Performance investigation of a solar thermal collector provided with air jets impingement on multi V-shaped protrusion ribs absorber plate

Abstract

In the present work, the heat transfer through a solar thermal collector (STC) provided with jet air impingement on the absorbent plate fitted with multi V-shaped protrusion ribs is investigated experimentally. The investigation is carried out for geometric parameters such as Relative width ratio (W_PR/W_APR), Relative protrusion rib height (h_PR/d_PR), Relative pitch ratio (P_PR/h_PR), Angle of attack (α_PR) respectively. The values of the streamwise pitch ratio (X_SW/d_h) = 0.40, spanwise pitch ratio (Y_SW/d_h) = 0.85 and jet diameter ratio (d_j/d_h) = 0.064 are kept constant. The overall performance of STC is effectively evaluated by varying Reynolds number (Re) in the range 2500–35,000. The results obtained from the experiments shows that the impingement jets flow on multi V-shaped protrusion ribs absorber plate accelerated the heat transfer through the solar collector channel. The optimal augmentation is obtained at W_PR/W_APR= 5, h_PR/d_PR= 0.9, P_PR/h_PR = 8 and α_PR = 65° respectively. Thermal-hydraulic performance parameter ( η_PR) has also been investigated and the maximum value of 3.44 is obtained for the range of parameters studied.

1 Introduction

The world is facing the energy crises and severe climate change that exceed the ability of usual managed human systems to acclimatize. The only solution to this difficulty is to exploit renewable energy sources where solar energy coming from the sun in the form of radiant energy is by far the mainly outstanding one [1, 2]. The solar thermal collector (STC) used ambient air as the heat carrying medium [3]. It is a prime component of the utilization of solar energy [4, 5]. Such type of solar thermal collectors requires low maintenance and having fewer prices as compared to other collectors [6,7,8]. The thermal performance of STC is low because of the low heat transfer coefficient between moving fluid and heated plate [9, 10]. Thermal performance can be improved either by increasing the heat transfer area or by enhancing the absorber to air convective heat transfer coefficient and can be achieved by modification in the stream passage of STC [10,11,12]. Nadda et al. [13] investigated Nu and f_r of an impingement jets SAH. They obtained the highest value of η_PR= 3.14 at P_PR/h_PR= 9.5, W_PR/W_APR= 5.0, h_PR/d_PR= 1.0 and α_PR= 55°. Chauhan et al. [14] carried out an exergy-based analysis of an impinging jet SAC. They found that exergetic efficiency of impinging jet SAC rises at smaller Re and increase in temperature parameter. Chauhan et al. [15] reviewed the performance enhancement techniques of an impinging jet STC based upon thermodynamic structure, Nu and f_r behavior and the multi-criteria option creation methods. Matheswaran et al. [16] examine the influence of different parameter m_a, X_SW/d_h, Y_SW/d_h and d_j/d_h on the exergy efficiency of a SAH. Based on the simulation consequences the augmented exergy efficiency was 4.36%. Aboghrara et al. [17] compared Nu and f_r of smooth jet impinging SAH with the corrugated rough funned channel. The outcome shows that the average thermal efficiencies of a rough funned SAH increase 14%. Brideau and Collins [18] developed a model for enhancement of the thermal efficiency of a collector with jets impingements. During analysis, they studied the effect of time set up and thermal mass on the reliability of the model. Chauhan et al. [19] investigated the effect of various parameter X_SW/d_h, Y_SW/d_h and d_j/d_h on Nu and f_r of impinging jets, SAH with Re varies from 3800 to 16,000. The outcome shows that there is significant augmentation in Nu and f_r. Guo et al. [20] analyzed Nu and f_r of a circular jets impingement STC. During the investigation the Re number was varied from 14,000 to 53,000, space among nozzle exit and plate from 4 to 8 and inner nozzle diameter was kept constant 6 mm. Nadda et al. [21] performed the experimental study on impingement jet SAH by using multiple arcs protrusion ribs and reported a THP of 3.64 for Re of 13,000. Rajaseenivasan et al. [22] incorporate a jets impingement arrangement in the SAH. They examined the effect of α_PR, m_a and nozzle diameter on Nu and f_r of SAH. The higher η_PR of 2.19 was achieved with m_a of 0.016 kg/s, nozzle diameter of 5 mm and α_PR of 30°. Nadda et al. [23] examine Nu and f_r of a jets impingement arc obstacle SAH. Testing was performed by varying Re from 4000 to 18,000, P_PR/h_PR (9 to 12), h_PR/d_PR (0.8 to 1.7), X_SW/d_h (0.39 to 0.56), Y_SW/d_h(0.82 to 0.99) and α_PR= 60°. They reported that the highest η_PR was obtained at P_PR/h_PR=10, h_PR/d_PR=1.1, X_SW/d_h= 0.43, Y_SW/d_h=0.86 and α_PR= 60°. Mishra et al. [24] used AHP-TOPSIS method to determine the optimum set of multi-arc protrusion ribs employed in impingement jet SAH. They found that the whole performance of impingement jet SAH was improved up to 3.64 times as compared to other SAH having a flat surface. Geers et al. [25] employed the PIV method to determine mean and fluctuation velocity constituent in a single and multiple both jet impingement streams. Kercher and Tabakoff [26] examine Nu of a perforated plate of a number of the square array and circular air jets impingements. During experimentation, they studied the influence of the jet used air flowing at right angles to the jets, d_j, X_SW and Z. The outcome shows that Nu rise with rising open area. Metzger et al. [27] experimentally investigated the effects of channel height and hole spacing on Nu. The outcomes show that considerable periodic variations obtain in the streamwise Nu profiles. Matheswaran et al. [16] examine the influence of m_a, X_SW/d_h, Y_SW/d_h and d_j/d_h on the η_EXR of a SAH. The outcomes are obtained at the optimized values of X_SW/d_h = 1.739, Y_SW/d_h = 0.869 d_j/d_h = 0.065 and m_a of 0.0035 kg/s. The calculated utmost η_EXR was 4.36%. Brideau et al. [28] developed a model of the collector and validated it with the outcome obtained from the prototype of the system. Model is used to compare and optimize the design of the collector. The results provided by the model were found to be reasonable. Nadda et al. [29] examine the outcomes of an impingement jet SAH. During experimentation, they analyze Nu and f_r. Also, PSI approach has been employed to optimize the design parameter for utmost yield. Goodro et al. [30] analyzed the influence of Mach number on Nu, coefficient of discharge & recovery factor for an array of impinging jets. During experimentation both Mach number and Re were varied. They found that the best outcomes were obtained at a Mach number of 0.74 and Re of 60,000. Goodro et al. [31] analyzed the influence of hole spacing on spatially-resolved Nu from impinging jets on a flat plate. The parameters range were varied Re from 8200 to 30,500, Mach number from 0.1 to 0.6, X_SW/d_h and Y_SW/d_h both 8D and 12D. They found that at Mach numbers larger than 0.2 whereas Re kept constant show that Mach number has a considerable impact on overall Nu. For 8D spacing, Nu is increased significantly as the Mach number increases and for hole spacing of 12D, Nu also increases considerably as the Mach number increases. Lee et al. [32] examine the effect of impingement cross-streams on local, line-averaged and spatially. During testing, they varied the Z. They reported that the better outcome is obtained at hole spacing of 5D, Z of 1.5D and 3.0 D, X_SW/d_h and Y_SW/d_h= 5 and Z/D = 3.0. Nayak and Singh [33] compare η_pof a modified SAH with traditional SAH. They found η_p, Nu & exit fluid temperature of a cross-stream staggered hole jet plate SAH are considerably superior at m_a= 0.064 kg/s and Re = 5205 as compared to traditional SAH. Soni and Singh [34] examine the effect of Re , m_a, X_SW/d_h, Y_SW/d_hand d_j/d_h on the Nu and f_r of a Jet plate SAH. The stream parameter such as Re varied from 4600 to 12,000, X_SW/d_h and Y_SW/d_h both varied from 0.53 to 0.63 and d_j/d_h from 0.053 to 0.084. They also developed a correlation for these parameters. Yu et al. [35] numerically investigated the Nu characteristic of a small-air-jet impingement channel. They concluded that with the drop off of jet-to-plate distance the Nu close to stagnation point is improved, while it is reduced close to a boundary point. Zukowski [36] gives the use of micro jet method to improve the amount of heat transfer in their investigation. They reported in their analysis that the single glass covering considerably increase the efficiency of solar energy change from 16 to 24%.

