1 Introduction

Most manufacturing processes release waste heat in various forms—hot solid wastes, hot air or gases, or hot water, depending on the process. Waste heat can be recovered and further used. There are various devices and tools that enable waste heat reuse. Heat exchangers have been widely used for many years. Generally, a heat exchanger allows the transfer of heat from one liquid to another, where the liquids do not necessarily mix. This type of equipment is crucial in a wide variety of industries and engineering systems. For example, in the oil industry, heat exchangers are used to heat raw oil, condense vapor in a distillation tower into liquid, or decrease the temperature of an oil or gas. They are widely used in the food industry for the thermal treatment of foods to concentrate them or to assure public health.

As there are various uses for heat exchangers, selecting an optimal heat exchanger is complicated and an unsophisticated user generally would require professional assistance to select a suitable model. Heat exchanger software and manufacturers often evaluate heat exchangers according to various factors, although pricing and manufacturing costs play an important role in decision making. Important factors that need to be considered include pressure limitations, thermal efficiency, temperature range, product composition, the pressure drop within the heat exchanger, required liquid flow rates, ease of cleaning, maintenance and repair, required materials of construction, future expansion, and materials of construction [1,2,3]. There are three common types of technique used to enhance the efficiency/performance of heat exchangers: (1) active methods, or techniques, that require external energy to aid in heat transfer (e.g., pulsation by cams [4], mechanical aids [5], surface and fluid vibration [6], suction or injection [7], and electrostatic fields [8]), (2) passive methods, or techniques, that modify the characteristics of the heat transfer channel (e.g., treated surfaces [9], rough surfaces [10], extended surfaces [11,12,13], swirl flow devices [14], and additives to fluids [15]), and (3) compound methods, or techniques, that combine both the active method and the passive method (e.g., rough surfaces with twisted tapes [16] and rough surfaces with fluid vibration [17]).

Passive methods have been applied extensively to improve heat transfer. Most studies examining them have dealt with the heat transfer characteristics of circular tubes, while rectangular channels have been scarcely reported. Changcharoen and Eiamsa-ard [18] investigated the flow pattern and heat transfer characteristics in a rectangular channel with a width-to-height aspect ratio of 6:1. The rectangular channel was equipped with detachable ribs placed on one side of the walls. The dependence of the Nusselt number on the Reynolds number was implicit, while an indirect association was observed for the friction factor. The ribs with a detached-clearance value (c/a) of 0.1 gave the maximum thermal efficiency at the lowest Reynolds number of 8000. Promvonge [19] found that incorporating multiple 60° V-baffle turbulators into a rectangular channel significantly improved heat transfer. Experiments were performed at various baffle pitch spacing ratios, (i.e., P/H = 1.0, 2.0, and 3.0) and baffle blockage ratios (i.e., e/H = 0.1, 0.2, and 0.3), while the transverse pitch remained unchanged at 2 H. The results showed that the Nusselt number increased with increasing Reynolds numbers. The optimal e/H and P/H ratios, where the maximum thermal enhancement factor (η = 1.87) took place, were 0.1 and 1.0, respectively, at a minimum Reynolds number. The effect of the aspect ratio of a rectangular channel on both heat and mass transfer was studied by Lee et al. [20]. Their study was carried out in a rectangular channel, which had two types of V-shaped ribs placed inside—multiple-stagger ribs with a 45° attack angle and 60° continuous ribs. The results showed that the aspect ratio had a significant impact on both heat and mass transfer, and the impact was even more pronounced for the continuous 60° V-shaped rib. The effect of the multiple twisted tape vortex generators on thermal and flow characteristics in a turbulent flow channel was studied by Eiamsa-ard [21]. A rectangular channel with a low free-spacing ratio (s/w) and a low twist ratio (y/w) has been proven successful in enhancing heat transfer. The pressure loss, however, has been found to increase.

A diversity of baffle geometrics (e.g., straight-shaped, V-shaped, and arc-shaped) and baffle arrangements, as shown in Fig. 1, has attracted a lot of attention in the heat transfer enhancement field for many years [1, 19,20,21,22,23,24,25,26,27]. To study the effects of the baffle on the local and average heat transfer coefficient and pressure drop, most of these studies have arranged the baffles perpendicular to the flow passage, i.e., placing the baffles straight up with respect to the x–y plane (the bottom surface of a channel), see Fig. 1a, b. The influences of the baffle angle orientation have been performed by varying the attach angle about the z-axis (pointing out of the paper), see Fig. 1c–f.

