FLOW AND HEAT TRANSFER CHARACTERISTICS OF AIR IN SQUARE CHANNEL HEAT EXCHANGER WITH C-SHAPED BAFFLE: A NUMERICAL STUDY Frontiers in Heat and Mass Transfer

The purpose of the present work is to study flow configuration and heat transfer behavior in a square channel heat exchanger equipped with C-shaped baffle. The influences of flow attack angle and baffle size on flow and heat transfer characteristics are considered for the laminar flow regime with the Reynolds number around 100 – 2000. The numerical study with finite volume method is selected for the present investigation. The SIMPLE algorithms is opted to solve the numerical problem. The numerical results are concluded in terms of flow and heat transfer mechanisms in the tested section. The thermal performance analysis; Nusselt number ratio (Nu/Nu 0 ), friction factor (f/f 0 ) and thermal enhancement factor (TEF), are also summarized. The numerical model of the smooth square channel is validated with the correlations on both Nusselt number and friction factor. The numbers of grid cell for the computational domain are also compared. The numerical results reveal that the C-shaped baffle in the tested section leads to the appearance of the thermal boundary layer disturbance on the channel walls that the important cause for heat transfer rate and thermal efficiency enhancements. The maximum TEF of the square duct with C-shaped baffle is around 3.89. In addition, the optimum gap spacing value for the square channel inserted with C-shaped baffle is around 5%.


INTRODUCTION 1
The enhancements of the heat transfer rate and thermal performance in various types of heat exchangers or engineering devices had been done by two methods; active and passive methods. In the present research, the passive method is focused. The passive method is not required the additional power to augment heat transfer rate. The passive method is to generate the vortex flow, swirling flow, impinging flow in the heating section and also increases the turbulent mixing of the tested fluid. These phenomena is the reason for heat transfer and thermal efficiency enhancements. The device, which generates the vortex flow/swirling flow, is called vortex generators or turbulators. Rib, baffle, conical ring, wing, winglet, etc., are types of the vortex generators.
Many researchers reported about the heat transfer rate, pressure loss and thermal performance in heat exchanger with various vortex generators. For examples, Boonloi (2014) numerically studied the effects of 20 o V-rib on flow and heat transfer in a square duct. The influences of rib height and flow direction were considered for the Re = 100 -2000. Boonloi (2014) found that the best thermal performance is around 4.2. Jedsadaratanachai and Boonloi (2014) studied the thermo-hydraulic performance in the heat exchanger square channel with 30 o double Vbaffle. They concluded that the best thermo-hydraulic performance is around 3.2. The numerical study on flow and heat transfer in a circular tube with 45 o V-baffle was reported by Jedsadaratanachai et al. (2015). The effects of flow direction and baffle height on thermal performance were considered for Re = 100 -2000. They summarized that the best thermal performance of the heat exchanger tube with V-baffle is around * Corresponding author. Email: kjwithad@kmitl.ac.th 3.2. Kumar and Layek (2018a) presented the Nusselt number and friction loss for a twisted rib roughened rectangular duct by liquid crystal technique. Kumar et al. (2017a) experimentally investigated on Nusselt number and friction factor for discretized broken V-baffle in a solar air channel. The width to height ratio, relative baffle gap distance, relative baffle gap width, relative baffle height, relative baffle pitch and flow attack angle of the baffled channel were considered. Kumar et al. (2017b) experimentally examined the heat transfer rate and pressure loss augmentations in a solar channel with discretized broken V-pattern baffle. They pointed out that the optimal thermal performance for the channel with V-baffle is around 3.14. Kumar and Layek (2018b) experimentally examined the influences of relative roughness pitch, inclination angle and twist ratio on flow and heat transfer in a solar air heater channel for Re = 3500 -21,000. The thermal performance analysis for laminar flow in a square channel with 30 o V-baffle was presented by Boonloi and Jedsadaratanachai (2014). They claimed that the V-baffle in the channel gives thermal enhancement factor around 4.25. Boonloi and Jedsadaratanachai (2016) numerically presented the discrete combined V-baffle and V-orifice in a square channel on convective heat transfer for Re = 5000 -20,000. They detected that the increment on heat transfer rate is around 2.8 -6.0 time higher than the plain channel. Gormaa et al. (2017) reported the enhancement of cooling characteristics for a triple concentric tube fitted with rib. The parameter optimization of a solar air collector with holes on baffle was reported by Hu et al. (2018). Li et al. (2018) simulated the thermal performance in a channel with multi Vbaffle for turbulent flow regime. Menasria et al. (2017) numerically studied the thermo-hydraulic performance in a solar air heater duct fitted with novel rectangular baffle with high aspect ratio. They found that the