From the above-cited literature survey, it is concluded that numerous investigations have been carried out by the different researchers with an array of impinging jets onto the heated surface in solar thermal collectors for its thermal improvement. Few types of research have been reported in the literature for an array of jets impingements in STC with artificial roughness provided on the heated plate. The present experimental analysis is an attempt to link this gap by presenting an in-depth experimental examination of impinging jets STC provided with multi V-shaped protrusion ribs type artificially roughness on the heated plate. The current study is novel in a sense that no such type of examination in earlier times has been examined on impinging jets STC with this type of roughness.

2 Experimental setup detail and range of roughness parameters

The schematic design of the indoor experimental unit is depicted in Fig. 1. It involves inlet section of 500 mm, experimentally examine a section of 1200 mm length and outlet section of 300 mm length trailed by the suction blower which was propelled by a motor having 5KW, 3-phase and 230 V. To run the air through the collector channel, the motor was adjusted at the alternate end. The m_a of the air transferring through the channel was determined by employing an orifice meter combined with the U tube manometer, which contains propyl alcohol. To regulate the m_a the regulator valves were used before and afterward the blower outlet. A 18 SWG black galvanized iron sheet used for heat transfer on the surface where the heater was placed to provide a continuous flux of 1000 W/m². The STC was installed in parallel and series arrangements by adding different loops of nichrome wire situated on the upper wall of examination section with rest of the portions insulated. An adjustable transformer was attached to sustain a precise voltage and current to record the current travelling through the circuit to provide a controlled uniform heat flux of 1000 W/m². To avoid over-heating and back heating from STC, 0.5 mm thick size mica sheet was inserted between 5 mm thick asbestos sheet and nichrome wire. The whole channel was insulated. The collector was located 30 mm above the target plate using wooden insertions. The loss of f_rwithin the testing the unit was determined by employing the micro-manometer, which estimates how much power, is required to run the air in the channel. Standardized copper thermocouples were employed to record the target plate temperature at 29 positions and were connected with quick drying thermal adhesive. Figure 2 presented the position of the variant thermocouples on the target plate. Five copper thermocouples were located at an outlet in an oblique direction and three thermocouples were located at the entry to record the temperature of the air at entry and exit respectively. The entire 29 thermocouples were connected to a temperature scanner unit to show the scanned temperature. The rectangular channel was designed so precisely so that the impinging jet plate is significantly located at its position. Figure 3 depicts the position of X_SW/d_h and Y_SW/d_hon the impingement jet plate. The deviation in the impinging jet plate alternatives and the flow Re for optimization of the parameters are shown in Table 1. These geometric parameters had been well optimized to achieve optimal results, which offer the highest value of Nu and lesser value of f_r inside the impingement jet STC.

Fig. 1

Schematic design of the experimental setup

Fig. 2

Position of thermocouples on the target plate

Fig. 3

Schematic design of spanwise and streamwise pitch on impingement jet plate

Table 1 Range of variant parameters used in experimental investigation

3 Impingement jets hydrodynamics

Generally, the imposing jet is turbulent on the nozzle’s outlet and is identified as a constant velocity shape. However, by raising distance from the outlet, momentum interchange among impinging jet and the ambient generates the potential core and unrestricted boundary of the jet to expand. At the downward flow of the potential core, the velocity shape is not constant above the complete jet area and a maximum of the middle velocity reduces with raising space from the outlet of the nozzle. The part of the stream on which the situations are unaffected by impinging the surface is known as free jet. In the stagnation area, the stream is affected by the surface of impulse and normally slows down and becomes hastened in the normal and crossword direction. However, the current continues to meet the zero momentum fluid from the ambient environment, crosswise acceleration in the stagnation zone in the wall jet cannot be quite stable. The shapes of velocity in the wall impinging jet are identified by nil velocity at the corresponding impingement and free plane, therefore m_a takes place in both the impinging wall jet stagnation zone. For multiple impinging jets, the stream field is affected by two types of interfaces which are not in the case of single impingement jets. The multi impingement jets stream shape can be categorized into six descriptions section: impingement section, wall jet section and free jet section, jet up wash section, jet origination section and entrainment. Because of the turbulence caused by the shear among the wall jet section and the proximal fluid, the voltage section shows the maximum heat transmission which is transferred to the edges layer in the heat convey plane. Roughened multi V-shaped protrusion ribs absorber plates with different values of W_PR/W_APR on which the fluid strikes after the impingement is shown in Fig. 4. While compared to the conventional convection cooling by the comparable restricted flow of the smooth surface, the impinging jets generate heat transfer coefficient which are three times greater due to the thin impinging jet boundary layers.

