Assessment of the Thermo-Hydraulic Efficiency of an Indoor-Designed Jet Impingement Solar Thermal Collector Roughened with Single Discrete Arc-Shaped Ribs

Abstract

This study illustrates the impact of single discrete arc-shaped ribs (SDASR)-type artificial roughness on the performance of a jet impingement solar thermal collector (JISTC). The impact of parametric variations of SDASR on the Nusselt number $(N{u}_{sdr})$, friction factor $(f_{sdr})$, and thermohydraulic performance $({\eta }_{sdr})$ is examined. The spacer length ($S_{sdr}$) of the SDASR was changed from 0 mm to 300 mm in stages of 100 mm during the experiment. The fixed parameters of the SDASR were a relative discrete distance $\left(D_d/L_v\right)$ of 0.67, relative discrete width $\left(g_w/H_r\right)$ of 0.87, relative rib height $\left(H_r/H\right)$ of 0.047, relative rib pitch $\left(P_r/H\right)$ of 1.7, angle of an arc $\left({\alpha }_{sdr}\right)$ of 60°, jet diameter ratio $\left(D_j/D_{hy}\right)$ of 0.065, streamwise pitch ratio $\left(X/D_{hy}\right)$ of 1.72, and spanwise pitch ratio $\left(Y/D_{hy}\right)$ of 0.82. The Reynolds number $\left(Re\right)$ was altered from 3000 to 19,000. The $N{u}_{sdr}$ and $f_{sdr}$ of a JISTC with a roughened absorber plate was found to be enhanced by 5.25 and 5.98 times as compared to an STC without artificial roughness. The optimal findings of $N{u}_{sdr}$, $f_{sdr},$ and ${\eta }_{sdr}$ were achieved at $S_{sdr}$ = 0 mm. The maximum value of the ${\eta }_{sdr}$ obtained at $S_{sdr}$ = 0 mm was 2.9.

1. Introduction

The consumption of energy has been rising exponentially due to the revolution in manufacturing sectors, industrial sectors, and population growth worldwide. This need for energy is fulfilled by using petroleum, natural gas, coal, etc. Effective and efficient use of energy resources is the requirement of the present era. A flat STC is basically a heat exchanger which transfers the radiant energy of the incident sunlight to the sensible heat of a working fluid (liquid or air). It is used for space heating, solar crop drying, seasoning of timber, curing of industrial products, etc. The TP of an STC is generally poor because of low $h_c$ among the absorber pate and the moving fluid (air) which rises the absorber plate temperature, leading to larger heat losses resulting in poor TP of such collectors. In order to enhance the TP of such collectors, heat has to be transferred efficiently.

Various heat transfer augmentation methods (HTAM) being used to raise HTR in heat exchangers have been described in studies [1,2,3,4]. Various techniques for the optimization of geometrical parameters have been proposed [5]. Out of various HTAM, an impinging jet raises HTR significantly. Turbulence promoters such as impinging jet and obstacles have been used extensively to improve HTR. The impinging fluid jets (IMFJ) are used for different manufacturing functions, and a variety of jets are commonly used to attain a stable high HTR on the entire surface. Provision of blockage on the tested plate led to enhancement in the performance of solar air heater (SAH). The controlled IMFJ has been used in many fields, such as paper, gas turbine, textile, food, and low and high temperature surfaces. Various factors influence the HTR in the methods of multiple jet impingements. The solar receivers operate under the equivalent principle, dissipating solar energy and effectively transmitting heat energy to the fluid [6,7,8]. The IMFJ effectively employed partial air gaps and caused higher HTR. Primarily through the highest flow speed, the HTR provided by the IMFJ is three times greater than those produced by traditional convection cooling equipment. IMFJ is utilized in industrial fields such as plane ventilation, paper materials, etc. Many studies on the HT and friction factor characteristics have been performed [9,10,11].