Frontiers in Heat and Mass Transfer
Available at www.ThermalFluidsCentral.org Frontiers in Heat andMass Transfer (FHMT), 13, 23 (2019) DOI: 10.5098/hmt.13.23 Global Digital Central ISSN: 2151-8629 2 heat transfer and friction factor in the solar air heater duct are around 2.16 and 15.95 times above the smooth duct, respectively. They also reported that the greatest thermo-hydraulic performance factor in the solar air heater duct is around 0.857. Promvonge (2010), Promvonge and Kwankaomeng (2010) and Promvonge et al. (2012) claimed that the baffle or thin rib has high effectiveness to enhance heat transfer rate in the heating system, especially, V-shaped baffle and inclined baffle.
In the present work, the C-shaped baffle is created. The C-shaped baffle are modified from the inclined baffle with inline arrangement (placed on the upper and lower walls of the channel). The gap spacing between outer edges of the baffle and the channel walls is generated to reduce pressure loss in the tested section and also helps to induce the turbulent mixing of the fluid flow. The numerical investigation with commercial code is selected for the present work. The numerical result can describe the mechanisms in the tested section. The understanding on mechanisms in the tested section is important factor to improve the heat exchanger. The influences of the baffle height, flow attack angle, gap spacing for the C-shaped baffle on heat transfer rate, pressure loss and thermal performance are studied. The laminar flow regime with the Reynolds number in the range 100 -2000 is considered. The numerical results for the square channel heat exchanger equipped with C-shaped baffle are reported in terms of streamline, longitudinal flow, temperature contour and local Nusselt number contour. The numerical results are also concluded in forms of Nusselt number ratio (Nu/Nu0), friction factor ratio (f/f0) and thermal enhancement factor (TEF).

Physical domain
The physical domain for the square channel inserted with C-shaped baffle is presented as Figs. 1 and 2 for g/H = 0 (no gap spacing) and g/H = 0.15, respectively. The influences of baffle height, flow attack angle and gap spacing on heat transfer and flow structure are investigated numerically for the laminar regime (Re = 100 -2000). The baffle height represents with "b", while b/H or BR is called "blockage ratio". The gap spacing between the outer edges of baffle and the channel wall represents with "g". g/H or GR is named "gap spacing ratio". The blockage ratio is varied in the range 0.05 -0.30, while the gap spacing ratio is varied in the range 0 -0.30. The distance between the baffle is "P". The pitch spacing ratio or P/H is fixed at 1 in all investigated cases. The flow attack angles of the C-shaped baffle is separated into 2 groups; 30 o and 45 o .

Assumption, boundary condition and initial condition
The flow and heat transfer in the heating section are assumed to be steady in three dimensions. The flow is incompressible and laminar with the Reynolds number around 100 -2000 (at the inlet condition). The thermal properties of the tested fluid (air) are constant at the average bulk mean temperature. The convective heat transfer is considered, while the radiation and natural convection are disregarded. The body forced and viscous dissipation is ignored. The periodic condition (Patankar et al. (1998)) on flow and heat transfer is set for the inlet and outlet of the computational domain. The C-shaped baffle is set as insulator. The uniform temperature around 310K is set for all sides of the square channel walls. The temperature of the tested fluid is set around 300K at the inlet. The commercial program (FLUENT) is selected to solve the present problem.