Fig. 1
figure 1

Configurations of eight different primary shapes: a rectangular ribs, b wires, c inclined baffles, d V-type baffles, e multiple V-baffles, f inclined single baffle and ribs, and g inclined continuous baffles

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In contrast to previous works, in this study, the baffles were mounted on the x–z plane (on two side-walls of a channel), see Fig. 1h, so that we could orient them either in parallel (θ = 0° or 180°) or perpendicular (θ = 90°) to the flow direction or even position them in-between (baffles are able to rotate about the y-axis). The study with most relevance to this work was by Khan et al. [27], see Fig. 1g). However, they utilized only a single inclined baffle combined with periodic ribs, and they had only a marginal change in attack angles (3.5°–7°), while our study used inclined baffles placed in series (continuous baffles) and allowed them to rotate with different attack angles from 0° to 180°. The differences in the numbers of baffles and attack angles will definitely result in dissimilar flow patterns and heat transfer rates. Furthermore, this current study distinguished itself by implementing the thermochromic liquid crystal (TLC) technique for surface temperature measurement without direct contact. This temperature measuring technique enabled us to determine the temperature of the entire heated surface, whereas it would likely have been very difficult for the conventional thermocouple method, as typically applied in the literature [20, 28], due to the constrained space and a need for numerous thermocouples [19, 23,24,25,26,27]. It is also important to note that by analyzing image processing the detailed temperature contours of the heated surface can be produced effectively. This study was aimed at evaluating the impacts of the attack angle of inclined baffles incorporated into a rectangular channel on heat transfer and pressure loss characteristics. Unlike previous studies, the baffles were differentiated by their configuration and capability to regulate any inclination from horizontal (θ = 0°, 180°) and vertical (θ = 90°). Instead of a conventional thermocouple technique, the TLC image processing technique was utilized to clarify the temperature distributions on the heated surface. The resulting Nusselt numbers, frictional factors, and thermal enhancement factors were examined for the Reynolds number ranging from 9000 to 24,000. For comparison, experiments for a bare channel were also performed.

2 Experimental Setup

2.1 Thermochromic Liquid Crystal

Being manageable, economical, reliable, and almost nonintrusive, the thermochromic liquid crystal (TLC) technique is becoming an increasingly interesting technique for measuring the surface temperature. It is highly sensitive and responsive to temperature by changing its color against the modified temperature. To measure the surface temperature, either direct placement of TLCs on a surface or suspension in the fluid is possible. The uniform, steady-state surface temperature method proposed by Abdullah et al. [29] and Grassi et al. [30] was applied for calibrating the TLCs in this study. The calibrated surface was heated to a selective temperature range of TLCs, while the color was quantified by a digital camera. An image processing program enabled us to interpret the color of each of the obtained entire color images for a known temperature and convert them to either a fraction of the individual three primary colors—red (R), green (G), and blue (B)—or RGB coordinates. Although all colors were a weighted combination of three primary colors, it was more convenient to associate them with another three characteristics—hue, saturation, and value (HSV coordinates). However, only hue (H) representing the spectral colors could transform these primary colors to the corresponding temperature. A relationship of H and RGB can be mathematically formulated as shown in Eq. 1 [30]:

$$H = \frac{{\cos^{ - 1} \left[ {\frac{{R - \frac{G}{2} - \frac{B}{2}}}{{\sqrt {\left( {R - G} \right)^{{}} + \left( {R - B} \right)\left( {G - B} \right)} }}} \right]}}{2\pi },\quad H,R,G,B \in \left[ {0.1} \right]$$
(1)

Figure 2 shows the temperature varying with the H value. By least-squares fitting with a third order polynomial, a T–H correlation is available as follows:

Fig. 2
figure 2

Hue–temperature calibrations of TLC sheets (TLCs were heated or cooled)

