers, the heat transfer enhancement (Nu/Nu0) of the SDITW channel is 7.4–17.5% higher than that of the IDW channel, while its pressure loss (f/f 0) is only 21.9–25.7% higher. The overall heat transfer performance (PEC) of the SDITW channel is 0.5–8.9% higher than that of the IDW channel and 1.7–4.9% higher than that of the ITW channel. The SDITW channel has better overall heat transfer performance than the IDW and ITW channels at different Reynolds numbers. Therefore, the SDITW is more efficient than the delta wing (IDW) and trapezoidal wing (ITW).

Figure 13 Variations in Nu/Nu0, f/f 0, and PEC with Re in different vortex generator channels. (a) Nu/Nu0. (b) f/f 0. (c) PEC.
Figure 13

Variations in Nu/Nu0, f/f 0, and PEC with Re in different vortex generator channels. (a) Nu/Nu0. (b) f/f 0. (c) PEC.

4.2 Effect of geometric parameters on the flow and heat transfer performances of the SDITW channel

4.2.1 Effect of relative separation height and longitudinal pitch

Figure 14 presents the temperature and vortex intensity distributions at yz plane (x = 772 mm) in the SDITW channel with different relative separation heights (e 1/e 2) when Re = 10,250, p l = 70 mm, e/(0.5H) = 0.3, and α = 30°. As the e 1/e 2 decreases, the projected area of the vortex generator increases, and the flow disturbance is enhanced. The intensity and influence range of the main, corner, and induced vortices are increased, and the average vortex intensity rises from 19.8 to 34.1 s−1. The corner vortex in the near-wall region enhances the convective heat transfer near the wall, and the main vortex in the core region promotes the mixing of hot and cold air. Therefore, as the e 1/e 2 decreases, the cross-sectional average air temperature increases and temperature uniformity improves. Furthermore, the triangular region in the left lower corner of Figure 14 indicates a high-temperature region, which is a flow deterioration region formed by the movement of the hot fluid from the wall to the core region. The collision of two adjacent transverse vortices near the wall causes flow deterioration, resulting in fluid momentum loss and heat transfer degradation. As the e 1/e 2 decreases, the induced vortex in the edge region is strengthened, which can reduce the fluid momentum loss and the heat transfer deterioration effect, and narrow the deterioration region.

Figure 14 Temperature (left) and vortex intensity (right) distributions at yz plane (x = 772 mm) in the SDITW channel with different relative separation heights (e 1/e 2) (Re = 10,250, p l = 70 mm, α = 30°, and e/(0.5H) = 0.3).
Figure 14

Temperature (left) and vortex intensity (right) distributions at yz plane (x = 772 mm) in the SDITW channel with different relative separation heights (e 1/e 2) (Re = 10,250, p l = 70 mm, α = 30°, and e/(0.5H) = 0.3).

Figure 15 shows the effects of relative separation height (e 1/e 2) and longitudinal pitch (p l) of SDITW channel on the Nusselt number ratio (Nu/Nu0), friction factor ratio (f/f 0), and PEC. As e 1/e 2 decreases, both the Nu/Nu0 and f/f 0 increase, which means that the heat transfer enhancement is improved and the pressure loss is increased. A smaller e 1/e 2 represents a larger projected area and transverse span of the vortex generator, which can enhance the disturbance and vortex intensity in the fluid, thereby increasing the convective heat transfer and the pressure loss. Moreover, the Nu/Nu0 and f/f 0 increase with the decrease in p l. As p l decreases, the fluid disturbance per unit length increases, and the longitudinal vortex in the SDITW channel is enhanced, which will enhance the heat transfer and increase pressure losses. It is observed that a decrease in p l from 50 to 40 mm will lead to a small increase in the heat transfer enhancement of the SDITW channel, but a large increase in pressure loss. Therefore, p l should not be too small. Furthermore, Figure 15(c) shows that the variation in PEC in SDITW channel is complex at different p l and e 1/e 2. When p l = 70 mm, the PEC variation with e 1/e 2 is insignificant, the PEC value is relatively high and its overall heat transfer performance is better.