Mesh development
The computational models of the duct heat exchanger inserted with the C-shaped baffle with mesh are plotted as Figs. 3a and b, respectively, for g/H = 0 and 0.15, at b/H = 0.15 and α = 45 o . The hexahedron mesh is applied for the numerical model in all investigated cases. The comparison for the number of grid system is done in this part. The five sets of grid; 80000, 120000, 160000, 240000 and 360000, for the case BR = GR = 0.15 with α = 30 o are compared (see Fig. 4). As the result, the grid around 120000 -360000 gives similar values for both Nusselt number and friction factor. Therefore, the grid around 120000 is selected for all investigated cases when considered both time for investigation and accuracy result.  (Cengel and Ghajar (2015)). The deviations of the numerical results are within ±0.03% on both Nusselt number and friction factor. Therefore, it can be concluded that the numerical model has more reliability to predict flow and heat transfer in the tested channel.

MATHEMATICAL FOUNDATION AND NUMERICAL METHOD
The mathematical foundation and numerical method for the present work are referred from Promvonge et al. (2012). The numerical problem is sloved by the commercial code (finite volume method with SIMPLE algorithm). The important variables in term of dimensionless for the present research are Reynolds number, friction factor, Nusselt number and thermal enhancement factor. The air velocity is reported in term of the Reynolds number, which can be printed as Eq. 1.
The pressure loss across the tested section is concluded in terms of the friction factor value. Eq. 2 shows the calculations of the friction factor across the heating section.
The heat transfer rate is presented with the local Nusselt number (Nux) and average Nusselt number (Nu). The calculations of the local Nusselt number and the average Nusselt number are illustrated as Eqs. 3 and 4, respectively. The thermal performance in the heat exchanger square channel is shown with the thermal enhancement factor or TEF. The TEF can determine as Eq. 5.

NUMERICAL RESULT AND DISCUSSION
The numerical results are reported in terms of flow structure and heat transfer characteristics in the heat exchanger square channel inserted with C-shaped baffles. The flow and heat transfer structures can help to describe the mechanisms in the heating system and the change of the boundary layer. The understanding of the mechanisms in the testing section is an important data to support the development of the heat exchanger. The plots of average Nusselt number, friction factor and thermal enhancement factor are also presented.

Mechanisms on flow and heat transfer in the tested section
The streamlines in y-z planes and longitudinal vortex flow are depicted to describe the flow structure in the tested channel. Figs wall can change the flow configuration in the test section. The number of the vortex flow has change due to some parts of the air flow passes the gap spacing. The increment for the number of the vortex flow helps to a better fluid mixing, but the strength of the vortex flow may decrease. Moreover, the flow direction of the vortex flow reverses when changing the gap value. The change of the flow direction may effect for the change of the peak position for heat transfer rate on the channel wall. This situation will discuss from the local Nusselt number on the heat transfer surface. In conclusion, the optimum gap spacing may bring the augmentations on both heat transfer rate and thermal performance in the heat exchanger square channel.    To check the change of the thermal boundary layer on the channel walls, the temperature distribution in y-z planes is plotted. The temperature contour also describes the fusion of the tested fluid in the test section. Figs. 9a, b, c, d, e, f and g show the temperature distribution in transverse planes of the square channel heat exchanger placed with 30 o C-shaped baffle at BR = 0.15, Re = 800 for GR = 0, 0.05, 0.10, 0.15, 0.20, 0.25 and 0.30, respectively. Generally, the red layer of the hot fluid is found near the channel wall, while the blue contour of the cold fluid is detected at the center of the square channel. When inserting the C-shaped baffle in the test section, the contour of the temperature has change. The red layer seems to be thinner, while the blue contour distributes from the   For BR = 0.05, α = 30 o and GR = 0, the peak of heat transfer regime is clearly found at the left sidewall of the channel, while the poor heat transfer region is detected at the right sidewall of the channel. In the range 0.05 ≤ GR ≤ 0.10, the red contour for the local Nusselt number of the left sidewall decreases, but increases for the upper-lower walls. The heat transfer rate of the right sidewall is enhancing when augmenting the GR  17 values. It is clearly seen in the figure that the highest heat transfer regime appears at the right sidewall of the square channel for the GR = 0.30. The similar pattern of the heat transfer behavior is found in all BR, α and Re values.