Aboghrara et al. [12] designed an SAH to explore the influence of jet impingement on the corrugated heated plate by altering the mass flow rate of the air. They observed that the thermal efficiency of the heated plate rises with a rise in mass flow rates of air because of the disturbing of the laminar sub-layer that produces elevated turbulence of air, which results in more heat transfer. Thermal efficiency of the designed SAH was found to be fourteen percent more as compared to the smooth heated plate. Roy et al. [13] examined the $N{u}_{rs}$ and $f_{rs}$ of a jet impingement SAH with an inclined surface. The Reynolds number was varied from 500 to 20,000 to analyze the $N{u}_{rs}$ and $f_{rs}$ of SAH. Chauhan et al. [14] studied the thermo-hydraulic performances of JISTC. During the investigation, the $Re$, $X/D_{hy}$, $Y/D_{hy}$, and $D_j/D_{hy}$ were varied. The results showed that the maximum efficiency of 70% was attained for a JISTC compared with a smooth STC. Babic et al. [15] developed a new cooling approach with a grinding cooling method. The grinding method mostly depends on water and air. In this process, a small amount of water is injected into the air jet, which further hits the grinding wheel and provides the cooling, whose results are better than those of the conventional coolants. A high-speed mist jet is a more effective and inexpensive way to clean the wheel and lessen the specific energies. Roger et al. [16] numerically examined the system with multiple air jets cooling for solar thermal applications. The multiple air jets impinge on the concave window surface of transparent window glass to acquire cooling. Symmetric arrangement with six and nine nozzles uniformly dispersed on the window circumference was evaluated. The findings show that the multiple air-cooling jet system with periodically modulated airflow has superior performance. Caliskan et al. [17] studied the HT characteristic of the circular jet impingement on the surface with V-SR and CD-SR ribs. Five surfaces with distinct rib height were investigated, and their influence on the HT along the wall was explored. The findings of impinging jet with ribs roughness were compared with the findings of conventional SAH. The outcomes indicated that the maximum HTR increase of 4.26% was attained with the V-SR arrangement. Chang et al. [18] explored the impact of rib roughness parameters with a circular jet on a heat transfer rate. The Reynolds number varied from 7000–15,000. The influence of the parameters on the HTR was further used to evaluate the efficiency of rib roughness within the 2D array of the circular jet. Yan et al. [19] analyzed the HT characteristics of the rib-roughened surface by using impinging elliptical jets. The experiment was conducted to explore the impact of angled ribs. The results show that with 45° V-ribs, a maximum heat transfer was obtained as compared with other angles of the ribs. Xing et al. [20] studied the impact of jet impingement with micro-rib roughness on the HT characteristics. The parameters considered during the investigation were cross-flow schemes, jet-to-plate spacing, and $Re$. The jet-to-plate distance of 3 resulted in the highest HT coefficients for the flat as well as the micro-rib-roughened plate. Goodro et al. [21] explored the impact of the hole distance on the $h_c$. In this experiment, the range of $Re$ was from 8200 to 32,500, whereas the range of the Mach number was from 0.1 to 0.6. Spacing of the holes was either 8D or 12D, made by impinging jets. The results showed that the Mach number significantly affects the heat transfer coefficient. The findings suggested that the HT for both 8D and 12D spacing of holes increases with the increase in the Mach number. Huber et al. [22] experimentally compared the HT to the perimeter and center jet confined using an impinging array of air jets. Contour plots were used to observe the difference between local $N{u}_{rs}$ distribution for perimeter and center jets. The results indicated that the contour for a constant Nusselt number for the perimeter jets had an oval shape. There was only a very small difference (15%) between the perimeter and center jet contours. Chambers et al. [23] proposed a computational and experimental study to