Fig. 4

Roughened multi V-shaped protrusion ribs absorber plates with different values of W_PR/W_APR

4 Data reduction

Composed data has been used to calculate h_t, Nu and f_r. The following are the expressions used for calculation of h_t, Nu, f_r and other parameters.

• Temperature measured

Weighted average plate air temperature:

The average temperature of the tested plate is the average of all the temperatures of the tested plate:

$$ {T}_p=\frac{\sum {T}_{pi}}{N} $$

(1)

The average air temperature is an arithmetic mean of the entrance and exit temperature flowing through the test section:

$$ {T}_f=\frac{T_i+{T}_o}{2} $$

(2)

Here, T_o = (T_A2 + T_A3 + T_A4 + T_A5 + T_A6)/5 and T_i = T_A1

• Mass stream rate measurement(m_a)

m_a has been calculated from the (∆p)₀ by using the following formula:

$$ {m}_a={C}_{do}{A}_o{\left[\frac{2{\rho}_a{\left(\Delta p\right)}_0}{1-{\beta_R}^4}\right]}^{0.5} $$

(3)

• Velocity of air through the channel(V)

The velocity of air (V) is calculated from the m_aand given below

$$ V=\frac{m_a}{\rho_a{W}_{PR}{H}_C} $$

(4)

• Equivalent hydraulic diameter(d_h)

The hydraulic diameter (d_h) is calculated by using the equation given below

$$ {d}_h=\frac{4.\left({W}_{PR}.{H}_C\right)}{2.\left({W}_{PR}+{H}_C\right)} $$

(5)

• Reynolds number(Re)

Re of the air stream in the channel is determined by using equation as given below

$$ \mathit{\operatorname{Re}}=\frac{V.{d}_h}{\nu_a} $$

(6)

• Friction factor(f_r)

The f_r is calculated from the measured value of (∆_p)_d using the Darcy equation as

$$ {f}_r=\frac{2{\left({\Delta }_p\right)}_d{d}_h}{4{\rho}_a{L}_t{V}^2} $$

(7)

• Heat Transfer Coefficient (Q_u)

Q_u from the absorber to the air is given by

$$ {Q}_u={m}_a{c}_p\left({T}_0-{T}_i\right) $$

(8)

The h_t for the heated test, the section has been calculated from

$$ {h}_t=\frac{Q_u}{A_p\left({T}_p-{T}_f\right)} $$

(9)

• Nusselt Number(Nu)

The h_t is used to determine the Nu which is given by

$$ Nu=\frac{h_t{d}_h}{K_a} $$

(10)

5 Validation and uncertainty study

While executing any experiment on setup, it is necessary to confirm that the structure is giving the same response as per the previous check. Therefore, a validation inspection is done for the smooth absorber plate on the investigation system. The results obtained from the method are estimated by the reactions of the first established correlations for the rectangular channel and respectively determined by employing Eq. (11) for Nu_ss and Blasius Eq. (12) for f_ss respectively. The Nu_ss for smooth absorber plate in a rectangular channel is determined with Dittus – Boelter eq. as shown in Eq. (11) [37].

$$ {Nu}_{ss}=0.023\times {\mathit{\operatorname{Re}}}^{0.8}\times {\mathit{\Pr}}^{0.4} $$

(11)

The f_ss for smooth absorber plate in a rectangular channel is determined by using Blasius eq. as shown in Eq. (12)

$$ {f}_{ss}=0.085\times {\mathit{\operatorname{Re}}}^{-0.25} $$

(12)

The estimation of experimental and predicted responses of Nu_ss and f_ss as a function of Re is depicted in Fig. 5a, b respectively.

Fig. 5

a Comparison of expected and experimental results of Nu_ssb Comparison of expected and experimental results of f_ss

Alternatively, the uncertainty analysis of measured values ​​has been determined and is found in controlled constraints. The analysis of uncertainty for various types of operating options is given below:

6 Uncertainty study

Due to the presence of random errors, experimental results can vary from its actual results. There is a possible ratio of uncertainty error. Therefore it is important to describe the uncertainty in calibration and to estimate how these certain uncertainties increase in the analyzed outcomes [38]. The uncertainty intervals of various measurements are depicted in Table 2 and equations employed to calculate uncertainty data are given below:

• Uncertainty in the measurement of A_p

$$ {\displaystyle \begin{array}{c}{A}_p={W}_{PR}\times {L}_t\\ {}\frac{\delta {A}_p}{A_p}={\left[{\left(\frac{\delta {L}_t}{L_t}\right)}^2+{\left(\frac{\delta {W}_{PR}}{W_{PR}}\right)}^2\right]}^{0.5}\\ {}\begin{array}{c}\frac{\delta {A}_p}{A_p}={\left[{\left(\frac{0.1}{1200}\right)}^2+{\left(\frac{0.1}{300}\right)}^2\right]}^{0.5}\\ {}\frac{\delta {A}_p}{A_p}=0.00034359\end{array}\end{array}} $$

(13)

• Uncertainty in the measurement of A _f

$$ {\displaystyle \begin{array}{c}{A}_f={W}_{PR}\times {H}_C\\ {}\frac{\delta {A}_f}{A_f}={\left[{\left(\frac{\delta {H}_C}{H_C}\right)}^2+{\left(\frac{\delta {W}_{PR}}{W_{PR}}\right)}^2\right]}^{0.5}\\ {}\begin{array}{c}\frac{\delta {A}_f}{A_f}={\left[{\left(\frac{0.1}{30}\right)}^2+{\left(\frac{0.1}{300}\right)}^2\right]}^{0.5}\\ {}\frac{\delta {A}_f}{A_f}=0.00334995\end{array}\end{array}} $$

(14)