Thermal efficiency analysis
The thermal performance analysis in the square channel heat exchanger placed with various parameters of the C-shaped baffle are plotted in terms of relations of the Nusselt number ratio (Nu/Nu0), friction factor ratio (f/f0) and thermal enhance factor (TEF) with gap spacing ratio. In general, the heat transfer rate and pressure loss in the test section increase when augmenting the Reynolds number for all investigated cases. The insertion of the C-shaped baffle in the heat exchanger system brings higher heat transfer rate than the smooth square channel (Nu/Nu0 > 1) due to the creation of the vortex flow, swirling flow, longitudinal vortex flow and the change of the thermal boundary layer. However, the pressure loss in the test section also increases greater than the smooth square channel (f/f0 > 1) when fitted the C-shaped baffle in the test section, especially, at high Re and BR values. For the 30 o C-shaped baffle with BR = 0.05, the heat transfer rate, friction loss are around 1.00 -5.50 and 1.00 -7.40 times above the smooth channel, respectively. The maximum TEF of the BR = 0.05 and α = 30 o is around 2.89. The 30 o C-shaped baffle with the BR = 0.10 gives the Nu/Nu0 and f/f0 around 1.00 -5.50 and 1.00 -11.60, respectively, while the optimum TEF is around 2.90. The heat transfer, friction loss around 1.30 -8.80 and 1.90 -20.00 times higher than the smooth channel with the maximum TEF around 3.30 are found at BR = 0.15 and α = 30 o . The BR = 0.20 and α = 30 o performs the heat transfer rate and pressure loss around 1.50 -12.40 and 2.90 -31.00 greater than the plain channel, respectively, with the peak of TEF around 3.85. The Nu/Nu0 of BR = 0.25 and 0.30 is around 1.80 -14.50 and 2.10 -16.50, respectively, while the f/f0 is around 2.50 -53.00 and 8.00 -94.00, respectively, at α = 30 o . The peak of thermal performance enhancement is around 3.90 at BR = 0.25, while around 3.60 at BR = 0.30 and α = 30 o .

CONCLUSION
Numerical predictions on flow topology and heat transfer behavior in the heat exchanger square channel placed with C-shaped baffle are performed. The influences of baffle height and position for placement in the channel are considered for the laminar flow regime with the Reynolds number around 100 -2000. The flow attack angles (α = 30 o and 45 o ) for the C-shaped baffle are also studied. The major findings of the present investigations can conclude as follows; The C-shaped baffle can produce the vortex flow or swirling flow through the test section in all investigated cases. The vortex flow disturbs the thermal boundary layer on the heat transfer surface that the cause for heat transfer rate and thermal performance augmentations. The better fluid mixing in the test section is also detected when inserting the Cshaped baffle in the test section.
The increment of the baffle height leads to higher heat transfer rate and pressure loss in the channel. The variation of the gap spacing value effects for the change of the heat transfer and flow patterns. The optimum gap value may support the enhancements of heat transfer rate and thermal efficiency. The difference of flow attack angles has no effect for heat transfer and flow configurations.
The best thermal performance is found at the BR of 0.20 and 0.15 for the flow attack angle of 30 o and 45 o , respectively. The suggestion gap spacing between baffle and channel wall is around 5%, which gives the optimum thermal enhancement factor for both attack angles.