enhance the cooling performance in the high cross-flow channel by designing elliptical and circular impingement holes. These holes increased the infiltration of the impinging jet inside the coolant channel. The findings suggested that the $N{u}_{rs}$ rose by 16% in the coolant passage (halfway downstream). For the first four holes, the $N{u}_{rs}$ increased by 28 to 77% under the condition that no extra cross-stream was present in the passage. Lewis et al. [24] optimized the rough surfaces’ thermohydraulic performances with new efficiency parameters. The roughness function, which is the function of momentum transfer and heat transfer, is the most important parameter that influences the TP of the rough surfaces. Matheswaran et al. [25] experimentally examined the exergy efficiency of an STC with a single-pass double duct jet. The experiment was conducted for different ranges of geometrical parameters, such as $X/D_{hy}$ = 0.435–1.739, $Y/D_{hy}$ = 0.435–0.869, and $D_j/D_{hy}$ = 0.043–0.109 and for $m_{sdr}$ = 0.002–0.023 Kg/s. The results show that the exergy and energy efficiency of single-pass double duct jet SAH was enhanced by 22.4 and 21.2%, respectively, compared to SAH. Yadav et al. [26] used CFD analysis to compare the HT performances of a simple and impinging jet SAH. ANSYS fluent 14 software was employed to analyze the TP of JISAH and compared with a traditional air heater without jet impingement under similar circumstances. Both experiments were conducted under Reynold’s number variations from 3800–16,000. The results show that HT in a jet impingement STC was 2.16 times higher than conventional SAH. Aboghrara et al. [27] conducted a study to explore the thermal performances of a jet impingement SAH with a corrugated plate. They compared the thermal performances of the proposed SAH with those of a conventional SAH. The results show that the proposed SAH’s thermal performances were far superior to those of the conventional SAH. Rajaseenivasan et al. [28] analyzed the impact of the attack angle of jet impingement and the diameter of the nozzle on the heat transfer characteristic of the SAH. The attack angle and nozzle diameter were altered from 0° to 90° and 3 mm to 7 mm, respectively, during the experiment. The mass flow rate of the air was altered from 0.012 to 0.016 kg/s. The outcomes showed that the maximum performance was attained with an attack angle of 30° and a nozzle diameter of 5 mm. The highest thermal augmentation factor of 2.19 and efficiency of 55.8% were obtained with a mass flow rate of 0.016 kg/s. Goel et al. [29] experimentally explored the impact of $X/D_{hy}$, fin spacing ratio, and $D_j/D_{hy}$ on the thermal performances of jet impingement SAH integrated with the array of fins. The experiment was performed for $Re$ from 5700 to 11,700 and for $m_{sdr}$ from 0.056 to 0.112. The results show that heat transfer was enhanced by 2.5 times for a JISTC with fins compared to conventional SAH. Similar works are also in the literature [30,31,32,33,34] which refer to the solar device operated using nanofluids with their mathematical models, jet impingements, numerical analysis, etc. [35,36,37]. D. García and J.I. Prieto [38] presented a heat exchanger for use in a solar engine micro co-generation unit. The different selection criteria were followed in designing the engine. The authors described the geometrical characteristics of the heater. They discussed the variables that can affect the pressure drop and HT characteristics. They also developed the correlations for the $f_r$ and Stanton number under steady stream conditions. In all these studies, the previous works of distinct researchers reported that impinging jets enhance transfer rate and improve the performance of the SAH. However, no previous work has investigated the impact of spacer length variation on the ${\eta }_{sdr}$ of a JISTC with single discrete arc-shaped ribs. Therefore, this work intends to investigate $N{u}_{sdr}$, $f_{sdr}$, and ${\eta }_{sdr}$ in a JISTC with single discrete arc-shaped ribs at distinct values of spacer lengths. The impinging jet STC diagram is depicted in Figure 1a. Jet impingement provides triple heat transfer coefficients due to thin impingement boundary layers, as presented in Figure 1b.