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$$T_{\text{w}} = 0. 0 0 0 2 6 2\,H^{ 3} - 0. 1 1 2 7 1 5\,H^{ 2} + 1 6. 1 6 7 9 7 3\,H - 7 4 4. 0 4 1 4 8 1$$
(2)

2.2 Roughness Geometry and Range of Parameters

Table 1 contains the experimental design and operating conditions. The roughness parameters associated with the inclined baffles were characterized by the baffle height (e), pitch length (P), and channel height (H). The pitch length to baffle height ratio (P/e) in this study was equal to 10, based on the optimum value reported in previous work [20, 22]. The baffle height to channel height ratio (e/H) was set to be 0.15 for efficient heat transfer [20, 31]. Figure 3 shows the arrangement of inclined baffles (side view) placed inside the rectangular channel. The baffles could freely rotate in a vertical plane about the y-axis (pointing out of the paper), allowing the attack angle to be varied from horizontal (θ = 0°, 180°) to vertical (θ = 90°) with a 15 degrees instrument. The configuration of the baffle was designed by a special engineering program (solidworks). The baffles, made of polylactic acid (PLA) plastic, were molded by a 3D plastic printer.

Table 1 Dimensionless quantities and other parameters used in test section experiments
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Fig. 3
figure 3

Geometry of rectangular channel flow with inclined baffles at various attack angles

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2.3 Experiment Apparatus and Procedure

The experimental apparatus, schematically shown in Fig. 4, consisted of three parts—rectangular channel, image processing, and analysis and computerized data acquisition sections. A rectangular channel was made of 10 mm thick acrylic with 40 mm (width) × 150 mm (height) × 3500 mm (length). The channel contained inlet, test, and outlet sections with lengths of 2000 mm, 900 mm, and 600 mm, respectively. The unheated inlet section had a length of 2000 mm, which was quantified from the correlation developed by Ower and Pankhurst [32], to ensure the fully developed turbulent flow before entering the heated test section. The test section bottom wall was electrically heated under a constant heat flux condition by the controlled heating elements. The electrical power supplied was held constant at 60 W throughout the test period. The entire heated test section was well insulated to minimize heat loss. Air flow was supplied through a high-pressure blower equipped with a frequency invertor and measured by a well-calibrated orifice plate.

Fig. 4
figure 4

Schematic diagram of experimental apparatus

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Three resistant temperature detectors (RTDs) were mounted at the test section inlet and another eight were mounted at the outlet for measuring the inlet and outlet air temperature. Pressure drop, used to determine the friction factor, was determined by a digital differential transmitter. Both temperature and pressure drop were continuously monitored via a computerized data acquisition system. The bottom surface of the heated test surface section was instrumented with TLCs to quantify the temperature distribution on the heated surface. The TLCs used in this study were manufactured by Omega Engineering Co., Ltd., and they were designed to operate in a temperature range of 30–35 °C. The clear acrylic walls of the test section were visible to a digital camera which communicated with a computer. The obtained images were then analyzed by an image processing program.

The uncertainties of average velocity (U), volumetric air flow rate (V), static pressure (P), and temperature (T), which were estimated based on ANSI/ASME [33], were found to be within ± 5.2%, ± 4.7%, ± 4.2%, and ± 0.5%, respectively. The uncertainty of the non-dimensional parameters of Reynolds number, Nusselt number, and friction factor were within ± 4.6%, ± 7.5%, and ± 5.9%, respectively.

Prior to running the experiments, all measuring devices were carefully calibrated and the system was checked for leakage. The experiments were performed at a constant heat flux. All experimental data were taken under steady-state conditions that had remained stable for over 60 min. The recorded data are listed as follows:

  1. (i)

    Temperature of the surface of the test channel;

  2. (ii)

    Inlet and outlet temperatures of air;

  3. (iii)

    Pressure drop across the test section;

  4. (iv)

    Voltage and current through the electrical heating plate.

3 Theoretical Aspects

The recorded data were used to evaluate the heat transfer coefficient (h), friction factor (f), and the thermal enhancement factor (η).

The Reynolds number, based on the hydraulic diameter of the test section, was evaluated from [34]:

$$Re = \frac{{V_{\text{i}} D_{\text{h}} }}{v}$$
(3)

where Vi is the inlet air velocity, Dh is the hydraulic diameter of test channel, and v is the kinematic viscosity of air.