• Uncertainty in the measurement of d _h

$$ {\displaystyle \begin{array}{c}{d}_h=\frac{4\times \left({W}_{PR}\times {H}_C\right)}{2\times \left({W}_{PR}\times {H}_C\right)}=2\left({W}_{PR}{H}_C\right){\left({W}_{PR}+{H}_C\right)}^{-2}\\ {}\frac{{\delta d}_h}{\delta {H}_C}=\left[2\left({W}_{PR}{H}_C\right)\left(-1\right){\left({W}_{PR}+{H}_C\right)}^{-2}\right]+\left[{\left({W}_{PR}+{H}_C\right)}^{-1}\left(2{W}_{PR}\right)\right]\\ {}\begin{array}{c}\frac{{\delta d}_h}{\delta {H}_C}=\frac{2{W}_{PR}}{\left({W}_{PR}+{H}_C\right)}-\frac{2{W}_{PR}{H}_C}{{\left({W}_{PR}+{H}_C\right)}^2}\\ {}\frac{{\delta d}_h}{\delta {H}_C}=\frac{2\times 300}{\left(300+30\right)}-\frac{2\times 300\times 30}{{\left(300+30\right)}^2}=1.65289\\ {}\begin{array}{c}{\delta d}_h={\left[{\left(\frac{{\delta d}_h}{\delta {W}_{PR}}\delta {W}_{PR}\right)}^2+{\left(\frac{{\delta d}_h}{\delta {H}_C}\delta {H}_C\right)}^2\right]}^{0.5}\\ {}\frac{{\delta d}_h}{d_h}=\frac{{\left[{\left(\frac{{\delta d}_h}{\delta {W}_{PR}}\delta {W}_{PR}\right)}^2+{\left(\frac{{\delta d}_h}{\delta {H}_C}\delta {H}_C\right)}^2\right]}^{0.5}}{2\left({W}_{PR}\times {H}_C\right){\left({W}_{PR}+{H}_C\right)}^{-1}}\\ {}\begin{array}{c}\frac{{\delta d}_h}{d_h}=\frac{{\left[{\left(1.65289\times O.1\right)}^2+{\left(0.0165289\times 0.1\right)}^2\right]}^{0.5}}{2\left(300\times 30\right){\left(300+30\right)}^{-1}}\\ {}\frac{{\delta d}_h}{d_h}=0.0030304246\end{array}\end{array}\end{array}\end{array}} $$

(15)

• Uncertainty in the measurement of A _o

$$ {\displaystyle \begin{array}{c}{A}_o=\frac{\pi }{4}{D_o}^2\\ {}\frac{A_o}{\delta {D}_o}=\frac{2\pi {D}_o}{4}\\ {}\begin{array}{c}\delta {A}_o={\left[{\left(\frac{\delta {A}_o}{\delta {D}_o}\delta {D}_o\right)}^2\right]}^{0.5}={\left[{\left(\frac{\pi {D}_o}{2}\delta {D}_o\right)}^2\right]}^{0.5}=\frac{\pi {D}_o\times \delta {D}_o}{2}\\ {}\frac{A_o}{\delta {A}_o}=\frac{\frac{\pi {D}_o\times \delta {D}_o}{2}}{\frac{\pi }{4}{D_o}^2}=\frac{2\times \delta {D}_o}{D_o}=\frac{2\times 0.1}{42.96}\\ {}\frac{A_o}{\delta {A}_o}=0.0047\end{array}\end{array}} $$

(16)

• Uncertainty in the measurement of ρ _a

$$ {\displaystyle \begin{array}{c}{\rho}_a=\frac{P_a}{R\times {T}_o}\\ {}\delta {\rho}_a={\left[{\left(\left(\frac{\delta {\rho}_a}{\delta {P}_a}\right)\times 1\times \delta {P}_a\right)}^2+{\left(\left(\frac{\delta {\rho}_a}{\delta {T}_o}\right)\times 1\times \delta {T}_o\right)}^2\right]}^{0.5}\\ {}\begin{array}{c}\delta {\rho}_a={\left[{\left(\left(\frac{1}{R\times {T}_o}\right)\times \left(\frac{\rho_aR{T}_o}{P_a}\right)\times \delta {P}_a\right)}^2+{\left(\left(-\frac{P_a}{R\times {T_o}^2}\right)\times \left(\frac{\rho_aR{T}_o}{P_a}\right)\times \delta {T}_o\right)}^2\right]}^{0.5}\\ {}\frac{\delta {\rho}_a}{\rho_a}={\left[{\left(\frac{\delta {P}_a}{P_a}\right)}^2+{\left(\frac{\delta {T}_o}{T_o}\right)}^2\right]}^{0.5}\end{array}\end{array}} $$

(17)

Taking P_a = 97500 Pa

$$ \frac{\delta {\rho}_a}{\rho_a}={\left[{\left(\frac{0.1}{97500}\right)}^2+{\left(\frac{0.1}{25.33}\right)}^2\right]}^{0.5}=3.94\times {10}^{-3} $$

${m}_a={C}_d{A}_o{\left[\frac{2{\rho}_a{\left(\Delta p\right)}_0}{1-{\beta}^4}\right]}^{0.5}$6. Uncertainty in the measurement of m_a

$$ {\displaystyle \begin{array}{c}{m}_a={C}_d\times {A}_o\times {\rho_a}^{0.5}\times {{\left(\Delta p\right)}_0}^{0.5}\times {\left[\frac{2}{1-{\beta}^4}\right]}^{0.5}\\ {}\delta {m}_a={\left[{\left(\frac{\delta {m}_a}{\delta {C}_d}\delta {C}_d\right)}^2+{\left(\frac{\delta {m}_a}{\delta {A}_o}\delta {A}_o\right)}^2+{\left(\frac{\delta {m}_a}{\delta {\rho}_a}\delta {\rho}_a\right)}^2+{\left(\frac{\delta {m}_a}{\delta {\left(\Delta p\right)}_0}\delta {\left(\Delta p\right)}_0\right)}^2\right]}^{0.5}\\ {}\frac{\delta {m}_a}{m_a}={\left[{\left(\frac{\delta {C}_d}{C_d}\right)}^2+{\left(\frac{\delta {A}_o}{A_o}\right)}^2+{\left(\frac{\delta {\rho}_a}{\rho_a}\right)}^2+{\left(\frac{\delta {\left(\Delta p\right)}_0}{{\left(\Delta p\right)}_0}\right)}^2\right]}^{0.5}\end{array}} $$

(18)

The value of

$$ \frac{\delta {C}_d}{C_d}=1.5\% $$

The uncertainty in (∆p)₀ for U-tube manometer is 0.2 mm.