2. Roughness and Experimental Parameters

The aluminum wires were fixed on the galvanized iron plate (absorber plate) to create roughness. A standard-sized wooden cylinder was used to fabricate the desired shapes of wire on the absorber plate. The diameter of the cylinder used to construct the discrete arc-shaped ribs was determined using the following formula [38]:

$$D_c=C_L/\cos \left(90-\alpha \right)$$

(1)

where $C_L$ is the chord length and $\alpha$ is angle of the arc.

The channel size was specifically chosen based in previous studies where the length of the channel $(L_P)$ was 1200 mm, channel width ($W$) was 300 mm, and channel height ($H$) was 25 mm. The single discrete arc-shaped rib geometry has fixed values of $D_d/L_v$, $g_w/H_r$,$H_r/H$, $P_r/H$ ${\alpha }_{sdr}$, $X_s/D_{hy}$, $Y_s/D_{hy}$, and varying values of $S_{sdr}$, respectively. An array of different geometric factors selected to conduct the experiments are depicted in

Table 1. An array of flow and geometric factors.

Geometric Factors
Sr. No.	Factors	Symbols	Range
1.	Relative discrete distance	$D_d/L_v$	0.67
2.	Relative discrete width	$g_w/H_r$	0.87
3.	Relative rib height	$H_r/H$	0.047
4.	Relative rib pitch	$P_r/H$	1.7
5.	Angle of attack	${\alpha }_{sdr}$	60°
6.	Streamwise pitch ratio	$X/D_{hy}$	1.72
7.	Spanwise pitch ratio	$Y/D_{hy}$	0.82
8.	Jet diameter ratio	$D_j/D_{hy}$	0.065
9.	Spacer length	$S_{sdr}$	0 mm to 300 mm
10	Absorber plate surface area	$A_p$	$36\times {10}^4$ mm2
11	Orifice meter area	$A_0$	$10.17\times {10}^2$ mm2
12	Height of duct	$H$	25 mm
13	Width of duct	$W$	300 mm
14	Length of test section	$L_P$	1200 mm
Flow Factors
Sr. No.	Factors	Symbols	Range
1.	Reynolds number	$Re$	3000–19,000 (8 steps)
2	Mass flow rate	$m_{sdr}$	0.008–0.05 kg/s (8 steps)
3	Velocity	$V_a$	1.02–6.47 m/s (8 steps)

. Figure 2a shows the pictorial view of single discrete arc-shaped ribs mounted on the absorber plate. Figure 2b illustrates the schematic view of single discrete arc-shaped ribs with parameters.

3. Experimental Setup Details

The experimentation structure was fabricated and assembled as per the ASHRAE standard to examine the impact of single discrete arc-shaped ribs on the performance of JISTC. Significant parts of the test setup involve a wooden rectangular channel, a voltmeter, an ammeter, an orifice plate, an electric heater, a U-tube manometer, a high-pressure blower for propelling air, an inverter, control valves, a micro-manometer, thermocouples, a variable transformer, etc. Figure 3a presents a schematic diagram of a test arrangement with the impinging jet plate. Twenty-nine constantan-based thermocouples were used to measure the temperature at distinct places, as indicated in Figure 3b. The jet plate was made up of good quality plyboard with a sunmica sheet pasted on both sides to ensure a good smooth surface. Figure 3c illustrates the actual picture of the jet plate.

A well-armed nichrome wire electric heater was used to transfer 1000 ${\mathrm{W/m}}^2$ heat flux above an array of test portions. A variac and ammeter were employed to control and retain uniform heat flux throughout the experiment. Because of atmospheric effects, the peak solar insolation incident on a terrestrial surface normally oriented to the sun at noon on a clear day was on the order of 1 kW/m². Therefore, a uniform heat flux of 1000 ${\mathrm{W/m}}^2$ was used during the experiment. The electric heater was fabricated by combining loops of nichrome wire in series and parallel combinations located on the top wall of the test section. A sheet of mica was placed over the heater to ensure uniform radiations over the surface. The back side of the heater was insulated with glass wool to reduce the heat losses. A U-tube manometer was employed to record ${\left(\mathsf{∆}p\right)}_0$. Moreover, suitable insulation was provided to reduce heat losses.

In the current experimental set up, a high-pressure blower for propelling air was used. Due to the small cross-section of the outlet of the blower, the flow was not fully developed inside the duct of the STC. To overcome this problem, artificial roughness on the absorber plate and jet impingement was provided. Artificial roughness acting as flow-restricting devices and jet impingement make the flow fully developed. Flow restriction devices in the form of SDASR with varying parameters and jet impingement were used in present study. Therefore, the flow inside the JISTC channel was fully developed.

Experimental Process

Testing was performed to record the data of SDASR-roughened plate in a rectangular JISTC channel with a jet plate for analysis of $N{u}_{sdr}$ and $f_{sdr}$. Each gadget was inspected precisely for its appropriate functioning in the present work. The whole intersection of the test setup was examined using a soap solution to identify any type of leakage. The apparatus, namely the U-tube manometer, voltmeter, micro-manometer, and ammeter, was used to measure the data and checked for proper functioning prior to experimentation. Nine sets of readings were taken for every roughened plate, and the mass flow rate value was varied using control valves. A digital micrometer recorded the pressure over the examination portion. An impingement jet plate was fixed among a target and base plate. The stream control valves were used to adjust the $m_{sdr}$ of the air. For the confirmation of the steady state condition, the temperature was taken at an interval of fifteen minutes. After taking observations for the smooth absorber plate, the absorber plates with ARS in the form of SDASR of distinct parameters were fabricated for taking observations. The observations for air and absorber plate temperature at distinct locations in the channel were taken for roughened absorber plates. The recorded data for absorber plates with different geometrical parameters at distinct $m_{sdr}$ were used for determining $N{u}_{sdr}$ and $f_{sdr}$. The following experimental data were recorded for each absorber plate.