The mass flow rate was calculated by [34]:

$$\dot{m} = \rho V_{\text{i}} A_{\text{c}}$$
(4)

where ρ is the bulk density of air at a specific temperature and Ac is the cross-sectional area of a rectangular channel.

The total heat supplied by the electric heating plate was calculated as

$$Q_{\text{e}} = VI$$
(5)

where V and I are the supplied voltage and current to the electric heating plate, respectively.

The actual heat supplied to the test equipment by the electrical heating plate (Qact) was

$$Q_{\text{act}} = Q_{\text{e}} - Q_{1}$$
(6)

The heat loss (Ql) through the insulation evaluated from the average wall temperatures and the ambient air temperatures was approximately 1–3% of the total heat supplied from the heat source.

The heat transferred to air flow was evaluated by [35]

$$Q_{\text{abs}} = \dot{m}C(T_{\text{o}} - T_{\text{i}} )$$
(7)

where \(\dot{m}\) is the mass flow rate, C is the specific heat capacity of air, and Ti and To are the inlet and outlet air temperatures, respectively.

The difference between the heat supplied (Qact) and the heat absorbed by the fluid (Qabs) was less than 5% in all experiments. The heat transfer rate (Q) was estimated as the mean value of the actual heat supplied by the electric heating plate and the heat absorbed by the fluid as

$$Q = \frac{{Q_{\text{act}} + Q_{\text{abs}} }}{2}$$
(8)

Heat flux can be expressed as

$$q = \frac{Q}{WL}$$
(9)

where W and L are the width and length, respectively, of the electric heating plate.

The local convective heat transfer coefficient can be estimated from

$$h_{\text{x}} = \frac{q}{{(T_{\text{wx}} - T_{\text{bx}} )}}$$
(10)

where Tbx and Twx are the local bulk air and thermochromic liquid crystal surface temperatures, respectively.

The local bulk air temperatures were calculated by an energy balance:

$$T_{\text{bx}} = T_{\text{i}} + \frac{q(wx)}{{\dot{m}C}}$$
(11)

where w is the wetted perimeter and x is the local distance of the test section.

The local Nusselt number can be expressed as

$$Nu_{\text{x}} = \frac{{h_{\text{x}} D_{\text{h}} }}{k}$$
(12)

where k is the thermal conductivity of air.

The average local Nusselt number along the z-axis at any x-axis was called spanwise Nusselt number.

The average heat transfer coefficient was calculated from [35]

$$h = \frac{q}{{(T_{\text{w}} - T_{\text{b}} )}}$$
(13)

where Tb and Tw are the mean bulk air and thermochromic liquid crystal surface temperatures, respectively.

The average Nusselt number can be evaluated using the relationship [35]

$$Nu = \frac{{hD_{\text{h}} }}{k}$$
(14)

The friction factor was evaluated for a measured pressure drop from Darcy’s formula [34]:

$$f = \frac{\Delta P}{{\left( {\frac{L}{{D_{\text{h}} }}} \right)\left( {\rho_{\text{b}} \frac{{V^{2} }}{2}} \right)}}$$
(15)

where ΔP is the pressure drop across the test section.

The thermal enhancement factor (η) is defined as the ratio of the heat transfer coefficient of the channel with inclined baffles (h) to that of the channel with no baffles (h0). The thermal enhancement factor under a constant pumping power criterion is

$$\eta = \frac{h}{{h_{0} }} = \left( {\frac{Nu}{{Nu_{0} }}} \right)\left( {\frac{f}{{f_{0} }}} \right)^{ - 1/3}$$
(16)

where Nu and f are the Nusselt number and friction factor of the channel with inclined baffles, respectively. Nu0 and f0 are the Nusselt number and friction factor of the bare channel with no baffles, respectively.

4 Experimental Results

4.1 Channel Without Baffles

To validate the experimental measurements, preliminary experiments were performed in a bare channel without any baffles. The resulting Nusselt number and friction factor were then compared to those calculated from Dittus–Boelter and Blasius correlations [35], respectively.

The Dittus–Boelter correlation (Eq. 17) is valid for Re > 7000 and 0.5 < Pr < 120:

$$Nu = 0.023Re^{0.8} Pr^{n}$$
(17)

where n = 0.4 for heating and n = 0.3 for cooling.