$$ {\displaystyle \begin{array}{c}{\left(\Delta p\right)}_0=\Delta {(H)}_o\mathit{\sin}\ 30{}^{\circ}\times \mathit{\sin}\ 90{}^{\circ}=185\ \mathrm{mm}\\ {}\frac{\delta {m}_a}{m_a}={\left[{\left(\frac{1.5}{100}\right)}^2+{(0.0047)}^2+{(0.00394)}^2+{\left(\frac{0.2}{185}\right)}^2\right]}^{0.5}=0.016241\end{array}} $$

• Uncertainty in the measurement of V

$$ {\displaystyle \begin{array}{c}V=\frac{m_a}{\rho_a\times {W}_{PR}\times {H}_C}\\ {}\frac{\delta V}{V}={\left[{\left(\frac{{\delta m}_a}{m_a}\right)}^2+{\left(\frac{\delta {\rho}_a}{\rho_a}\right)}^2+{\left(\frac{\delta {W}_{PR}}{W_{PR}}\right)}^2+{\left(\frac{\delta {H}_C}{H_C}\right)}^2\right]}^{0.5}\\ {}\frac{\delta V}{V}={\left[{(0.016241)}^2+{(0.00394)}^2+{\left(\frac{0.1}{300}\right)}^2+{\left(\frac{0.1}{30}\right)}^2\right]}^{0.5}=0.017044\end{array}} $$

(19)

• Uncertainty in Q _u

$$ {\displaystyle \begin{array}{c}{Q}_u={m}_a{c}_p\left({T}_0-{T}_i\right)={m}_a{c}_p\Delta T\\ {}\frac{\delta {Q}_u}{Q_u}={\left[{\left(\frac{{\delta m}_a}{m_a}\right)}^2+{\left(\frac{\delta {c}_p}{c_p}\right)}^2+{\left(\frac{\delta \Delta T}{\Delta T}\right)}^2\right]}^{0.5}\end{array}} $$

(20)

Uncertainty in specific heat is 0.1.

So, the equation becomes

$$ \frac{\delta {Q}_u}{Q_u}={\left[{(0.016241)}^2+{\left(\frac{0.1}{1006.141}\right)}^2+{\left(\frac{0.1}{5.33}\right)}^2\right]}^{0.5}=0.02481 $$

• Uncertainty in h_t

$$ {\displaystyle \begin{array}{c}{h}_t=\frac{Q_u}{A_p\times \left({T}_p-{T}_f\right)}=\frac{Q_u}{A_p\times {\Delta T}_f}\\ {}\frac{\delta {h}_t}{h_t}={\left[{\left(\frac{\delta {Q}_u}{Q_u}\right)}^2+{\left(\frac{\delta {A}_p}{A_p}\right)}^2+{\left(\frac{\delta {\Delta T}_f}{{\Delta T}_f}\right)}^2\right]}^{0.5}\\ {}\frac{\delta {h}_t}{h_t}={\left[{(0.02481)}^2+{(0.00034359)}^2+{\left(\frac{0.1}{22.66}\right)}^2\right]}^{0.5}=0.0252017\end{array}} $$

(21)

• Uncertainty in the measurement of Nu

$$ {\displaystyle \begin{array}{c} Nu=\frac{h_t{d}_h}{K_a}\\ {}\frac{\delta Nu}{Nu}={\left[{\left(\frac{\delta {d}_h}{d_h}\right)}^2+{\left(\frac{\delta {h}_t}{h_t}\right)}^2+{\left(\frac{\delta {K}_a}{K_a}\right)}^2\right]}^{0.5}\\ {}\frac{\delta Nu}{Nu}={\left[{(0.0030304246)}^2+{(0.0252017)}^2+{\left(\frac{0.00001}{0.02529}\right)}^2\right]}^{0.5}0.0394161\end{array}} $$

(22)

• Uncertainty in the measurement of Re

$$ {\displaystyle \begin{array}{c}\mathit{\operatorname{Re}}=\frac{V.{d}_h}{\nu }=\frac{\rho_aV{d}_h}{\mu}\\ {}\frac{\delta Re}{\mathit{\operatorname{Re}}}={\left[{\left(\frac{\delta {d}_h}{d_h}\right)}^2+{\left(\frac{\delta V}{V}\right)}^2+{\left(\frac{\delta {\rho}_a}{\rho_a}\right)}^2+{\left(\frac{\delta \mu}{\mu}\right)}^2\right]}^{0.5}\\ {}\begin{array}{c}\frac{\delta Re}{\mathit{\operatorname{Re}}}={\left[{(0.0030304246)}^2+{(0.017044)}^2+{(0.00394)}^2+{\left(\frac{0.001\times {10}^{-5}}{1.87\times {10}^{-5}}\right)}^2\right]}^{0.5}\\ {}\frac{\delta Re}{\mathit{\operatorname{Re}}}=0.01776\end{array}\end{array}} $$

(23)

• Uncertainty in the measurement of f _r

$$ {\displaystyle \begin{array}{c}{f}_r=\frac{2{\left({\Delta }_p\right)}_d{d}_h}{4{\rho}_a{L}_t{V}^2}\\ {}\frac{\delta {f}_r}{f_r}={\left[{\left(\frac{\delta {d}_h}{d_h}\right)}^2+{\left(\frac{\delta V}{V}\right)}^2+{\left(\frac{\delta {L}_t}{L_t}\right)}^2+{\left(\frac{\delta {\rho}_a}{\rho_a}\right)}^2+{\left(\frac{\delta {\left({\Delta }_p\right)}_d}{{\left({\Delta }_p\right)}_d}\right)}^2\right]}^{0.5}\\ {}\begin{array}{c}\frac{\delta {f}_r}{f_r}={\left[{(0.0030304246)}^2+{(0.17044)}^2+{\left(\frac{0.1}{1200}\right)}^2+{(0.00394)}^2+{\left(\frac{0.1}{56.2}\right)}^2\right]}^{0.5}\\ {}\frac{\delta {f}_r}{f_r}=0.01784\end{array}\end{array}} $$

(24)

• Uncertainty in the measurement of η _PR

$$ {\displaystyle \begin{array}{c}\ {\eta}_{PR}=\left( Nu/{Nu}_{ss}\right)/{\left({f}_{rs}/{f}_{ss}\right)}^{0.33}\\ {}\frac{\delta\ {\eta}_{PR}}{\ {\eta}_{PR}}={\left[{\left(\frac{\delta Nu}{Nu}\right)}^2+{\left(\frac{\delta {f}_r}{f_r}\right)}^2\right]}^{0.5}\\ {}\begin{array}{c}\frac{\delta\ {\eta}_{PR}}{\ {\eta}_{PR}}={\left[{(0.0394161)}^2+{(0.01784)}^2\right]}^{0.5}\\ {}\frac{\delta\ {\eta}_{PR}}{\ {\eta}_{PR}}=0.043265=4.3265\%\end{array}\end{array}} $$

(25)

Table 2 Uncertainty intervals of various measurements

The single test run was conducted for uncertainty analysis. Uncertainty was analyzed for a complete test run for single geometry and outcomes are offered in Table 3.