• Pressure head variation across the orifice plate to find out the $m_{sdr}$.
• Target plate temperature ($T_{tp}$).
• Inlet air temperature ($T_i$).
• Outlet air temperature ($T_0$).
• Pressure head falls across the assessed segment ($\mathsf{∆}P$).

The absorber plates with different spacer lengths used in the examination are represented schematically in Figure 4a–d.

4. Validation of Experimental Values

The designed experimental setup was tested for desirable outcomes consistent with previous findings. A validation test with a smooth plate was conducted before the experiment with a roughened absorber plate. The observations recorded during the validity test were used to determine $N{u}_{ss}$ and $f_{ss}$. The obtained results for $N{u}_{ss}$ were compared with those for $N{u}_{ss}$ calculated using the Dittus–Bolter equation [26] and the obtained results for $f_{ss}$ were compared with those for $f_{ss}$ determined using a modified Blasius equation [28] for rectangular passage. The Dittus–Bolter equation used to calculate $N{u}_{ss}$ and the modified Blasius equation used to calculate $f_{ss}$ are given below:

Dittus–Bolter equation:

$$N{u}_{ss}=0.023R{e}^{0.8}{\mathrm{Pr}}^{0.4}$$

(2)

where Pr is the Prandtl number.

Modified Blasius equation:

$$f_{ss}=0.085R{e}^{-0.025}$$

(3)

After the insertion of flow restriction devices in the form of SDASR with varying parameters, the flow becomes fully developed. Therefore, after the validation test, the standard equations of fully developed flow and turbulent were used to study $N{u}_{sdw}$ and $f_{sdw}$. More standrad correlations such as Gnielinsky and Petukhov were used to verify the results, and they showed good agreement between the experimental and the theoretical values. The Gnielinsky equation for $N{u}_{ss}$ is

$$N{u}_{ss}=\frac{\frac{f_s}{8}\left(Re-1000\right)Pr}{1+12.7\left(\sqrt{\frac{f_s}{8}}\right)\left(P{r}^{2/3}-1\right)}$$

(4)

where $f_s={\left[0.7904\ln \left(Re\right)-1.64\right]}^{-2}$, $3000<Re<5\times {10}^6$.

The Petukhov equation for $f_{ss}$ is

$$f_{ss}={\left[0.7904\ln \left(Re\right)-1.64\right]}^{-2}$$

(5)

The expected and measured $N{u}_{ss}$ and $f_{ss}$ for the smooth plate were then calculated; they are plotted in Figure 5 and Figure 6, respectively.

5. Data Diminution

The data collected was used to calculate $h_c$, $N{u}_{sdr}$, and $f_{sdr}$. The essential terms for the calculation of all parameters are given below:

Temperature measured:

The weighted standard plate temperature was calculated using Equation (6) as given below:

$$T_{tp} = \frac{\sum T_i}{N}$$

(6)

Standard air temperature was also calculated using Equation (5) as given below:

$$T_{ma} = \frac{T_i+T_o}{2}$$

(7)

Mass flow rate ($m_{sdr}$):

The $m_{sdr}$ was determined by the pressure reduction quantity across the standardized orifice meter by using Equation (6):

$$m_{sdr} = C_d{A}_0{\frac{2{\rho }_{ar}{\left(\mathsf{∆}p\right)}_0}{1-{\beta }_{oR}^4}}^{1/2}$$

(8)

where $=\frac{D_o}{D_1}=0.45$, where $D_1$ and $D_0$ are the diameter of the pipe and the diameter of the orifice meter, respectively.