Figure 15 Variations in Nu/Nu0, f/f 0, and PEC with relative separation height (e 1/e 2) and longitudinal pitch (p l) in the SDITW channel (Re = 10,250, α = 30°, e/0.5H = 0.3). (a) Nu/Nu0. (b) f/f 0. (c) PEC.
Figure 15

Variations in Nu/Nu0, f/f 0, and PEC with relative separation height (e 1/e 2) and longitudinal pitch (p l) in the SDITW channel (Re = 10,250, α = 30°, e/0.5H = 0.3). (a) Nu/Nu0. (b) f/f 0. (c) PEC.

4.2.2 Effect of blockage ratio and inclination angle

Figure 16 presents the temperature and vortex intensity distributions at yz plane (x = 772 mm) in the SDITW channel with various blockage ratios (e/(0.5H)) and inclination angles (α) at Re = 10,250, e 1/e 2 = 0, and p l = 70 mm. As shown in Figure 16(a), when e/(0.5H) = 0.3, both the maximum vortex intensity and the vortex influence range in the cross-section decrease as α increase, while the variation of average vortex intensity is small. When α increases, the position of the vortex changes, with the corner and induced vortex shifting towards the centerline, while the main vortex moving towards the lower right corner. When α reaches 60°, three vortices merge into a single large vortex. Furthermore, as α increases, the airflow temperature uniformity deteriorates and the average temperature decreases. The vortex locations can affect the airflow average temperature in the cross-section, even though the average vortex intensity is comparable for α = 20° and 60°. The convective heat transfer is improved due to the stronger vortex near the wall at α = 20°, while it is weakened by the weaker vortex near the wall at α = 60°. As shown in Figure 16(b), when e/(0.5H) = 0.6, the cross-section averaged vortex intensity increases and the vortex influence range expands as α increases. There is a significant difference in the local vortex intensity in the near-wall region at different α. The local vortex intensity is maximum when α is 40° and minimum when α is 20°. Consequently, the convective heat transfer near the wall is the best when α is 40°, where airflow average temperature is the highest and the temperature distribution is most uniform in the cross-section. On the contrary, the heat transfer is the worst when α is 20°, where the airflow average temperature is the lowest and the temperature distribution is not uniform. Comparison of Figure 16(a) and (b) reveals that the effect of e/(0.5H) on the vortex intensity and the temperature distribution in the SDITW channel varies with α. When α is relatively large, the effect of e/(0.5H) is significant.

Figure 16 Temperature (left) and vortex intensity (right) distributions at yz plane (x = 772 mm) in the SDITW channel with different blockage ratios (e/(0.5H)) and inclination angles (α) (Re = 10,250, e 1/e 2 = 0, p l = 70 mm). (a) e/(0.5H) = 0.3. (b) e/(0.5H) = 0.6.
Figure 16

Temperature (left) and vortex intensity (right) distributions at yz plane (x = 772 mm) in the SDITW channel with different blockage ratios (e/(0.5H)) and inclination angles (α) (Re = 10,250, e 1/e 2 = 0, p l = 70 mm). (a) e/(0.5H) = 0.3. (b) e/(0.5H) = 0.6.

