Heat Transfer Potentiality and Flow Behavior in a Square Duct Fitted with Double-Inclined Baffles: A Numerical Analysis

Numerical analysis of heat transfer mechanisms and flow topologies for the heat exchanger square channel (HESC) installed with the double-inclined baffles (DIB) is reported. The main objective of the present research is to study the influences of DIB height to duct height (
 
 b
 /
 H
 =
 0.05
 –
 0.30
 
 ), DIB distance to duct height (
 
 P
 /
 H
 =
 1
 –
 1.5
 
 ), and flow attack angle (
 
 α
 =
 
 
 30
 
 
 °
 
 
  
 and
  
 
 
 45
 
 
 °
 
 
 
 ) on the flow topologies, heat transfer features, and thermal performances. The Reynolds numbers (based on the entry HESC around 100–2000) are analyzed for the present problem. The numerical models of the HESC installed with the DIB are solved with finite volume method (commercial code). The simulated results of the HESC installed with the DIB are reported in forms of flow topologies and heat transfer characteristics. The Nusselt numbers (Nu), friction factors (
 
 f
 
 ), and thermal enhancement factors (TEF) of the HESC placed with the DIB are offered. As the numerical results, it is seen that the DIB produces the vortex streams and impinging streams in all cases. The vortex streams and impinging streams disturb the thermal boundary layer on the HESC walls that is a key motive for the growth of heat transfer rate. The best TEF of the HESC installed with the DIB is about 3.87 at 
 
 P
 /
 H
 =
 1
 
 , 
 
 α
 =
 
 
 30
 
 
 °
 
 
 
 , 
 
 Re
 =
 2000
 
 , and 
 
 b
 /
 H
 =
 0.15
 
 . Additionally, the TEF contours, which help to design the HESC inserted with the DIB, are performed.


Introduction
Thermal development for production processes of many plants and engineering devices has been investigated by various research groups. The thermal development can be done by both passive and active techniques. The passive technique is an installation of turbulators or vortex generators in heat exchangers to produce vortex streams and impinging streams through heating/cooling sections. The vortex streams and impinging streams influence for a change of thermal boundary layer that is a main reason for heat transfer enhancement. Moreover, the vortex streams and impinging streams also grow fluid mixing power that is another cause for the heat transfer improvement. The flow features for different kinds of the vortex generators are not in similar patterns. Therefore, the vortex generator selection depends on applications of the heat exchangers. The active method is an addition of external power into heating/cooling processes to grow heat transfer rates. The active technique has great efficiency to extend heat transfer ability in the heat exchangers. However, the additional power brings higher production cost of the production processes. For the present investigation, the passive technique is picked to extend the heat transfer ability and thermal performance in the heat exchanger duct.
There are many works about the thermal improvement of various kinds for the heat exchangers with the passive method. The investigation methods can be separated into two ways: numerical and experimental studies. The experimental results from validated devices have high reliability and precision values. However, the experimental results could not explain the flow features and heat transfer patterns of the heat transfer processes in almost cases. The numerical investigation in the heat transfer processes is presented to explain the mechanisms in the tested sections. The knowledge on the flow features and heat transfer structures is important data to help to design the heat exchangers. However, numerical models must be validated to confirm reliance of the numerical results.
There are many published works about heat transfer and flow mechanisms, which are significant knowledge, for the heat exchangers and engineering devices [1][2][3][4][5][6][7][8][9]. The examples for the heat transfer improvement in various types of the heat exchangers with passive techniques of both numerical and experimental investigations are as follows. Bahiraei et al. [10] examined the growth of the heat transfer potentiality in a square section fitted with V-shaped rib combining with nanofluid. The effects of the 45°V-shaped rib on heat transfer potentiality, friction loss, and thermo-hydraulic performance were compared with those of the 60°V-shaped rib. They presented that the lower entropy generation is found at the 45°V-shaped rib. They also claimed that the larger rib height with smaller pitch spacing provides depressed exergy destruction and extends the higher second law efficiency. Bahiraei et al. [11] numerically investigated the thermo-hydraulic performance of Cu-water nanofluid in a square duct installed with 90°V-shaped rib. The influences of rib parameters (rib height and rib pitch) on heat transfer, thermal performance, and pressure loss were considered. They concluded that the heat transfer rate increases about 28.3% when augmenting the rib height from 2.5 to 7.5 mm at the pitch spacing of 50 mm. A direct simulation of the entry region heat transfer for a channel (with an isothermal wall) fitted with ribs at Re = 20460 was reported by Matsubara et al. [12]. They found that the modification of thermal boundary layer affects for the enhancement of heat transfer coefficient at the entry regime of the ribbed channel. Li