The present work involved heating, therefore, the correlation can be re-written as

$$Nu = 0.023Re^{0.8} Pr^{0.4}$$
(18)

The Blasius’s correlations are

$$f = 0.085Re^{ - 0.25} \quad {\text{for}}\;Re < 20,000\;{\text{and}}$$
(19)
$$f = 0.184Re^{ - 0.2} \quad {\text{for}}\;Re \ge 20,000.$$
(20)

Figures 5 and 6 show a validation of our measurements through a good agreement between the Nusselt number and the friction factor experimented in a bare rectangular channel and those calculated from the well-known correlation (Eqs. 18, 19, and 20). The experimental results deviated from the correlation by ± 6% for the Nusselt number and ± 4% for the friction factor.

Fig. 5
figure 5

Comparison of experimental and estimated values of the Nusselt number for a bare channel

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Fig. 6
figure 6

Comparison of experimental and estimated values of friction factor for a bare channel

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4.2 Distribution and Spanwise Nusselt Number

Nusselt number distributions over the heated bottom wall of a rectangular channel with inclined baffles at various attack angles (from 0° to 165°) are depicted in Fig. 7. The experiments for a rectangular channel with no baffles were also performed, and the results are shown in the same figure for comparison. The Reynolds number was held constant at 24,000 for all the results shown in the figure. Implicitly, the intermediate attack angles (45°–135°) were efficient in promoting a high local Nusselt number (in the x-direction) compared to the low and high attack angles (i.e, 0°–30° and 150°–165°, respectively). It is possible that the intermediate attack angles contributed a greater turbulence due to a high degree of blockage. This is in accordance with the results depicted in Fig. 8 showing that a strong flow disturbance and fluctuation took place at this angle range. Moreover, such a flow could effectively disturb the thermal boundary layer making it thinner, thereby reducing the resistance to heat transfer. As a result, the Nusselt number was greater. The maximum heat transfer coefficient enhanced by the turbulent flow in the vicinity of the reattachment point behind the baffles was also reported by Changcharoen et al. [18], Prasad et al. [22], and Karwa [23]. Such findings agree closely to the numerical results reported by Boonloi and Jedsadaratanachai [1] and Yongsiri et al. [24]. Alternatively, the flow across the baffles with low attack angles could have been subjected to a weaker disturbance.

Fig. 7
figure 7figure 7

Nusselt number field and spanwise Nusselt number of a channel with inclined baffles at a Reynolds number of 24,000: a bare channel and attack angles of b 0°, c 30°, d 60°, e 90°, f 120° and g 150°

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Fig. 8
figure 8

Distribution of local Nusselt number in the rectangular channel with inclined baffles at various attack angles

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4.3 Heat Transfer and Pressure Loss

The variation of the Nusselt number with the attack angle and with the Reynolds number are presented in Fig. 9a, b, respectively, to show the impact of inclined baffles on heat transfer. Additionally, to represent the improved heat transfer, the relative Nusselt number, defined as the ratio of the Nusselt number of a baffle integrated channel to the Nusselt number of a bare channel (Nu/Nu0), was plotted against the Reynolds number (Fig. 9c). In Fig. 9a, at a given Reynolds number, the Nusselt number associated with the intermediate range of the attack angle (45°–135°) was higher than those obtained from the two extreme conditions (i.e., 0°–30° and 150°–165°). Among the intermediate angles, the 60° and 120° angles yielded the highest Nusselt numbers. In Fig. 9b, the Nusselt number tended to increase with the Reynolds number. This was due to the intensified flow turbulence and consistent with results found elsewhere [18,19,20, 23, 36]. Although a direct relationship between the Nusselt and the Reynolds numbers is clear for all the attack angles (as shown in Fig. 9b), an inverse relationship between the relative Nusselt number (representative of improved heat transfer) and the Reynolds number can be seen in Fig. 9c. The maximum improvement in heat transfer at particular attack angles coincided with a Reynolds number of 9000 and ranged between 1.26 and 1.59 times of the bare channel. The most efficient heat transfer enhancement was achieved at attack angles of 60° and 120° with the respective relative Nusselt numbers of 1.59 and 1.57 times of the bare channel.