Figure 17 shows the effects of blockage ratios (e/(0.5H)) and inclination angles (α) in the SDITW channel on the Nusselt number ratio (Nu/Nu0), friction factor ratio (f/f 0), and PEC. As shown in Figure 17(a), the variation trend of Nu/Nu0 with e/(0.5H) is different under different α. When α = 50° and 60°, Nu/Nu0 increases with e/(0.5H), indicating that a higher blockage ratio is beneficial for the heat transfer enhancement in the SDITW channel at large inclination angles. In contrast, when α = 20°–40°, Nu/Nu0 first increases and then decreases with the increase in e/(0.5H), suggesting that there exists an optimum e/(0.5H) in this range of α, which will maximize the heat transfer enhancement in the SDITW channel. Furthermore, the sensitivity in SDITW channel caused by e/(0.5H) will diminish as α decreases. When α = 20°, the variation in Nu/Nu0 is minimum. As shown in Figure 17(b), f/f 0 increases with the increase in e/(0.5H) at different α, which indicates that the flow resistance in SDITW channel increases. The increment of f/f 0 varies with α, and it is small when α is small. As shown in Figure 17(c), when α changes from 30° to 60°, the PEC of SDITW channel increases first and then decreases with the increase in e/(0.5H), implying that there exists an optimum e/(0.5H) value, which will lead to the highest PEC for this range of α. The PEC of SDITW channel is maximum at e/(0.5H) = 0.3 at Re = 10,250 and α = 30°–60°, where the overall heat transfer performance of SDITW channel is the best.

Figure 17 Variations in Nu/Nu0, f/f 0, and PEC with blockage ratio (e/(0.5H)) and inclination angle (α) in the SDITW channel (Re = 10,250, e 1/e 2 = 0, and p l = 70 mm). (a) Nu/Nu0. (b) f/f 0. (c) PEC.
Figure 17

Variations in Nu/Nu0, f/f 0, and PEC with blockage ratio (e/(0.5H)) and inclination angle (α) in the SDITW channel (Re = 10,250, e 1/e 2 = 0, and p l = 70 mm). (a) Nu/Nu0. (b) f/f 0. (c) PEC.

5 Conclusion

In this study, the flow and heat transfer characteristics of SDITW vortex generator in a closed channel on the air-side of the panel-type radiator used for transformer were numerically investigated. The performance of SDITW was compared with that of IDW and ITW channels under the same geometric configuration. The effects of SDITW relative separation height (e 1/e 2), longitudinal pitch (p l), blockage ratio (e/(0.5H)), and inclination angle (α) on the flow and heat transfer in the SDITW channel were analyzed in detail. The major findings are as follows:

  1. Among the three vortex generators, SDITW has the highest local vortex intensity, followed by ITW and IDW. A stronger longitudinal vortex is formed in the SDITW channel as compared with IDW and ITW. On the other hand, more transverse vortices are created behind IDW and ITW. The semi-detached structure of SDITW can diminish the transverse vortices and flow resistance.

  2. For Re = 5,125–15,375, the heat transfer enhancement (Nu/Nu0) of ITW is 12.6–15.69% higher than that of IDW, while the pressure loss (f/f 0) is 39.1–48.3% higher. The heat transfer enhancement (Nu/Nu0) of SDITW is 7.4–17.5% higher than that of IDW, while the pressure loss (f/f 0) is 21.9–25.7% higher. Therefore, the overall heat transfer performance (PEC) of SDITW is 0.5–8.9% higher than that of IDW and 1.7–4.9% higher than that of ITW.

  3. For the same e/(0.5H) and α, the vortex intensity and influence range increase in the SDITW channel as e 1/e 2 decreases. As p l decreases, the longitudinal vortex in the SDITW channel strengthens, the heat transfer performance improves, and the pressure loss increases. Both Nu/Nu0 and f/f 0 of the SDITW channel increase as e 1/e 2 and p l decrease. The PEC of SDITW channel is relatively high and its overall heat transfer performance is better when p l = 70 mm.

  4. For the same e 1/e 2 and p l, the vortex intensity and influence range in the SDITW channel decrease as α increases when e/(0.5H) is 0.3, and its heat transfer performance deteriorates. When e/(0.5H) is 0.6, the vortex intensity and influence range in the SDITW channel increase as α increases, but its heat transfer is the best when α is 40° due to the difference in local vortex intensity near the wall region. For Re = 10,250 and α = 30°–60°, the PEC of the SDITW channel is maximum when e/(0.5H) = 0.3, and the overall heat transfer performance of the SDITW channel is the best.