Velocity of air ($V_a$):

$$V_a = \frac{m_{sdr}}{{\rho }_{ar}WH}$$

(9)

Hydraulic diameter:

$$D_{hy} = \frac{4\times \left(W\times H\right)}{2\times \left(W+H\right)}$$

(10)

Determination of Reynolds number:

$$Re = \frac{V_a\times D_{hy}}{\upsilon }$$

(11)

Friction factor calculation:

The $f_{sdr}$ was calculated by data of $\mathsf{∆}p$ across the assessed portion length with the Darcy equation as follows:

$$f_{sdr} = \frac{2\times \mathsf{∆}p\times D_{hy}}{4\times {\rho }_{ar}\times L_P\times V_a^{ 2}}$$

(12)

Heat transfer rate $(Q_{sdr})$:

$$Q_{sdr}=m_{sdr}{C}_P\left(T_o-T_i\right)$$

(13)

Heat transfer coefficient $(h_c)$:

$$h_c = \frac{Q_{sdr}}{A_p\times \left(T_{tp}-T_{ma}\right)}$$

(14)

Nusselt number:

$$N{u}_{sdr}=\frac{ h_c{D}_{hy}}{k_a}$$

(15)

6. Results and Discussion

The $N{u}_{sdr}$ and $f_{sdr}$ characteristics of the JISTC were calculated from experimental observations obtained for SDASR with distinct roughness and flow parameters. To examine the effect of the variation of the $S_{sdr}$ of SDASR on $N{u}_{sdr}$ and $f_{sdr}$ characteristics, the $S_{sdr}$ was altered from 0 mm to 300 mm in the step of 100 mm. The other parameters of SDASR, such as $D_d/L_v$, $g_w/H_r$, $H_r/H$, $P_r/H$, ${\alpha }_{sdr}$, $X_s/D_{hy}$, and $Y_s/D_{hy}$, were kept constant.

6.1. Effect on Heat Transfer Characteristics

The experiment was performed to analyze the heat transfer improvement in the JISTC roughened with single discrete arc-shaped ribs. The $D_j/D_{hy}$ was fixed at 0.065 because at a $D_j/D_{hy}$ of 0.065, the diverged air jets from the perforation strike on the larger area of the absorber plate [14]. Therefore, the area of contact among air jets and absorber plates increases. Further increases in the jet diameter ratio result in a larger contact area but also in decreases in air jet intensity, causing lower heat transfer. The plot illustrated in Figure 7 shows the impact of $S_{sdr}$ on the $N{u}_{sdr}$ as a function of $Re$. The other parameters of SDASR, such as $D_d/L_v$, $g_w/H_r$, $H_r/H$, $P_r/H$, ${\alpha }_{sdr}$, $X_s/D_{hy}$, and $Y_s/D_{hy}$, were kept constant. The present study explores the influence of parametric variations of SDASR mounted on the absorber plate on HT enhancement. The $Q_{sdr}$ of the air was significantly increased due to the turbulence created in the flow by the ribs. The previous studies concluded that artificial roughness mounted on the absorber plate in the STC augments the HT coefficient. Artificial roughness causes increases in the friction which in turn increase the pumping power required to maintain flow in the channel. Therefore, the SDASR parameters must be optimized to keep the lowest possible $f_{sdr}$ and maximum HT. Figure 7 shows the change in $N{u}_{sdr}$ with $Re$ at chosen values of $S_{sdr}$. A rise in the HT with SDASR mounted on the absorber plate of the STC was found. The experimental findings also show that SDASR with $S_{sdr}$ = 0 mm (single discrete arc-shaped ribs are mounted on the whole length of the absorber plate) had the greatest impact on HT augmentation. The findings illustrate that the $S_{sdr}$ of the SDASR strongly affects the HT. The experiment was performed at four distinct values of $S_{sdr}$, from 0 mm to 300 mm with stages of 100 mm. At $S_{sdr}$ = 100 mm, the flow became less turbulent and caused a drop in $N{u}_{sdr}$. Further increases in the $S_{sdr}$ of SDASR led to less turbulent flow. Therefore, the fluid flow became fast, and the HT of the fluid decreased, resulting in a decline in $N{u}_{sdr}$. At $S_{sdr}$ = 0 mm, the fluid was properly mixed and received the utmost heat, as shown in Figure 8. Therefore, HT was at its maximum value for the configuration in which the ribs were fixed on the entire length of the absorber plate. The impingement jets have two distinct rotating vortices that drive fluid from the colder region (internal core) towards the arc obstacle wall [39,40,41]. This causes the mixing of lower impingement jets with the main flow. Mixing interior stream with the main stream caused the HT among the arc ribs to suspend boundary layer formation. With rise in $Re$, the thickness of the boundary layer diminished due to a decrease in convective resistance, leading to enhanced $N{u}_{sdr}$. The SDASR created a sturdy resultant stream jet behind the ribs, leading to high turbulence at the separation of impinging jets from SDASR and amalgamation with the main stream. The increase in the number of vortices added air in the STC and increased HT from the absorber plate to air.