Fig. 9
figure 9

Effect of attack angle of inclined baffles on the Nusselt number: aNu versus θ, bNu versus Re, and cNu/Nu0 versus Re

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To explore the effect of the inclined baffles on the pressure drop in a rectangular channel, the friction factor (f) and relative friction factor (f/f0) were plotted against the attack angle (θ) and the Reynolds number (Re), as shown in Fig. 10a–c. As discussed above, a greater air flow blockage accompanied by high turbulence for intermediate attack angles (45°–135°) enhanced heat transfer, with a concurrent adverse effect on the frictional losses, as shown in Fig. 10a. As expected, the friction factor continued to decline as the Reynolds number increased, as is shown in Fig. 10b. A common agreement has also been addressed in the literature [10, 13, 14, 21, 23]. This contributed to an increased flow turbulence. The impact of the inclined baffles on the pressure drop over that of a bare channel is also seen in Fig. 10c. All the relative friction factors (f/f0) were in the range of 2.48–3.19, much greater than unity even for θ = 0°. At the minimum Reynolds number, 9000, each intermediate attack angle had a slightly different friction factor. This may have been due to the lower turbulence associated with these smaller Reynolds numbers not being high enough to significantly affect the pressure drop at these angles. For comparisons with similar Reynolds numbers, the obtained friction factors in this work (2.48–3.19) were lower than those obtained from the transverse rib (2.68–2.94), inclined rib (3.02–3.42), V-up continuous rib (3.40–3.93), and V-down continuous rib (3.32–3.65), as reported by [23]. The present inclined baffle, however, showed results superior to the V-up discrete rib (2.35–2.47) [23] and the V-down discrete rib (1.96–2.58) [23, 37].

Fig. 10
figure 10

Effect of attack angle of inclined baffles on the friction factor: af versus θ, bf versus Re, and cf/f0 versus Re

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4.4 Thermal Enhancement Factor

To investigate the synergetic effect of the attack angle on heat transfer and friction loss, the thermal enhancement factor (η), defined in Eq. (16), was plotted against the attack angle, as shown in Fig. 11a. Only at the intermediate attack angles (45–135°) was the thermal enhancement factor greater than unity. At these angles, there was more gain from heat transfer than loss from friction. The thermal enhancement factor reached its zenith (about 1.11) at the attack angles of 60° and 120° and at a Reynolds number of 9000. Figure 11b reveals that the thermal enhancement factor tended to decrease a little as the Reynolds number moved further from 9000.

Fig. 11
figure 11

Effect of attack angle of inclined baffles on the thermal enhancement factor: aη versus θ and bη versus Re

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Table 2 summarizes the maximum thermal enhancement factors reported in the relevant studies and the one obtained from the present study for comparisons. The current inclined baffle was more effective than the rectangular rib by 22% and the triangular rib by 7%. However, it was likely to be inferior to others by 10–25%, depending on the rib type.

Table 2 Comparison of different roughnesses
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5 Conclusions

The following conclusions can be drawn from the results of this study:

  1. 1.

    Introducing inclined baffles into a rectangular channel resulted in the fluctuation of the Nusselt number, as reflected by the local Nusselt number distribution in the direction of flow over the heated bottom of the channel. The fluctuations were more noticeable at the intermediate attack angles (45°–135°) than at the lower and higher angles (0°–30° and 150°–165°, respectively);

  2. 2.

    As a consequence of high blockage and turbulence, the baffles at the intermediate attack angles produced a higher pressure drop, but a markedly increased heat transfer;

  3. 3.

    Among the intermediate attack angles, 60° yielded the highest heat transfer rate, which was 1.59 times as much as that obtained from a bare rectangular channel;

  4. 4.

    Only the intermediate attack angles produced thermal enhancement factors greater than unity. The thermal enhancement factor represents the combined effects of heat transfer and frictional loss, implying the thermal advantage of using these inclined baffles although a larger pressure drop occurred. The maximum thermal enhancement factor of 1.11 took place when θ = 60° and at a Reynolds number of 9000;

  5. 5.

    The TLC technique employed in this work has been proven powerful and effective for quantifying the temperature distribution of the heated surface.