The results obtained in the present study is meaningful in revealing the mechanism of flow resistance reduction and heat transfer enhancement for SDITW in a closed channel on the air side of a panel-type radiator used for transformer. It can also provide a useful reference for the optimal design of vortex generator and corresponding heat dissipation channel for subsequent researchers.

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  1. Funding information: This work was supported by the S&T project of State Grid Shanghai Municipal Electrical Power Company under grant number 52094022000Y.

  2. Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  3. Conflict of interest: The authors state no conflict of interest.

  4. Data availability statement: The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Received: 2023-08-29
Revised: 2023-11-05
Accepted: 2024-01-04
Published Online: 2024-01-19

© 2024 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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  47. Numerical study of blood-based MHD tangent hyperbolic hybrid nanofluid flow over a permeable stretching sheet with variable thermal conductivity and cross-diffusion
  48. Fractional view analytical analysis of generalized regularized long wave equation
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  50. Inclined magnetized infinite shear rate viscosity of non-Newtonian tetra hybrid nanofluid in stenosed artery with non-uniform heat sink/source
  51. Estimation of monotone α-quantile of past lifetime function with application
  52. Numerical simulation for the slip impacts on the radiative nanofluid flow over a stretched surface with nonuniform heat generation and viscous dissipation
  53. Study of fractional telegraph equation via Shehu homotopy perturbation method
  54. An investigation into the impact of thermal radiation and chemical reactions on the flow through porous media of a Casson hybrid nanofluid including unstable mixed convection with stretched sheet in the presence of thermophoresis and Brownian motion
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  60. Study on cavitation and pulsation characteristics of a novel rotor-radial groove hydrodynamic cavitation reactor
  61. Optimizing heat transport in a permeable cavity with an isothermal solid block: Influence of nanoparticles volume fraction and wall velocity ratio
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  63. Thermal analysis of generalized Cattaneo–Christov theories in Burgers nanofluid in the presence of thermo-diffusion effects and variable thermal conductivity
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  66. Double diffusion convection of Maxwell–Cattaneo fluids in a vertical slot
  67. Thermal analysis of extended surfaces using deep neural networks
  68. Steady-state thermodynamic process in multilayered heterogeneous cylinder
  69. Multiresponse optimisation and process capability analysis of chemical vapour jet machining for the acrylonitrile butadiene styrene polymer: Unveiling the morphology
  70. Modeling monkeypox virus transmission: Stability analysis and comparison of analytical techniques
  71. Fourier spectral method for the fractional-in-space coupled Whitham–Broer–Kaup equations on unbounded domain
  72. The chaotic behavior and traveling wave solutions of the conformable extended Korteweg–de-Vries model
  73. Research on optimization of combustor liner structure based on arc-shaped slot hole
  74. Construction of M-shaped solitons for a modified regularized long-wave equation via Hirota's bilinear method
  75. Effectiveness of microwave ablation using two simultaneous antennas for liver malignancy treatment
  76. Discussion on optical solitons, sensitivity and qualitative analysis to a fractional model of ion sound and Langmuir waves with Atangana Baleanu derivatives
  77. Reliability of two-dimensional steady magnetized Jeffery fluid over shrinking sheet with chemical effect
  78. Generalized model of thermoelasticity associated with fractional time-derivative operators and its applications to non-simple elastic materials