Table 3 Range of uncertainty (for measurement of necessary parameters)

7 Results and discussion

The Nu and f_r characteristics of the STC are explained below with multi V-shaped protrusion ribs attached on the heated plate and tested data are collected for distinct types of geometrical factors such as W_PR/W_APR, h_PR/d_PR, P_PR/h_PR and α_PR .

7.1 Heat transfer

In STC, the influence of W_PR/W_APR on the Nu in the stream of air-fluid is presented. The plots for Nu as a function of W_PR/W_APR for the data of Re has been presented in Fig. 6a and the remaining geometrical factors like h_PR/d_PR = 0.9, P_PR/h_PR = 8, α_PR= 65^o, X_sw/d_h = 0.40, Y_sw/d_h = 0.85 and d_j/d_h = 0.064 were kept constant. It has been observed that Nu rises with a rise in W_PR/W_APR from 1 to 6 and achieves the extreme viable data correspondent to W_PR/W_APR of 5 and afterward the data of Nu begins to decrease. The graph for Nu/Nu_ss as a purpose of W_PR/W_APR for multi V-shaped protrusion ribs at variant selected Re is presented in Fig. 6b. It has been found that in every situation, the multi V-shaped protrusion ribs wall produces superior Nu compared to that of without multi V-shaped protrusion ribs wall. An ideal Nu is produced by the multi V-shaped protrusion ribs because multi V-shaped protrusion ribs hilltop forms a secondary flow jet. Such ensuing flow jets have the profile of two different spinning vortices which transfers the cold air fluid from the internal central portion area to the multi V-shaped protrusion ribs wall. These lower flow jets associated with the main stream. The smaller stream jets combine with the central flow generally affect the flow retraction, retransmission among the multi V-shaped protrusion ribs and downstream suspended boundary layer growth of the restriction regions. Such an upcoming flow jet shapes two different spinning vortices, which transfers the cold air fluid from the internal central part area to the multi V-shaped protrusion ribs STC wall. These lower streams are connected to the mainstream. The smaller stream jets combine with the central flow, which usually affects the flow retraction. It can be observed that after increasing the data of W_PR/W_APR = 3, the volume of upper and lower end also increased, which improves the secondary stream elements and gives a recognized improvement in Nu_. However, Nu only improved continuously just up to a value of 5. After that as the value of W_PR/W_APR further increases the Nu decreases. The multi V-shaped protrusion ribs create a strong secondary stream jet near the limbs and when the disruption from the area of ​​the V-shaped ribs goes out and combines with the mainstream, the disturbance conducts the turbulence mixing. It has been obtained that the extreme result for Nu is achieved at W_PR/W_APR of 5 for each data of Re.

Fig. 6

a Effect of W_PR/W_APR on Nub Effect of W_PR/W_APR on Nu/Nu_ss at selected Re

The alteration of Nu with Re for various data of h_PR/d_PR has been shown in Fig. 7a. The rest of the geometrical parameters like W_PR/W_APR = 5, P_PR/h_PR = 8, α_PR= 65^o, X_sw/d_h = 0.40, Y_sw/d_h = 0.85 and d_j/d_h = 0.064 were kept constant. It has been observed that due to expanding flow every value of Nu increases with the increase in value of h_PR/d_PR for each value of Re, which causes the maximum turbulence and result in an enhancement in Nu. The highest Nu was obtained at h_PR/d_PR = 0.9. Figure 7b shows the graph for Nu/Nu_ss as a function of h_PR/d_PR for a multi V-shaped protrusion ribs STC at variant selected Re. It has been found that from different values of h_PR/d_PR the Nu was ideal for h_PR/d_PR = 0.9 at each data of Re.

Fig. 7

a Effect of h_PR/d_PR on Nub Effect of h_PR/d_PR on Nu/Nu_ss at selected Re

Figure 8a presents the distinction of Nu as a function of Re for alternative data of P_PR/h_PR and rest of the geometrical parameters like W_PR/W_APR = 5, h_PR/d_PR = 0.9, α_PR= 65^o, X_sw/d_h = 0.40, Y_sw/d_h = 0.85 and d_j/d_h = 0.064 were reserved fixed. For every data of Re, the extreme values of Nu have been achieved at P_PR/h_PR of 8, while the smallest values of Nu have been observed to increase the range of selected parameter P_PR/h_PR up to 10. This change in the results of Nu is due to the development of vital vortices combined with each other to eliminate the flow of V-shaped ribs and maintain the optimum value of P_PR/h_PR. Figure 8b shows the graphs for Nu/Nu_ss as a function of P_PR/h_PR for a multi V-shaped protrusion ribs STC at variant selected Re. It has been obtained from different values of P_PR/h_PR the Nu was highest for P_PR/h_PR= 8 at each value of Re.

Fig. 8

a Effect of P_PR/h_PRon Nub Effect of P_PR/h_PR on Nu/Nu_ss at selected Re

The plot presented in Fig. 9a depicts the distinction of Nu with Re for distinctive data of α_PR and fixed values of the rest of the geometrical parameters like W_PR/W_APR = 5, h_PR/d_PR = 0.9, P_PR/h_PR = 8, X_sw/d_h = 0.40, Y_sw/d_h = 0.85 and d_j/d_h = 0.064 . In the above plot Nu has been presented as an influence of α_PR for entire values of Re and remaining constant solar air passage parameters. The Nu improved with the increase in α_PR and reaches the results consistent to 65° after that, there was a decrease in Nu due to an increase in the data of α_PR. The enhancement in α_PR causes a decrease in interruption of end-to-end impinging jets compared to absorber plate and hence highest Nu was found. Figure 9b shows the plot of Nu/Nu_ss for a multi V-shaped protrusion ribs STC at different selected values of Re. This plot depicts that at different values of α_PR, Nu/Nu_ss has been maximum for an array of 65° to entire data of Re.