Start
Step 1: solve discretised momentum equation Step 2: solve pressure correction equation Step 3: correct pressure and velocities Step 4: solve all other discretised transport equation   et al. [13] studied the heat transfer potentiality and flow features in a microchannel with solid and porous ribs. They found that the thermal performance in the microchannel installed with the rib is greater than plain section with no rib. Bahiraei et al. [14] reported the second law analysis for nanofluid in a channel fitted with conical rib. The effects of rib arrangement and nanoparticle shape on flow configuration and heat transfer were considered. Jiang et al. [15] illustrated the two-phase flow and heat transfer profiles in a rectangular tested section with column-row-rib. Bai et al. [16] investigated the rib disturbed effect at the entry of a pin-fin array on pressure loss, thermal performance, and heat transfer ability for Re = 7000 -40000. The influences of rib configurations (60°rib, V-shaped rib, and W-shaped rib) on flow topology and heat transfer pattern were compared. They pointed out that the entry effect not only develops the heat transfer potentiality but also relieves the pressure loss that is a reason for the thermal performance increment. Li et al. [17] studied the pressure drop, heat transfer potentiality in a channel with miniature structured rib on one wall for Re = 10000 -60000 (turbulent regime) by both numerical and experimental investigations. Their results revealed that the averaged Nusselt number and overall Nusselt number are greater than those of the smooth channel with no rib around 2.2-2.6 and 2.9-3.3 times, respectively. Bai et al. [18] simulated the pressure loss and heat transfer ability in a pin-fin array installed with rib turbulators. They summarized that the rib induces the secondary flow that is a reason for the heat transfer augmentation. They also informed that the 90°rib lets the best overall performance. The forced convective heat transfer and pressure loss of a square section with discrete combined baffle was reported by Boonloi and Jedsadaratanachai [19]. The impacts of flow directions and baffled heights on thermal performance in the square channel were considered for Re = 5000 -20000. They found that the heat transfer ability of the square channel equipped with the discrete combined baffle is greater than the plain channel with no baffle around 2.8-6.0 times. For the present investigation, heat transfer mechanisms and flow features in the heat exchanger square channel (HESC) installed with the double inclined baffles (DIB) are presented numerically. The effects of DIB height, DIB distance, and flow attack angle on the flow streams and heat transfer features are considered for laminar flow. The DIB is designed with the main aim to produce corotating flows. The corotating flows are compared with counter-rotating flows, which are produced by V-shaped vortex generators [9,19]. The corotating flows may give a higher heat transfer rate with a lower pressure loss when comparing with the counter-rotating flows. The thermal performance assessments in the HESC equipped with the DIB are also reported. The TEF contours, which help to select the DIB parameters,

Mathematical Foundation and Initial and Boundary Conditions
The methodology of the present work is referred from Reference [20]. The fluid flow and heat transfer in the HESC are assumed to be steady in three dimensions. The tested fluid, air (Prandtl number about 0.707 at 300 K), is defined as incompressible flow. The Reynolds number based on the hydraulic diameter of about 100-2000 (laminar flow) is regarded for the present work. The thermal properties of the air are known to be constant at average bulk mean temperature. Considering at heat transfer mode, the forced con-vective heat transfer in the HESC is measured, while the other modes (radiation and natural convection) are ignored. Body force and viscous dissipation of the HESC is also neglected. No slip wall condition is applied for all HESC surfaces and DIB. The Reynolds number can be determined as Equation (1).
The friction factor, f , in the HESC is calculated as Equation (2).
The heat transfer ability in the HESC inserted with the DIB is presented with the local Nusselt number and average Nusselt number as Equations (3) and (4), respectively.
The thermal efficiency in the HESC inserted with the DIB is illustrated in form of thermal efficiency factor, TEF. The TEF is defined as the ratio of the heat transfer coefficient of an augmented surface, h, to that of a smooth surface, h 0 , at a similar pumping power and given by the following: where Nu 0 and f 0 stand for Nusselt number and friction factor for the smooth duct, respectively. The boundary conditions for the present work can be summarized as Table 1.