  79. Migration of two rigid spheres translating within an infinite couple stress fluid under the impact of magnetic field
  80. A comparative investigation of neutron and gamma radiation interaction properties of zircaloy-2 and zircaloy-4 with consideration of mechanical properties
  81. New optical stochastic solutions for the Schrödinger equation with multiplicative Wiener process/random variable coefficients using two different methods
  82. Physical aspects of quantile residual lifetime sequence
  83. Synthesis, structure, I–V characteristics, and optical properties of chromium oxide thin films for optoelectronic applications
  84. Smart mathematically filtered UV spectroscopic methods for quality assurance of rosuvastatin and valsartan from formulation
  85. A novel investigation into time-fractional multi-dimensional Navier–Stokes equations within Aboodh transform
  86. Homotopic dynamic solution of hydrodynamic nonlinear natural convection containing superhydrophobicity and isothermally heated parallel plate with hybrid nanoparticles
  87. A novel tetra hybrid bio-nanofluid model with stenosed artery
  88. Propagation of traveling wave solution of the strain wave equation in microcrystalline materials
  89. Innovative analysis to the time-fractional q-deformed tanh-Gordon equation via modified double Laplace transform method
  90. A new investigation of the extended Sakovich equation for abundant soliton solution in industrial engineering via two efficient techniques
  91. New soliton solutions of the conformable time fractional Drinfel'd–Sokolov–Wilson equation based on the complete discriminant system method
  92. Irradiation of hydrophilic acrylic intraocular lenses by a 365 nm UV lamp
  93. Inflation and the principle of equivalence
  94. The use of a supercontinuum light source for the characterization of passive fiber optic components
  95. Optical solitons to the fractional Kundu–Mukherjee–Naskar equation with time-dependent coefficients
  96. A promising photocathode for green hydrogen generation from sanitation water without external sacrificing agent: silver-silver oxide/poly(1H-pyrrole) dendritic nanocomposite seeded on poly-1H pyrrole film
  97. Photon balance in the fiber laser model
  98. Propagation of optical spatial solitons in nematic liquid crystals with quadruple power law of nonlinearity appears in fluid mechanics
  99. Theoretical investigation and sensitivity analysis of non-Newtonian fluid during roll coating process by response surface methodology
  100. Utilizing slip conditions on transport phenomena of heat energy with dust and tiny nanoparticles over a wedge
  101. Bismuthyl chloride/poly(m-toluidine) nanocomposite seeded on poly-1H pyrrole: Photocathode for green hydrogen generation
  102. Infrared thermography based fault diagnosis of diesel engines using convolutional neural network and image enhancement
  103. On some solitary wave solutions of the Estevez--Mansfield--Clarkson equation with conformable fractional derivatives in time
  104. Impact of permeability and fluid parameters in couple stress media on rotating eccentric spheres
  105. Review Article
  106. Transformer-based intelligent fault diagnosis methods of mechanical equipment: A survey
  107. Special Issue on Predicting pattern alterations in nature - Part II
  108. A comparative study of Bagley–Torvik equation under nonsingular kernel derivatives using Weeks method
  109. On the existence and numerical simulation of Cholera epidemic model
  110. Numerical solutions of generalized Atangana–Baleanu time-fractional FitzHugh–Nagumo equation using cubic B-spline functions
  111. Dynamic properties of the multimalware attacks in wireless sensor networks: Fractional derivative analysis of wireless sensor networks
  112. Prediction of COVID-19 spread with models in different patterns: A case study of Russia
  113. Study of chronic myeloid leukemia with T-cell under fractal-fractional order model
  114. Accumulation process in the environment for a generalized mass transport system