Fig. 9

a Effect of α_PR on Nub Effect of α_PR on Nu/Nu_ss at selected Re

7.2 Friction factor

The continuous implementation of roughness in the multi V-shaped protrusion ribs on the hot surface improves the effectiveness of Nu from the heated surface of an STC with subsequent growth in f_r losses. In the present experimental investigation, it has been proposed that how f_r characteristics of the STC were affected once multi V-shaped protrusion ribs parameters i.e. W_PR/W_APR are altered and rest of the geometrical roughness parameters like h_PR/d_PR = 0.9, P_PR/h_PR = 8, α_PR= 65^o, X_sw/d_h = 0.40, Y_sw/d_h = 0.85 and d_j/d_h = 0.064 were kept fixed as described in Fig. 10a. The plot demonstrates that f_rvaries with Re for different data of W_PR/W_APR, so due to the decrease of Re in each situation f_rwas increased. From Fig. 10b it has been obtained that f_r/f_ss rises at values of W_PR/W_APR = 6 and the extreme value of f_r/f_ss has been achieved. The volume of secondary stream jets was increased in the expansion value of W_PR/W_APR. This causes an increase in the results of Nu up to a series of W_PR/W_APR= 5. With the rise in W_PR/W_APR the results of f_r/f_ss rises and achieves the highest value corresponding to W_PR/W_APR value of 6 in the range of specified parameters. Due to the partition of flow, the results of f_r/f_ss occurs interpretation of the structure of vortices. Some of the vortices air accumulation and this causes an increase in Nu. Usually, Nu enhances from the target plate to air and such vortices as mentioned above also improves Nu during the flow around the STC. The number of vortices in case of W_PR/W_APR= 6.0 was more as compared to W_PR/W_APR of 5. Therefore, for W_PR/W_APR of 6 air and vortices mixing was huge, which gives a large amount of f_r/f_ss.

Fig. 10

a Effect of W_PR/W_APRon f_rb Effect of W_PR/W_APR on f_r/f_ss at selected Re

The variance of f_r with Re for different data of h_PR/d_PR has been shown in Fig. 11a. The remaining roughness geometrical parameters such as W_PR/W_APR = 5.0, P_PR/h_PR = 8, α_PR= 65^o, X_sw/d_h = 0.40, Y_sw/d_h = 0.85 and d_j/d_h = 0.064 were kept fixed. The graph plotted for f_r in Fig. 11a proposed that for defined values of h_PR/d_PR, f_r reduces with increase in Re_. Figure 11a clearly states that f_r raises because of the increase in h_PR/d_PR and the highest value of f_rwere obtained corresponding to h_PR/d_PR value of 0.9. Figure 11b depicts the values of f_r/f_ss as a meaning of h_PR/d_PR for multi V-shaped protrusion ribs STC at variant selected series of Re. It has been realized that at dissimilar values of h_PR/d_PR,the f_r/f_ss was maximum for h_PR/d_PR= 0.9 for respective data of Re. Due to the rise in the value of h_PR/d_PR the multi V-shaped protrusion ribs increase up to a large extent in the center of the stream and resulting in the growth in f_r/f_ss as well as turbulence fact.

Fig. 11

a Effect of h_PR/d_PR on f_rb Effect of h_PR/d_PR on f_r/f_ss at selected Re

Figure 12a depicts the variance of f_rwith Re for different data of P_PR/h_PR and remaining of the roughness parameters viz. W_PR/W_APR = 5.0, h_PR/d_PR = 0.9, α_PR= 65^o, X_sw/d_h = 0.40, Y_sw/d_h = 0.85 and d_j/d_h = 0.064 were kept fixed. From Fig. 12a it has been found that for all value of P_PR/h_PR, f_r decreases with increase in Re. For P_PR/h_PR the values of 8 and 10 provides the highest and lowest value of f_r. Figure 12b represents the data of f_r/f_ss as a function of P_PR/h_PR for multi V-shaped protrusion ribs STC at variant arrays of Re_. It has been found that at different values of P_PR/h_PR, f_r/f_ss was higher for P_PR/h_PR= 8 at respective values of Re.

Fig. 12

a Effect of P_PR/h_PR on f_rb Effect of h_PR/d_PR on f_r/f_ss at selected Re

The change of f_r with Re for different data of α_PR and remaining roughness parameters like W_PR/W_APR = 5.0, h_PR/d_PR = 0.9, P_PR/h_PR = 8, X_sw/d_h = 0.40, Y_sw/d_h = 0.85 and d_j/d_h = 0.064 which reserved steadily were shown in Fig. 13a. It has been found that for all data of α_PR, f_r reduces with the rise in Re. The plot depicts that f_r rises with a rise in α_PR value from 45 to 65° and later it decreases with increase in α_PR and receives the highest possible value correspondent to α_PR of 65°. The maximum and minimum values of f_r has been found at α_PR values of 45 and 65° respectively. Figure 13b shows the results of f_r/f_ss as a meaning of α_PR for multi V-shaped protrusion ribs, STC at variant elected arrays of Re. It has been found that at different values of α_PR the f_r/f_ss was highest for α_PR= 65°for all data of Re.