Numerical Method
The finite volume method with SIMPLE algorithm (as depicted in Figure 2) is opted to solve the numerical problem for the HESC inserted with the DIB. Based on the assumptions, the flow in the HESC is governed by the continuity, the Navier-Stokes, and the energy equations. The continuity equation, the momentum equation, and the energy equation      Modelling and Simulation in Engineering are discretized by the power law scheme, power law scheme, and QUICK scheme, respectively. In the numerical process, the solutions are considered to be converged when the normalized residual values are less than 10 -5 for all variables, but less than 10 -9 only for the energy equation.

Numerical Validation
For the laminar flow, there are two parts in the numerical validation: (1) verification of the smooth HESC without DIB and (2) optimum grid cell or grid independence. The verification of the plain duct without DIB is done of both heat transfer and pressure loss. The comparisons between the present results with the values from the correlations [21] on Nusselt number and friction factor are done and depicted in Figure 3. As the figure, it is detected that the absolute average deviations of the Nusselt number are around 2%, while around 3.2% for the friction factor. For the grid test, the different grid cells (120000, 240000, 360000, and 480000 cells) for the HESC inserted with the DIB (b/H = 0:15, P/H = 1, and α = 30°) are compared both Nusselt number and friction factor. It is seen that the growth of the cells from 120000 to 240000 has no impact for both the heat transfer and pressure loss in the HESC installed with the DIB. Thus, the grid around 120000 cells is picked for all investigated tests of the current research. As the validated results, it can be summarized that the numerical model has high reliability to predict flow topologies and heat transfer features of the HESC installed with the DIB.  The temperature contour of the HESC placed with the DIB is a guide to see the variation of the thermal boundary layer (see Figure 8). As seen in the figures, the vortex streams, which are created by the DIB, disrupt the thermal boundary layer on the HESC walls. When inserting the DIB in the HESC, the red layer thickness of the hot air near the HESC wall decreases, the blue layer of the cold fluid at the middle of the plane distributes to the HESC walls. The best distribution of the fluid temperature is detected when b/H ≥ 0:15, while the poor distribution is detected at b/H = 0:05. This is because the vortex strength directly affects for the fluid distribution and thermal boundary layer disturbance. The temperature contours in y-z planes in the HESC located with the DIB are plotted as Figures 12(a)-12(c) for P/H = 1, 1:25, and 1:5, respectively, at Re = 1000, b/H = 0:20 , and α = 30°. As the figure, the temperature contours of the HESC are similarly seen when varying the P/H (see Figure 13). The cold fluid spreads from the core of the HESC, while the hot fluid layer near the duct walls reduces. This means that the variations of the P/H have slightly affect for the change of the heat transfer behavior.

Conclusion
In this paper, the numerical analysis on heat transfer potentiality, pressure loss, and thermo-hydraulic performance in the HESC installed with the DIB is performed. The effects of flow attack angle, DIB height, DIB distance on flow, and heat transfer features are considered. As the simulated results, the main findings of the current investigation can be concluded as follows.
(i) The DIB creates vortex streams and impinging streams through the HESC for all investigated cases. The vortex streams and impinging streams are a disruptor of thermal boundary layer on the HESC surfaces. The disturbed thermal boundary layer is a significant key to improve the heat transfer potentiality. The vortex streams and impinging streams also help to enhance the power of a turbulent mixing. The improved fluid blending is another reason for the development of the heat transfer ability. The vortex power depends on the flow attack angle, DIB height, DIB distance, and Reynolds number. The vortex force increases when growing the DIB height and Reynolds number and with reducing the DIB distance (ii) In comparison, the flow attack angle of 30°operates nearly values of heat transfer ability with lower pressure loss when compared with the flow attack angle of 45°. Therefore, the thermal enhancement factor of the flow attack angle of 30°is higher than the flow attack angle of 45°. The best thermal enhancement factor of the current work is around 3.87 at α = 30°, b/H = 0:15, and P/H = 1. As the range investigates, the Nusselt number and friction factor values of the HESC installed with the DIB are upper than the plain duct without DIB around 1.00-15.91 and 1.00-220.86 times, respectively. The optimum TEF for both flow attack angles is found in the range of b/H ≈ 0:15 -0:20 and P/H ≈ 1 as depicted in Figure 18 (iii) The peaks of heat transfer rate due to the impinging streams are obviously found at the side wall (side A) for all investigated cases. The knowledge about the impinging regime in the HESC is an advantage for some types of the heat exchangers such as solar air heaters, which require only one side for a heating surface (iv) When considering about installation, the DIB is more stable vortex generator when compared with baffle, rib, or winglet, which are placed on the duct walls. The heat transfer rate, pressure loss, and thermal performance of the DIB and V-shaped vortex generators [9] are very close