  115. Analysis of a generalized proportional fractional stochastic differential equation incorporating Carathéodory's approximation and applications
  116. Special Issue on Nanomaterial utilization and structural optimization - Part II
  117. Numerical study on flow and heat transfer performance of a spiral-wound heat exchanger for natural gas
  118. Study of ultrasonic influence on heat transfer and resistance performance of round tube with twisted belt
  119. Numerical study on bionic airfoil fins used in printed circuit plate heat exchanger
  120. Improving heat transfer efficiency via optimization and sensitivity assessment in hybrid nanofluid flow with variable magnetism using the Yamada–Ota model
  121. Special Issue on Nanofluids: Synthesis, Characterization, and Applications
  122. Exact solutions of a class of generalized nanofluidic models
  123. Stability enhancement of Al2O3, ZnO, and TiO2 binary nanofluids for heat transfer applications
  124. Thermal transport energy performance on tangent hyperbolic hybrid nanofluids and their implementation in concentrated solar aircraft wings
  125. Studying nonlinear vibration analysis of nanoelectro-mechanical resonators via analytical computational method
  126. Numerical analysis of non-linear radiative Casson fluids containing CNTs having length and radius over permeable moving plate
  127. Two-phase numerical simulation of thermal and solutal transport exploration of a non-Newtonian nanomaterial flow past a stretching surface with chemical reaction
  128. Natural convection and flow patterns of Cu–water nanofluids in hexagonal cavity: A novel thermal case study
  129. Solitonic solutions and study of nonlinear wave dynamics in a Murnaghan hyperelastic circular pipe
  130. Comparative study of couple stress fluid flow using OHAM and NIM
  131. Utilization of OHAM to investigate entropy generation with a temperature-dependent thermal conductivity model in hybrid nanofluid using the radiation phenomenon
  132. Slip effects on magnetized radiatively hybridized ferrofluid flow with acute magnetic force over shrinking/stretching surface
  133. Significance of 3D rectangular closed domain filled with charged particles and nanoparticles engaging finite element methodology
  134. Robustness and dynamical features of fractional difference spacecraft model with Mittag–Leffler stability
  135. Characterizing magnetohydrodynamic effects on developed nanofluid flow in an obstructed vertical duct under constant pressure gradient
  136. Study on dynamic and static tensile and puncture-resistant mechanical properties of impregnated STF multi-dimensional structure Kevlar fiber reinforced composites
  137. Thermosolutal Marangoni convective flow of MHD tangent hyperbolic hybrid nanofluids with elastic deformation and heat source
  138. Investigation of convective heat transport in a Carreau hybrid nanofluid between two stretchable rotatory disks
  139. Single-channel cooling system design by using perforated porous insert and modeling with POD for double conductive panel
  140. Special Issue on Fundamental Physics from Atoms to Cosmos - Part I
  141. Pulsed excitation of a quantum oscillator: A model accounting for damping
  142. Review of recent analytical advances in the spectroscopy of hydrogenic lines in plasmas
  143. Heavy mesons mass spectroscopy under a spin-dependent Cornell potential within the framework of the spinless Salpeter equation
  144. Coherent manipulation of bright and dark solitons of reflection and transmission pulses through sodium atomic medium
  145. Effect of the gravitational field strength on the rate of chemical reactions
  146. The kinetic relativity theory – hiding in plain sight
  147. Special Issue on Advanced Energy Materials - Part III
  148. Eco-friendly graphitic carbon nitride–poly(1H pyrrole) nanocomposite: A photocathode for green hydrogen production, paving the way for commercial applications
https://doi.org/10.1515/phys-2023-0180
Keywords for this article
panel-type radiator; longitudinal vortex generator; heat transfer enhancement; numerical simulation
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BY 4.0