Fig. 13

a Effect of α_PR on f_rb Effect of α_PR on f_r/f_ss at selected Re

7.3 THP

The complete examination of Nu and f_r performances proposed that Nu in multi V-shaped protrusion ribs STC was enhanced with a significant improvement in f_r. Hence, it has been essential to select profiles which not just affect Nu but also resist the f_r on the lowest working stage. In order to achieve such resolution synchronized consideration of η_PR Lewis [39] presented a η_PR criterion recognized as efficiency criterion i.e. η_PR. Selecting the Nu through W_PR/W_APR, h_PR/d_PR, P_PR/h_PR, α_PR, X_sw/d_h, Y_sw/d_h and d_j/d_h of multi V-shaped protrusion ribs per unit driving energy determined with Nu for the completely formed turbulent flow in STC by flat surfaces and is specified by Eq. (26) as below:

$$ {\eta}_{PR}=\left( Nu/{Nu}_{ss}\right)/{\left({f}_r/{f}_{ss}\right)}^{0.33} $$

(26)

Figure 14a–d presents the influence of multi V-shaped protrusion ribs factors on η_PR parameters (Nu/Nu_ss)/(f_r/f_ss)^0.33 as a function of Re. Figure 14a shows the effect of η_PR with Re on W_PR/W_APR for a fixed value h_PR/d_PR = 0.9, P_PR/h_PR = 8, α_PR = 65⁰, X_sw/d_h = 0.40, Y_sw/d_h = 0.85 and d_j/d_h = 0.064. Variation of η_PRwith respect to Re has also been plotted in Fig. 14a to show the augmentation in η_PR by providing multi V-shaped protrusion ribs on the beneath of the absorber plate. The maximum η_PRof multi V-shaped protrusion ribs collector has been found to rise from 2.60 to 3.44 with a raise in Re from 2500 to 35,000 for W_PR/W_APRvalue of 5. As the Re increases the turbulence decreases which leads to augment in heat transfer. Figure 14a shows that η_PR rises with the increase in W_PR/W_APR and receiving an utmost value at W_PR/W_APR of 5. With further increase in W_PR/W_APR, η_PR starts decreasing. This is because of the fact that multi V-shaped protrusion ribs creates a strong secondary stream jet close to the limbs and when the disruption from the area of the V-shaped protrusion ribs goes out and combines with the mainstream, the disturbance conducts the turbulence mixing. With the increase in number of ribs (W_PR/W_APR), it would increase number of secondary stream which improves heat transfer. By further increase in rib (beyond 5), it may outcome in the stream separation from top of rib surfaces hence drop in heat transfer. The influence of h_PR/d_PR on the η_PR at distinct Re is shown by the Fig. 14b. The η_PR rises with rise in value of h_PR/d_PR for every value of Re, which causes the highest turbulence and attaining utmost value 0.9 and then reduces for the entire Re. This is because of the fact as we raise the h_PR/d_PR height beyond the 0.9, the flows experience the high resistance which leads to large pressure drop and lesser η_PR. Figure 14c presents the consequence of P_PR/h_PR on η_PR at fixed parameters of W_PR/W_APR = 5, h_PR/d_PR = 0.9, α_PR = 65⁰, X_sw/d_h = 0.40, Y_sw/d_h = 0.85, d_j/d_h = 0.064 and selected Re. It can be seen that the η_PR increases with P_PR/h_PR from 7 to 8, attains a utmost at a P_PR/h_PR of 8, and therefore it reduces with an increase in the P_PR/h_PR for all Re. It may be due to fact that stream separation may occur downstream of a multi V-shaped protrusion ribs, and reattachment of free shear layer may occur and mix with main stream, if relative pitch equal to 8 utmost η_PR occurs. Figure 14d shows the variation of η_PR with α_PR for distinct values of Re and fixed values of other parameters as W_PR/W_APR = 5, P_PR/h_PR = 8, h_PR/d_PR = 0.9, X_sw/d_h = 0.40, Y_sw/d_h = 0.85 and d_j/d_h = 0.064. When α_PR increases from 30 to 65° beyond which it again impedes. This is due to fact that an increase in α_PR the region developed as a outcome of multi V-shaped protrusion ribs insertion gets enriched with secondary flow streams which adds up to heat transfer from the plate to the air flowing beneath and hence increase η_PR. Beyond α_PR 65° the flow again becomes skinny and thus lesser the η_PR. From the η_PR plots, it can be seen that the value of η_PR increases with the Re initially up to a certain range of the Re after which it starts decreasing further. This value of the Re is an optimum value for the operation of STC at which the system is the most efficient. The physical mechanism of the thermo-hydraulic parameter is that its value for any system suggests the thermo-hydraulic performance equal to the times multiplied by the thermo-hydraulic performance of the conventional STC. This means that if the value of η_PR is less than 1 (one), the modification carried out inside the STC for enhancement of the performance has led to decrease in the performance than that of the conventional STC too. This can be due to low thermal enhancement parameter of increased value of friction factor in the STC. However, in the present study, an appreciable value of the η_PR has been obtained about 3.44 which show that the modification in the form of multi V-shaped protrusion ribs can augment the performance of the STC to a marginal value. Table 4 shows the values of roughness profiles parameters with which η_PR parameters (Nu/Nu_ss)/(f_r/f_ss)^0.33 has been obtained to be maximum. The highest data of (Nu/Nu_ss)/(f_r/f_ss)^0.33 has been attained to be 3.44 consistent to W_PR/W_APR = 5, h_PR/d_PR = 0.9, P_PR/h_PR = 8, α_PR = 65⁰, X_sw/d_h = 0.40, Y_sw/d_h = 0.85 and d_j/d_h = 0.064 for complete values of Re selected for present investigation. The best results of η_PR parameter for different experimental factors are represented in Table 4.

Fig. 14

Variation of multi V-shaped protrusion ribs on η_PR parameters aW_PR/W_APRbh_PR/d_PRcP_PR/h_PRdα_PR

Table 4 Ideal values of η_PR

8 Conclusions

This article presents experimental analysis carried out to find out Nu and f_r characteristics of a multi V-shaped protrusion ribs absorber plate of an impingement jet STC. The effects of various control parameters such as W_PR/W_APR, h_PR/d_PR, P_PR/h_PR and α_PR on Nu and f_r characteristics of STC are studied and the main conclusions of the study are listed below:

• 1. The multi V-shaped protrusion ribs on the absorber surface assist in generating vortices and creating shear layer instability which tends to increase the heat transfer to the air flowing underneath.

• 2. The highest value of Nu was obtained at W_PR/W_APR = 5, h_PR/d_PR = 0.9, P_PR/h_PR = 8, α_PR = 65⁰, X_sw/d_h = 0.40, Y_sw/d_h = 0.85 and d_j/d_h = 0.064.

• 3. The thermal enhancement factor achieve a better value which shows that the present modification in the solar collector channel helps is accelerating the heat transfer, however at some cost of increased friction factor. This has been evaluated in terms of thermo-hydraulic performance parameter.

• 4. The η_PR of an impinging jet, STC attached with multi V-shaped protrusion ribs on the absorbent plate is higher than the conventional STC. The highest value of the η_PR is found to be 3.44 for the range of parameters experimentally analyzed.