6.2. Friction Factor Characteristics

Variation of $f_{sdr}$ with Re at $S_{sdr}$ = 0 mm, 100 mm, 200 mm, and 300 mm is shown in Figure 9. The $S_{sdr}$ of the SDASR had a substantial influence on the friction factor characteristics. The fluid has to flow from obstacles after its entrance into the channel due to the presence of SDASR. The single discrete arc-shaped ribs on the absorber plate made the fluid flow turbulent and slowed down the air stream, leading to adequate HT among the air and absorber plate. Besides the enhancement in HT, the obstacles enhanced the $f_{sdr}$. The repetitive obstacles caused augmented HT, albeit with enhanced friction. The influence of the obstacles on the air stream decreases with an increase in the spacer length [42,43,44,45]. This is due to the discharge of the stream resulting from the presence of SDASR and the amalgamation of lower streams with the main stream.

7. Thermohydraulic Performance

In the present investigation, the $N{u}_{sdr}$ and $f_{sdr}$ of the JISTC increased with SDASR fixed on the absorber plate. As discussed in Section 6.1, the $S_{sdr}$ of the SDASR has a significant influence on HT enhancement. The single discrete arc-shaped ribs make airflow turbulent and slow down the stream of air. This causes adequate HT among air and absorber plates. The repetitive obstacles cause augmented HT, albeit with enhanced friction. The influence of the obstacles on the air stream lowers with the increase in the spacer length. Therefore, selection of the configuration that enhances HT with the least penalty of $f_{sdr}$ is essential. To achieve a considerable increase in heat transfer with the least penalty of $f_{sdr}$, the investigators [24] suggested a parameter, ${\eta }_{sdr}$, which is a function of $N{u}_{sdr}$ and $f_{sdr}$. The desired geometry must result in extreme augmentation of HT with the lowest possible friction. The ${\eta }_{sdr}$ is determined by using following equation:

$${\eta }_{sdr} = \left(N{u}_{sdr}/N{u}_{ss}\right)/{\left(f_{sdr}/f_{ss}\right)}^{0.33}$$

(16)

Figure 10 depicts different values of ${\eta }_{sdr} = \left(N{u}_{sdr}/N{u}_{ss}\right)/{\left(f_{sdr}/f_{ss}\right)}^{0.33}$ at selected $S_{sdr}$ and Re, keeping other parameters constant. At $S_{sdr}$ = 0 mm, the calculated value of ${\eta }_{sdr}$ is 2.9, which is greater than 1. The maximum value of ${\eta }_{sdr}$ is obtained at $S_{sdr}$ = 0 mm, which suggests that the optimum performance of JISAC is at $S_{sdr}$ = 0 mm.

8. Conclusions

From the experimental analysis of the $N{u}_{sdr}$ and $f_{sdr}$ characteristics of the JISTC with SDASR on the absorber plate, the following conclusions can be drawn.

Attaching an SDASR on the absorber plate of a JISTC results in considerable enhancement of $N{u}_{sdr}$. This enhancement is a strong function of jet impingement and single discrete arc-shaped ribs.

• The single discrete arc-shaped ribs with a spacer length $S_{sdr}$ = 0 mm results in increased $N{u}_{sdr}$ and $f_{sdr}$ compared with other values of $S_{sdr}$.
• The $N{u}_{sdr}$ and $f_{sdr}$ of the JISTC with SDASR were improved by 5.25 and 5.98 times compared to the STC without SDASR.
• The highest % increase in $N{u}_{sdr}$ and $f_{sdr}$ of the JISTC with SDASR at $S_{sdr}=0 \mathrm{mm}$ compared to $S_{sdr}=300 \mathrm{mm}$ was 77% and 18%, respectivey.
• The single discrete arc-shaped ribs JISTC provided the highest ${\eta }_{sdr}$ of 2.9 at $S_{sdr}$ = 0 mm.