Articles in the same Issue

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  2. Numerical study of flow and heat transfer in the channel of panel-type radiator with semi-detached inclined trapezoidal wing vortex generators
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  12. Thermal proficiency of magnetized and radiative cross-ternary hybrid nanofluid flow induced by a vertical cylinder
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  46. Numerical investigation of acoustic streaming vortices in cylindrical tube arrays
  47. Numerical study of blood-based MHD tangent hyperbolic hybrid nanofluid flow over a permeable stretching sheet with variable thermal conductivity and cross-diffusion
  48. Fractional view analytical analysis of generalized regularized long wave equation
  49. Dynamic simulation of non-Newtonian boundary layer flow: An enhanced exponential time integrator approach with spatially and temporally variable heat sources
  50. Inclined magnetized infinite shear rate viscosity of non-Newtonian tetra hybrid nanofluid in stenosed artery with non-uniform heat sink/source
  51. Estimation of monotone α-quantile of past lifetime function with application
  52. Numerical simulation for the slip impacts on the radiative nanofluid flow over a stretched surface with nonuniform heat generation and viscous dissipation
  53. Study of fractional telegraph equation via Shehu homotopy perturbation method
  54. An investigation into the impact of thermal radiation and chemical reactions on the flow through porous media of a Casson hybrid nanofluid including unstable mixed convection with stretched sheet in the presence of thermophoresis and Brownian motion
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  59. A short report on a probability-based interpretation of quantum mechanics
  60. Study on cavitation and pulsation characteristics of a novel rotor-radial groove hydrodynamic cavitation reactor
  61. Optimizing heat transport in a permeable cavity with an isothermal solid block: Influence of nanoparticles volume fraction and wall velocity ratio
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  63. Thermal analysis of generalized Cattaneo–Christov theories in Burgers nanofluid in the presence of thermo-diffusion effects and variable thermal conductivity
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  76. Discussion on optical solitons, sensitivity and qualitative analysis to a fractional model of ion sound and Langmuir waves with Atangana Baleanu derivatives
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  78. Generalized model of thermoelasticity associated with fractional time-derivative operators and its applications to non-simple elastic materials
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  80. A comparative investigation of neutron and gamma radiation interaction properties of zircaloy-2 and zircaloy-4 with consideration of mechanical properties
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  84. Smart mathematically filtered UV spectroscopic methods for quality assurance of rosuvastatin and valsartan from formulation
  85. A novel investigation into time-fractional multi-dimensional Navier–Stokes equations within Aboodh transform
  86. Homotopic dynamic solution of hydrodynamic nonlinear natural convection containing superhydrophobicity and isothermally heated parallel plate with hybrid nanoparticles
  87. A novel tetra hybrid bio-nanofluid model with stenosed artery
  88. Propagation of traveling wave solution of the strain wave equation in microcrystalline materials
  89. Innovative analysis to the time-fractional q-deformed tanh-Gordon equation via modified double Laplace transform method
  90. A new investigation of the extended Sakovich equation for abundant soliton solution in industrial engineering via two efficient techniques
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  92. Irradiation of hydrophilic acrylic intraocular lenses by a 365 nm UV lamp
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  94. The use of a supercontinuum light source for the characterization of passive fiber optic components
  95. Optical solitons to the fractional Kundu–Mukherjee–Naskar equation with time-dependent coefficients
  96. A promising photocathode for green hydrogen generation from sanitation water without external sacrificing agent: silver-silver oxide/poly(1H-pyrrole) dendritic nanocomposite seeded on poly-1H pyrrole film
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  98. Propagation of optical spatial solitons in nematic liquid crystals with quadruple power law of nonlinearity appears in fluid mechanics
  99. Theoretical investigation and sensitivity analysis of non-Newtonian fluid during roll coating process by response surface methodology
  100. Utilizing slip conditions on transport phenomena of heat energy with dust and tiny nanoparticles over a wedge
  101. Bismuthyl chloride/poly(m-toluidine) nanocomposite seeded on poly-1H pyrrole: Photocathode for green hydrogen generation
  102. Infrared thermography based fault diagnosis of diesel engines using convolutional neural network and image enhancement
  103. On some solitary wave solutions of the Estevez--Mansfield--Clarkson equation with conformable fractional derivatives in time
  104. Impact of permeability and fluid parameters in couple stress media on rotating eccentric spheres
  105. Review Article
  106. Transformer-based intelligent fault diagnosis methods of mechanical equipment: A survey
  107. Special Issue on Predicting pattern alterations in nature - Part II
  108. A comparative study of Bagley–Torvik equation under nonsingular kernel derivatives using Weeks method
  109. On the existence and numerical simulation of Cholera epidemic model
  110. Numerical solutions of generalized Atangana–Baleanu time-fractional FitzHugh–Nagumo equation using cubic B-spline functions
  111. Dynamic properties of the multimalware attacks in wireless sensor networks: Fractional derivative analysis of wireless sensor networks
  112. Prediction of COVID-19 spread with models in different patterns: A case study of Russia
  113. Study of chronic myeloid leukemia with T-cell under fractal-fractional order model
  114. Accumulation process in the environment for a generalized mass transport system
  115. Analysis of a generalized proportional fractional stochastic differential equation incorporating Carathéodory's approximation and applications
  116. Special Issue on Nanomaterial utilization and structural optimization - Part II
  117. Numerical study on flow and heat transfer performance of a spiral-wound heat exchanger for natural gas
  118. Study of ultrasonic influence on heat transfer and resistance performance of round tube with twisted belt
  119. Numerical study on bionic airfoil fins used in printed circuit plate heat exchanger
  120. Improving heat transfer efficiency via optimization and sensitivity assessment in hybrid nanofluid flow with variable magnetism using the Yamada–Ota model
  121. Special Issue on Nanofluids: Synthesis, Characterization, and Applications
  122. Exact solutions of a class of generalized nanofluidic models
  123. Stability enhancement of Al2O3, ZnO, and TiO2 binary nanofluids for heat transfer applications
  124. Thermal transport energy performance on tangent hyperbolic hybrid nanofluids and their implementation in concentrated solar aircraft wings
  125. Studying nonlinear vibration analysis of nanoelectro-mechanical resonators via analytical computational method
  126. Numerical analysis of non-linear radiative Casson fluids containing CNTs having length and radius over permeable moving plate
  127. Two-phase numerical simulation of thermal and solutal transport exploration of a non-Newtonian nanomaterial flow past a stretching surface with chemical reaction
  128. Natural convection and flow patterns of Cu–water nanofluids in hexagonal cavity: A novel thermal case study
  129. Solitonic solutions and study of nonlinear wave dynamics in a Murnaghan hyperelastic circular pipe
  130. Comparative study of couple stress fluid flow using OHAM and NIM
  131. Utilization of OHAM to investigate entropy generation with a temperature-dependent thermal conductivity model in hybrid nanofluid using the radiation phenomenon
  132. Slip effects on magnetized radiatively hybridized ferrofluid flow with acute magnetic force over shrinking/stretching surface
  133. Significance of 3D rectangular closed domain filled with charged particles and nanoparticles engaging finite element methodology
  134. Robustness and dynamical features of fractional difference spacecraft model with Mittag–Leffler stability
  135. Characterizing magnetohydrodynamic effects on developed nanofluid flow in an obstructed vertical duct under constant pressure gradient
  136. Study on dynamic and static tensile and puncture-resistant mechanical properties of impregnated STF multi-dimensional structure Kevlar fiber reinforced composites
  137. Thermosolutal Marangoni convective flow of MHD tangent hyperbolic hybrid nanofluids with elastic deformation and heat source
  138. Investigation of convective heat transport in a Carreau hybrid nanofluid between two stretchable rotatory disks
  139. Single-channel cooling system design by using perforated porous insert and modeling with POD for double conductive panel
  140. Special Issue on Fundamental Physics from Atoms to Cosmos - Part I
  141. Pulsed excitation of a quantum oscillator: A model accounting for damping
  142. Review of recent analytical advances in the spectroscopy of hydrogenic lines in plasmas
  143. Heavy mesons mass spectroscopy under a spin-dependent Cornell potential within the framework of the spinless Salpeter equation
  144. Coherent manipulation of bright and dark solitons of reflection and transmission pulses through sodium atomic medium
  145. Effect of the gravitational field strength on the rate of chemical reactions
  146. The kinetic relativity theory – hiding in plain sight
  147. Special Issue on Advanced Energy Materials - Part III
  148. Eco-friendly graphitic carbon nitride–poly(1H pyrrole) nanocomposite: A photocathode for green hydrogen production, paving the way for commercial applications
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